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ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.TOPIC TEXTS
Unit 15 - Rational Expressions Lesson 1 - Operations with Rational Expressions Topic 1 - Introduction to Rational Expressions Topic 1 - Introduction to Rational Expressions (spanish) Topic 2 - Multiplying and Dividing Rational Expressions Topic 2 - Multiplying and Dividing Rational Expressions (spanish) Topic 3 - Adding and Subtracting Rational Expressions Topic 3 - Adding and Subtracting SUBTRACTING WHOLE NUMBERS AND APPLICATIONS Subtracting involves finding the difference between two or more numbers. It is a method that can be used for a variety of applications, such as balancing a checkbook, planning a schedule,cooking, or travel.
THE METRIC SYSTEM
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
SQUARE ROOTS AND COMPLETING THE SQUARE Ignore it for now and focus on the x2 and x terms on the left side of the equation. The left side has the form x2 + bx, so you can identify b. x2 + 6x + 9 = 8 + 9. To complete the square, add to the left side. b = 6, so. This is an equation, though, so you must add the same number to the right side as well. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor OverviewORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.TOPIC TEXTS
Unit 15 - Rational Expressions Lesson 1 - Operations with Rational Expressions Topic 1 - Introduction to Rational Expressions Topic 1 - Introduction to Rational Expressions (spanish) Topic 2 - Multiplying and Dividing Rational Expressions Topic 2 - Multiplying and Dividing Rational Expressions (spanish) Topic 3 - Adding and Subtracting Rational Expressions Topic 3 - Adding and Subtracting SUBTRACTING WHOLE NUMBERS AND APPLICATIONS Subtracting involves finding the difference between two or more numbers. It is a method that can be used for a variety of applications, such as balancing a checkbook, planning a schedule,cooking, or travel.
THE METRIC SYSTEM
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
SQUARE ROOTS AND COMPLETING THE SQUARE Ignore it for now and focus on the x2 and x terms on the left side of the equation. The left side has the form x2 + bx, so you can identify b. x2 + 6x + 9 = 8 + 9. To complete the square, add to the left side. b = 6, so. This is an equation, though, so you must add the same number to the right side as well. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
INTRODUCTION TO RATIONAL EXPRESSIONS Introduction. Rational expressions are fractions that have a polynomial in the numerator, denominator, or both. Although rational expressions can seem complicated because they contain variables, they can be simplified in the same way that numeric fractions, also called numerical fractions, are simplified.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations.THE METRIC SYSTEM
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds.QUADRILATERALS
There is another special type of quadrilateral. This quadrilateral has the property of having only one pair of opposite sides that are parallel.Here is one example of a trapezoid.. Notice that , and that and are not parallel. You can easily imagine that if you extended sides and , they would intersect above the figure.. If the non-parallel sides of a trapezoid are congruent, the trapezoid is UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF WHOLE NUMBERS TEACHING TIPS: CHALLENGES Developmental Math—An Open Program Instructor Guide 1.1 Unit 1: Whole Numbers Learning Objectives 1.2 Instructor Notes The Mathematics of Whole Numbers Teaching Tips: Challenges and Approaches Additional Resources 1.5 Instructor Overview Tutor Simulation: Shopping For Office Supplies 1.12 ORDEN DE OPERACIONES Primero, considera expresiones que incluyan una o más operaciones aritméticas: suma, resta, multiplicación, y división. El orden de operaciones requiere que todas las multiplicaciones y divisiones se hagan primero, yendo de izquierda a derecha en la expresión.El orden en el cual se calculan la multiplicación y división está determinado por cuál aparece primero, de izquierda a derecha. ESCALAS DE TEMPERATURA Observando los dos termómetros mostrados, puedes hacer comparaciones generales entre las escalas. Por ejemplo, mucha gente se siente cómoda a una temperatura de entre 50 ° F y 80 ° F (o entre 10 ° C y 25 ° C). Si un meteorólogo predice una temperatura promedio de 0 C (o 32 ° F), entonces será mejor que se salga de casa con una chamarra.. Algunas veces, es necesario convertir de RESOLVIENDO ECUACIONES EXPONENCIALES Y …TRANSLATE THIS PAGE Puedes ver una ecuación como 4 x = 16 y la resuelves preguntándote, “¿4 a qué potencia es 16? 4 2 es 16, entonces x = 2.” Ecuaciones como 4 x = 17 son un poco más difíciles. Sabes que x debe ser un poco más de 2, porque 17 es un poco más que 16. Una manera de encontrar x con más precisión, es usando logaritmos.. Cuando resolvías otras ecuaciones algebraicas, normalmente te EL MÉTODO DE ELIMINACIÓN El método de eliminación para resolver sistemas de ecuaciones lineales usa la propiedad de la igualdad de la suma. Puedes sumar el mismo valor a cada lado de la ecuación. Entonces si tienes un sistema: x – 6 = −6 y x + y = 8, puedes sumar x + y al lado izquierdo de la primera ecuación y suma 8 a la derecha de la ecuación. Y como x + y = 8, estas sumando el mismo valor a cada ladode
SIMPLIFICANDO Y EVALUANDO POLINOMIOS CON MÁS DE …TRANSLATE THISPAGE
Has estudiado polinomios hechos de constantes y/o variables combinadas con suma o resta. Las variables pueden incluir exponentes. Los ejemplos hasta ahora han estado limitados a expresiones como 5x 4 + 3x 3 – 6x 2 + 2x que contienen una variable, pero los polinomios también pueden contener múltiples variables. Un ejemplo de un polinomio con dos variables es 4x 2 y – 2xy 2 + x – 7.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds.QUADRILATERALS
There is another special type of quadrilateral. This quadrilateral has the property of having only one pair of opposite sides that are parallel.Here is one example of a trapezoid.. Notice that , and that and are not parallel. You can easily imagine that if you extended sides and , they would intersect above the figure.. If the non-parallel sides of a trapezoid are congruent, the trapezoid is UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF WHOLE NUMBERS TEACHING TIPS: CHALLENGES Developmental Math—An Open Program Instructor Guide 1.1 Unit 1: Whole Numbers Learning Objectives 1.2 Instructor Notes The Mathematics of Whole Numbers Teaching Tips: Challenges and Approaches Additional Resources 1.5 Instructor Overview Tutor Simulation: Shopping For Office Supplies 1.12 ORDEN DE OPERACIONES Primero, considera expresiones que incluyan una o más operaciones aritméticas: suma, resta, multiplicación, y división. El orden de operaciones requiere que todas las multiplicaciones y divisiones se hagan primero, yendo de izquierda a derecha en la expresión.El orden en el cual se calculan la multiplicación y división está determinado por cuál aparece primero, de izquierda a derecha. ESCALAS DE TEMPERATURA Observando los dos termómetros mostrados, puedes hacer comparaciones generales entre las escalas. Por ejemplo, mucha gente se siente cómoda a una temperatura de entre 50 ° F y 80 ° F (o entre 10 ° C y 25 ° C). Si un meteorólogo predice una temperatura promedio de 0 C (o 32 ° F), entonces será mejor que se salga de casa con una chamarra.. Algunas veces, es necesario convertir de RESOLVIENDO ECUACIONES EXPONENCIALES Y …TRANSLATE THIS PAGE Puedes ver una ecuación como 4 x = 16 y la resuelves preguntándote, “¿4 a qué potencia es 16? 4 2 es 16, entonces x = 2.” Ecuaciones como 4 x = 17 son un poco más difíciles. Sabes que x debe ser un poco más de 2, porque 17 es un poco más que 16. Una manera de encontrar x con más precisión, es usando logaritmos.. Cuando resolvías otras ecuaciones algebraicas, normalmente te EL MÉTODO DE ELIMINACIÓN El método de eliminación para resolver sistemas de ecuaciones lineales usa la propiedad de la igualdad de la suma. Puedes sumar el mismo valor a cada lado de la ecuación. Entonces si tienes un sistema: x – 6 = −6 y x + y = 8, puedes sumar x + y al lado izquierdo de la primera ecuación y suma 8 a la derecha de la ecuación. Y como x + y = 8, estas sumando el mismo valor a cada ladode
SIMPLIFICANDO Y EVALUANDO POLINOMIOS CON MÁS DE …TRANSLATE THISPAGE
Has estudiado polinomios hechos de constantes y/o variables combinadas con suma o resta. Las variables pueden incluir exponentes. Los ejemplos hasta ahora han estado limitados a expresiones como 5x 4 + 3x 3 – 6x 2 + 2x que contienen una variable, pero los polinomios también pueden contener múltiples variables. Un ejemplo de un polinomio con dos variables es 4x 2 y – 2xy 2 + x – 7.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. SOLVING RATIONAL EQUATIONS AND APPLICATIONS Equations that contain rational expressions are called rational equations.For example, is a rational equation. You can solve these equations using the techniques for performing operations with rational expressions and the procedures for solving algebraic equations. PROJECT: LET’S GET COOKING Task. You are having a get together and are expecting 30 guests. You plan on serving Banana Bread, Chocolate Chip Cookies, and Sugar Cookies. Using the three recipes given, work with your group to create recipe cards to feed 30 people. Next, total up the ingredients needed. Then, check to see how much of each product needs to be purchasedbased
AMPLITUDE AND PERIOD The amplitude is 3 and the period is . In this example, you could have found the period by looking at the graph above. One complete cycle is shown, for example, on the interval , so the period is . In the functions and , multiplying by the constant a only affects the amplitude, not the period. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview INTRODUCCIÓN FRACCIONES Y NÚMEROS MIXTOSTRANSLATE THIS PAGE Para encontrar la fracción, primero necesitamos la distancia total de la carrera y la obtenemos sumando las distancias que los tres van a a correr (2 + 5 + 3 = 10). Entonces consideramos la distancia que va a correr Daphne. La respuesta correcta es . B) Correcto. La carreracompleta mide 10
INTRODUCCIÓN A LAS FUNCIONES LOGARÍTMICASTRANSLATE THIS PAGE Una familia útil de las funciones que se relacionan con las funciones exponenciales son las funciones logarítmicas.Has estado calculando el resultado de b x y esto te daba funciones exponenciales. Un logaritmo es un cálculo del exponente en la ecuación y = b x.Puesto de otro modo, encontrar un logaritmo es lo mismo que encontrar el exponente cuya base debe elevarse para obtener el valorEL SISTEMA MÉTRICO
El sistema métrico es un sistema alternativo usado en la mayoría de los países, así como en los Estados Unidos. El sistema métrico está basado en conjuntar uno de una seria de prefijos, incluyendo kilo-, hecto-, deca-, deci-, centi-, y mili-,con la unidad base de medida, como el metro, el litro, o el gramo. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds.QUADRILATERALS
There is another special type of quadrilateral. This quadrilateral has the property of having only one pair of opposite sides that are parallel.Here is one example of a trapezoid.. Notice that , and that and are not parallel. You can easily imagine that if you extended sides and , they would intersect above the figure.. If the non-parallel sides of a trapezoid are congruent, the trapezoid is UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF WHOLE NUMBERS TEACHING TIPS: CHALLENGES Developmental Math—An Open Program Instructor Guide 1.1 Unit 1: Whole Numbers Learning Objectives 1.2 Instructor Notes The Mathematics of Whole Numbers Teaching Tips: Challenges and Approaches Additional Resources 1.5 Instructor Overview Tutor Simulation: Shopping For Office Supplies 1.12 ORDEN DE OPERACIONES Primero, considera expresiones que incluyan una o más operaciones aritméticas: suma, resta, multiplicación, y división. El orden de operaciones requiere que todas las multiplicaciones y divisiones se hagan primero, yendo de izquierda a derecha en la expresión.El orden en el cual se calculan la multiplicación y división está determinado por cuál aparece primero, de izquierda a derecha. ESCALAS DE TEMPERATURA Observando los dos termómetros mostrados, puedes hacer comparaciones generales entre las escalas. Por ejemplo, mucha gente se siente cómoda a una temperatura de entre 50 ° F y 80 ° F (o entre 10 ° C y 25 ° C). Si un meteorólogo predice una temperatura promedio de 0 C (o 32 ° F), entonces será mejor que se salga de casa con una chamarra.. Algunas veces, es necesario convertir de RESOLVIENDO ECUACIONES EXPONENCIALES Y …TRANSLATE THIS PAGE Puedes ver una ecuación como 4 x = 16 y la resuelves preguntándote, “¿4 a qué potencia es 16? 4 2 es 16, entonces x = 2.” Ecuaciones como 4 x = 17 son un poco más difíciles. Sabes que x debe ser un poco más de 2, porque 17 es un poco más que 16. Una manera de encontrar x con más precisión, es usando logaritmos.. Cuando resolvías otras ecuaciones algebraicas, normalmente te EL MÉTODO DE ELIMINACIÓN El método de eliminación para resolver sistemas de ecuaciones lineales usa la propiedad de la igualdad de la suma. Puedes sumar el mismo valor a cada lado de la ecuación. Entonces si tienes un sistema: x – 6 = −6 y x + y = 8, puedes sumar x + y al lado izquierdo de la primera ecuación y suma 8 a la derecha de la ecuación. Y como x + y = 8, estas sumando el mismo valor a cada ladode
SIMPLIFICANDO Y EVALUANDO POLINOMIOS CON MÁS DE …TRANSLATE THISPAGE
Has estudiado polinomios hechos de constantes y/o variables combinadas con suma o resta. Las variables pueden incluir exponentes. Los ejemplos hasta ahora han estado limitados a expresiones como 5x 4 + 3x 3 – 6x 2 + 2x que contienen una variable, pero los polinomios también pueden contener múltiples variables. Un ejemplo de un polinomio con dos variables es 4x 2 y – 2xy 2 + x – 7.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram.TOPIC TEXTS
Unit 15 - Rational Expressions Lesson 1 - Operations with Rational Expressions Topic 1 - Introduction to Rational Expressions Topic 1 - Introduction to Rational Expressions (spanish) Topic 2 - Multiplying and Dividing Rational Expressions Topic 2 - Multiplying and Dividing Rational Expressions (spanish) Topic 3 - Adding and Subtracting Rational Expressions Topic 3 - Adding and Subtracting SUBTRACTING WHOLE NUMBERS AND APPLICATIONS Subtracting involves finding the difference between two or more numbers. It is a method that can be used for a variety of applications, such as balancing a checkbook, planning a schedule,cooking, or travel.
PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
SQUARE ROOTS AND COMPLETING THE SQUARE Ignore it for now and focus on the x2 and x terms on the left side of the equation. The left side has the form x2 + bx, so you can identify b. x2 + 6x + 9 = 8 + 9. To complete the square, add to the left side. b = 6, so. This is an equation, though, so you must add the same number to the right side as well. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor OverviewORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram.TOPIC TEXTS
Unit 15 - Rational Expressions Lesson 1 - Operations with Rational Expressions Topic 1 - Introduction to Rational Expressions Topic 1 - Introduction to Rational Expressions (spanish) Topic 2 - Multiplying and Dividing Rational Expressions Topic 2 - Multiplying and Dividing Rational Expressions (spanish) Topic 3 - Adding and Subtracting Rational Expressions Topic 3 - Adding and Subtracting SUBTRACTING WHOLE NUMBERS AND APPLICATIONS Subtracting involves finding the difference between two or more numbers. It is a method that can be used for a variety of applications, such as balancing a checkbook, planning a schedule,cooking, or travel.
PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
SQUARE ROOTS AND COMPLETING THE SQUARE Ignore it for now and focus on the x2 and x terms on the left side of the equation. The left side has the form x2 + bx, so you can identify b. x2 + 6x + 9 = 8 + 9. To complete the square, add to the left side. b = 6, so. This is an equation, though, so you must add the same number to the right side as well. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. FORMULAS - MONTEREYINSTITUTE.ORG Many real-world problems have well-known equations that describe relationships among different quantities. These equations that state a rule for a relationship are called formulas.You may have used formulas to figure out things like the area of a rectangle (area = length • width), the speed of a moving object (speed = distance ÷ time) or to convert from one system of measurement to another. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview ADDING FRACTIONS AND MIXED NUMBERS Adding Fractions and Mixed Numbers . Learning Objectives · Add fractions with like denominators. · Find the least common multiple (LCM) of two or more numbers. · Find the common denominator of fractions with unlike denominators. · Add fractions with unlike denominators. · Add mixed numbers with like and unlike denominators. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter.ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. MULTIPLYING SPECIAL CASES Multiplying a number by itself is often called squaring. You can represent this multiplication as a square. The number being squared is the length of the sides of the square and the product is represented by the area of that square. USE AND MISUSE OF GRAPHICAL REPRESENTATIONS The correct answer is Graph B. B) Correct. This graph uses a very small scale (10%, from 50% to 60%) and has eliminated the final two data points. This graph represents only a part of the data, and is designed to make the reader think that the politician is rated more favorably than he really is. THE MATHEMATICS OF REAL NUMBERS TEACHING TIPS: CHALLENGES Developmental Math – An Open Curriculum Instructor Guide 9.1 Unit 9: Real Numbers Learning Objectives 9.2 Instructor Notes The Mathematics of Real Numbers Teaching Tips: Challenges and Approaches Additional Resources 9.4 Instructor Overview THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. SQUARE ROOTS AND COMPLETING THE SQUARE Example. Problem. The formula for compounding interest annually is . A = P(1 + r) t, where A is the balance after t years, when P is the principal (initial amount invested) and r is the interest rate.. Find the interest rate r if $3,000 is invested and grows to $3,307.50 after 2 years.. A = P(1 + r) t. A = 3,307.50 t = 2. P = 3,000. First identify what you know. The amount after 2 years is THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. CONVERTING WITHIN THE METRIC SYSTEM Converting between measurements in the metric system is simply a matter of identifying the unit that you have, the unit that you want to convert to, and then counting the number of units between them. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE MATHEMATICS OF WHOLE NUMBERS TEACHING TIPS: CHALLENGES Developmental Math—An Open Program Instructor Guide 1.1 Unit 1: Whole Numbers Learning Objectives 1.2 Instructor Notes The Mathematics of Whole Numbers Teaching Tips: Challenges and Approaches Additional Resources 1.5 Instructor Overview Tutor Simulation: Shopping For Office Supplies 1.12 INTRODUCTION TO RATIONAL EXPRESSIONS Introduction. Rational expressions are fractions that have a polynomial in the numerator, denominator, or both. Although rational expressions can seem complicated because they contain variables, they can be simplified in the same way that numeric fractions, also called numerical fractions, are simplified. DIVIDING FRACTIONS AND MIXED NUMBERS Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHING Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. FACTORING TRINOMIALS Factoring Trinomials: x2 + bx + c. Trinomials in the form x2 + bx + c can often be factored as the product of two binomials. Remember that a binomial is simply a two-term polynomial. Let’s start by reviewing what happens when two binomials, such as (x + 2) and (x + PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. CIRCLES - MONTEREYINSTITUTE.ORG Circles are an important geometric shape. The distance around a circle is called the circumference, and the interior space of a circle is called the area. Calculating the circumference and area of a circle requires a number called pi (), which is a non-terminating, non-repeating decimal. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. PLACE VALUE AND NAMES FOR WHOLE NUMBERS For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixty-five.”. For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in PROJECT: SENSIBLE SLOPES AND INTRIGUING INTERCEPTS The numerator of the fraction represents a change in , and the denominator represents the corresponding change in . If either of the numbers is negative, the change is a decrease; otherwise it is anincrease.
DIVIDING FRACTIONS AND MIXED NUMBERS Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6 GRAPHING THE SINE AND COSINE FUNCTIONS The first coordinate is the input or value of the variable, and the second coordinate is the output or value of the function. Each point on the graph of the sine function will have the form , and each point on the graph of the cosine function will have the form . It is customary to use the Greek letter theta, , as the symbol for theangle.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. FACTORING TRINOMIALS Factoring Trinomials: x2 + bx + c. Trinomials in the form x2 + bx + c can often be factored as the product of two binomials. Remember that a binomial is simply a two-term polynomial. Let’s start by reviewing what happens when two binomials, such as (x + 2) and (x + PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. CIRCLES - MONTEREYINSTITUTE.ORG Circles are an important geometric shape. The distance around a circle is called the circumference, and the interior space of a circle is called the area. Calculating the circumference and area of a circle requires a number called pi (), which is a non-terminating, non-repeating decimal. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. PLACE VALUE AND NAMES FOR WHOLE NUMBERS For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixty-five.”. For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in PROJECT: SENSIBLE SLOPES AND INTRIGUING INTERCEPTS The numerator of the fraction represents a change in , and the denominator represents the corresponding change in . If either of the numbers is negative, the change is a decrease; otherwise it is anincrease.
DIVIDING FRACTIONS AND MIXED NUMBERS Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6 GRAPHING THE SINE AND COSINE FUNCTIONS The first coordinate is the input or value of the variable, and the second coordinate is the output or value of the function. Each point on the graph of the sine function will have the form , and each point on the graph of the cosine function will have the form . It is customary to use the Greek letter theta, , as the symbol for theangle.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. FACTORING TRINOMIALS Factoring Trinomials: x2 + bx + c. Trinomials in the form x2 + bx + c can often be factored as the product of two binomials. Remember that a binomial is simply a two-term polynomial. Let’s start by reviewing what happens when two binomials, such as (x + 2) and (x + PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. CIRCLES - MONTEREYINSTITUTE.ORG Circles are an important geometric shape. The distance around a circle is called the circumference, and the interior space of a circle is called the area. Calculating the circumference and area of a circle requires a number called pi (), which is a non-terminating, non-repeating decimal. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. PLACE VALUE AND NAMES FOR WHOLE NUMBERS For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixty-five.”. For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in PROJECT: SENSIBLE SLOPES AND INTRIGUING INTERCEPTS The numerator of the fraction represents a change in , and the denominator represents the corresponding change in . If either of the numbers is negative, the change is a decrease; otherwise it is anincrease.
DIVIDING FRACTIONS AND MIXED NUMBERS Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6 GRAPHING THE SINE AND COSINE FUNCTIONS The first coordinate is the input or value of the variable, and the second coordinate is the output or value of the function. Each point on the graph of the sine function will have the form , and each point on the graph of the cosine function will have the form . It is customary to use the Greek letter theta, , as the symbol for theangle.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Use the formula and the value for P. 2 = 1.011t. Divide by 6.9 to get the exponential expression by itself. log 2 = log (1.011)t. Since the variable t is an exponent, take logarithms of both sides. You can use any base, but base 10 or e will allow you to use the calculator easily. log 2 = t log 1.011. MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions. FINDING DOMAIN AND RANGE The correct answer is: The domain is all real numbers and the range is all real numbers f ( x) such that f ( x) ≥ 7. D) The domain and range are all real numbers. Incorrect. While it’s true that quadratic functions have no domain restrictions, the range is restricted because x 2 ≥ 0. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. WEIGHT - MONTEREYINSTITUTE.ORG Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is the largest unit. Whales are some of the largest animals in the world. Some species can reach weights of up to 200 tons--that’s equal to 400,000 pounds. FACTORING TRINOMIALS Factoring Trinomials: x2 + bx + c. Trinomials in the form x2 + bx + c can often be factored as the product of two binomials. Remember that a binomial is simply a two-term polynomial. Let’s start by reviewing what happens when two binomials, such as (x + 2) and (x + PROPERTIES OF LOGARITHMIC FUNCTIONS Remember that the properties of exponents and logarithms are very similar. With exponents, to multiply two numbers with the same base, you add the exponents. With logarithms, the logarithm of a product is the sum of the logarithms. Logarithm of a Product. The logarithm of a product is the sum of the logarithms: logb (MN) = logb M + logb N. CIRCLES - MONTEREYINSTITUTE.ORG Circles are an important geometric shape. The distance around a circle is called the circumference, and the interior space of a circle is called the area. Calculating the circumference and area of a circle requires a number called pi (), which is a non-terminating, non-repeating decimal. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. PLACE VALUE AND NAMES FOR WHOLE NUMBERS For example, for the number of days in a normal year, 365, the digit 3 is in the hundreds place. The word name for the number is “three hundred sixty-five.”. For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in PROJECT: SENSIBLE SLOPES AND INTRIGUING INTERCEPTS The numerator of the fraction represents a change in , and the denominator represents the corresponding change in . If either of the numbers is negative, the change is a decrease; otherwise it is anincrease.
DIVIDING FRACTIONS AND MIXED NUMBERS Dividing a Fraction or a Mixed Number by a Whole Number. When you divide by a whole number, you multiply by the reciprocal of the divisor. In the painting example where you need 3 quarts of paint for a coat and have 6 quarts of paint, you can find the total number of coats that can be painted by dividing 6 GRAPHING THE SINE AND COSINE FUNCTIONS The first coordinate is the input or value of the variable, and the second coordinate is the output or value of the function. Each point on the graph of the sine function will have the form , and each point on the graph of the cosine function will have the form . It is customary to use the Greek letter theta, , as the symbol for theangle.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right. FINDING DOMAIN AND RANGE Functions are a correspondence between two sets, called the domain and the range.When defining a function, you usually state what kind of numbers the domain (x) and range (f(x)) values can be.But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x.It also doesn’t mean that all real numbers can be function values, f(x). MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity). WEIGHT - MONTEREYINSTITUTE.ORG You often use the word weight to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is thelargest unit.
UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
ORDER OF OPERATIONS
First, consider expressions that include one or more of the arithmetic operations: addition, subtraction, multiplication, and division. The order of operations requires that all multiplication and division be performed first, going from left to right in the expression.The order in which you compute multiplication and division is determined by which one comes first, reading from left to right. FINDING DOMAIN AND RANGE Functions are a correspondence between two sets, called the domain and the range.When defining a function, you usually state what kind of numbers the domain (x) and range (f(x)) values can be.But even if you say they are real numbers, that doesn’t mean that all real numbers can be used for x.It also doesn’t mean that all real numbers can be function values, f(x). MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS Just as you can multiply and divide fractions, you can multiply and divide rational expressions.In fact, you use the same processes for multiplying and dividing rational expressions as you use for multiplying and dividing numeric fractions.THE METRIC SYSTEM
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.. In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. PROJECT: LET’S GET COOKING Let’s Get Cooking! Introduction . Fractions are a large part of baking. Ingredient measurements are often given in quarter cupincrements.
MATHEMATICAL MODELING WITH EXPONENTIAL AND LOGARITHMIC Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity). WEIGHT - MONTEREYINSTITUTE.ORG You often use the word weight to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is thelargest unit.
UNDERSTANDING PROPORTIONS A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale. PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. THE MATHEMATICS OF FRACTIONS AND MIXED NUMBERS TEACHINGADDING MIXED FRACTIONS PDFADDING MIXED FRACTIONS WORKSHEETS PDFADDING AND SUBTRACTING POSITIVE AND NEGATI…ADDING MIXED FRACTIONS WORKSHEETSMIXED FRACTIONS ADDING PRACTICEMIXED NUMBER FRACTIONS PDF Developmental Math—An Open Program Instructor Guide 2.3 Topic 2: Dividing Fractions and Mixed Numbers Learning Objectives Find the reciprocal of a number. Divide two fractions. Divide two mixed numbers. Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions or mixednumbers.
FACTORING TRINOMIALS For example, to factor x 2 + 7x +10, you are looking for two numbers whose sum is 7 (the coefficient of the middle term) and whose product is 10 (the last term).. Look at factor pairs of 10: 1 and 10, 2 and 5. Do either of these pairs have a sum of 7? Yes, 2 and 5. So you can rewrite 7x as 2x + 5x, and continue factoring as in the example above.Note that you can also rewrite 7x as 5x + 2x. THE PYTHAGOREAN THEOREM A long time ago, a Greek mathematician named Pythagoras discovered an interesting property about right triangles: the sum of the squares of the lengths of each of the triangle’s legs is the same as the square of the length of the triangle’s hypotenuse.This property—which has many applications in science, art, engineering, and architecture—is now called the Pythagorean Theorem. PROPERTIES OF LOGARITHMIC FUNCTIONS Properties of Logarithmic Functions . Learning Objective(s) · Express the logarithm of a product as a sum of logarithms. · Express the logarithm of a quotient as a difference. · Express the logarithm of a power as a product. · Simplify logarithmic expressions. CIRCLES - MONTEREYINSTITUTE.ORG The distance around a circle is called the circumference. (Recall, the distance around a polygon is the perimeter.) One interesting property about circles is that the ratio of a circle’s circumference and its diameter is the same for all circles. WEIGHT - MONTEREYINSTITUTE.ORG You often use the word weight to describe how heavy or light an object or person is. Weight is measured in the U.S. customary system using three units: ounces, pounds, and tons. An ounce is the smallest unit for measuring weight, a pound is a larger unit, and a ton is thelargest unit.
GRAPHING THE SINE AND COSINE FUNCTIONS You could simply plot all the points from the last column and continue the graph in the last example. But notice the following: the values in the third column (or y-coordinates of the points) have the opposite values of the points that we just graphed.This means that instead of plotting points above the -axis, you will be plotting points below the-axis.
DIVIDING FRACTIONS AND MIXED NUMBERS Dividing Fractions and Mixed Numbers . Learning Objective(s) · Find the reciprocal of a number. · Divide two fractions. · Divide two mixed numbers. · Divide fractions, mixed numbers, and whole numbers. Solve application problems that require division of fractions ormixed numbers.
PROPER AND IMPROPER FRACTIONS Mathematicians use three categories to describe fractions: proper, improper, and mixed. Fractions that are greater than 0 but less than 1 are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction.An improper fraction is always 1 or greater than 1. PROJECT: SENSIBLE SLOPES AND INTRIGUING INTERCEPTS The numerator of the fraction represents a change in , and the denominator represents the corresponding change in . If either of the numbers is negative, the change is a decrease; otherwise it is anincrease.
PLACE VALUE AND NAMES FOR WHOLE NUMBERS Place Value and Names for Whole Numbers . Learning Objective(s) · Find the place value of a digit in a whole number. · Write a whole number in words and in standard form. ·Monterey Institute
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