3.3 Division of Fractions and of Mixed Numbers

Size: px
Start display at page:

Download "3.3 Division of Fractions and of Mixed Numbers"

Transcription

1 CCBC Math 0 Division of Fractions and of Mixed Numbers Section.. Division of Fractions and of Mixed Numbers Introduction: What does it mean to divide? The basic division questions asks, How many of b are in a? Where a b gives the answer. Let s give an example that would require dividing fractions. A recipe calls for butter will we need for our recipe? cups of butter. A stick of butter is equal to of a cup. How many sticks of This problem asks us How many cups (sticks of butter) are in cups of butter? This follows the How many of b are in a? question. Therefore, we divide a by b. ab We will learn how to calculate this problem later in the chapter but let s get an answer to this problem visually. How many halves are in? The recipe requires sticks of butter. Therefore, There are several ways to divide two fractions. We will concentrate on the most popular way to divide fractions. Reciprocal of a Fraction RECIPROCAL The reciprocal of a is a. The reciprocal of a b is b a. In the examples to follow, let s find the reciprocal of a whole number, the reciprocal of a fraction, and the reciprocal of a mixed number. 77

2 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. Example : What is the reciprocal of? = Begin by writing as the fraction. Reciprocal: Switch the numerator and denominator to write the reciprocal. Practice : What is the reciprocal of? Answer: Example : What is the reciprocal of? Switch the numerator and denominator. The reciprocal of is. Practice : What is the reciprocal of? Answer: Example : What is the reciprocal of? ( ) 0 Begin by converting fraction. to an improper Reciprocal: Switch the numerator and denominator to write the reciprocal. Practice : What is the reciprocal of Answer: 7 7

3 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. Dividing Fractions Division is the inverse operation of multiplication. As we learned in Chapter, addition and subtraction are inverse operations (of each other.) The inverse relationship between addition and subtraction manifests itself in the opposite sign of a number. The inverse relationship between multiplication and division manifests itself in the reciprocal of a (nonzero) number. To illustrate the concept of reciprocal, let s consider a division problem, say We know from our study of division that divided by is the quotient. We know from our study of fractions that is another way of writing that division problem. If we look closely at this problem, we see that we can rewrite as the multiplication problem because when we multiply those fractions together, we are multiplying which equals. So, divided by is the same as multiplied by the fraction. This application of the inverse property is saying that dividing by (dividing by ) is equivalent to multiplying by its reciprocal,. Thus, can also be written as the multiplication problem or. We apply the principle of reciprocals to fractions when we divide. To divide fractions multiply the first fraction by the reciprocal of the second fraction. As with multiplication, all mixed numbers need to be rewritten as improper fractions. 7

4 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. DIVIDING FRACTIONS a c a d ad b d b c bc When b, c, and d do not equal 0. Example : Divide: Multiply the first fraction by the reciprocal of the second fraction. 7 7 Multiply the fractions. Simplify the answer. Of course, you could have simplified before multiplying: you would divide both the and the by and then multiply to get your final answer. Note that the problem must be in multiplied form before you can simplify. Multiply the first fraction by the reciprocal of the second fraction. Multiply the fractions. Here we reduce before multiplying. Make sure your answer is completely simplified. 0

5 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. Practice : Divide: 0 Answer: 7 Example : Divide: 6 Multiply the first fraction by the reciprocal of the 6 6 second fraction. In multiplied form, simplify before multiplying Simplify again. Multiply the numerators together and the denominators together. Practice : Divide: Answer: 6 0

6 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. Example 6: Divide: 6 6 (6) (6) 6 Convert each mixed number to an improper fraction. 6 6 Don t try to do too many steps all at once. Rewrite the original division problem with the improper fractions. 0 7 NEVER attempt to reduce fractions until the 6 problem has been turned into multiplication. 0 6 Multiply the first fraction by the reciprocal of the 7 second fraction Simplify before multiplying. 0 Check for other places to reduce. There are none 7 here Multiply the usual way and make sure your answer is completely simplified. Practice 6: Divide: Answer: Division with Zero Earlier you learned that any number multiplied by 0 produces the result 0. You also learned that division by 0 is undefined. RULES FOR DIVIDING WHEN 0 IS IN THE PROBLEM If 0 is divided by any number (except 0), the answer is 0. 0n 0 If any number is divided by 0, the answer is undefined. In other words, there is no answer. n0 undefined Note: In this section n will be a fraction.

7 CCBC Math 0 Division of Fractions and of Mixed Numbers Section. Example 7: Divide: 0 0 Multiply the first fraction by the reciprocal of the second fraction. = 0 Whenever you multiply by 0, the result is Thus, whenever you are dividing 0 by a number (but not 0), the result is 0. Dividing by 0 (where 0 is the divisor) is undefined. It cannot be done. Therefore, if the divisor is 0, the answer is automatically undefined because you cannot divide by 0. Practice 7: Divide: 0 Answer: Example : Divide: 0 0 Express the 0 in fraction form. Multiply the first fraction by the reciprocal of the second 0 fraction. 0 0 Division by zero is not possible. The answer is undefined. Practice : Divide: 0 Answer: Undefined Watch All:

8 CCBC Math 0 Division of Fractions and of Mixed Numbers Section.. Division of Fractions and of Mixed Numbers Exercises. Without determining the answer, set up the following division problem as an equivalent multiplication problem. Then write this multiplication problem in reduced form, but do not multiply. a. b Divide: 0. Divide: 6 7. Divide:. Divide: 0. Divide:. Divide: Divide: 7 7. Divide: 0 6. Divide:. Divide:. Divide: 6. Divide:. Divide: 6. Divide: 7 6. Divide: 7. Divide:. In the problem 0, which fraction is the quotient?. In the problem 0, which fraction is the divisor? 0. In the problem 0, which fraction is the dividend? 6 0 0

9 CCBC Math 0 Division of Fractions and of Mixed Numbers Section.. Division of Fractions and of Mixed Numbers Exercises Answers. a. 7 7 b = undefined

10 CCBC Math 0 Section. to.. The numerator of 0 denominator is. Mid-Chapter Review is and the. Write the problem as a fraction.. Simplify Simplify.. Convert 7 to an improper fraction Write form. as a mixed number in simplest 7. Write the problem in reduced 0 form, but do not multiply.. Multiply.. Multiply. 0. Multiply 6.. Multiply. 6. Multiply.. Multiply 0.. In the problem 6, a. What fraction is the quotient? b. What fraction is the divisor?. Set up the division problem as 0 an equivalent multiplication problem. Then write the multiplication problem in reduced form, but do not multiply. CHAPTER 6. Divide Divide Divide. 0. Divide Divide ( ).. Divide 6.. Divide 0.. Evaluate.. Evaluate.. Evaluate. 6. Find the mean of, 7,, and. 7. Find the median of,,,,.. Find the mode of,,,, Determine the area of the rectangle. 0. Determine the area of the triangle. m ft m m ft 6

11 CCBC Math 0 Section. to.. 0, a). 6 6 M i d - C h a p te r R e v i e w Answers 6 6 b) Undefined ft ft m m 7

3.1 Dividing a Whole into Fractional Parts. 3.1 Dividing a Set into Fractional Parts. 3.2 Identifying Parts of Wholes.

3.1 Dividing a Whole into Fractional Parts. 3.1 Dividing a Set into Fractional Parts. 3.2 Identifying Parts of Wholes. . Dividing a Whole into Fractional Parts Fraction: represents a part of a whole object or unit Numerator: (top number) represents number of parts of the whole Denominator: (bottom number) represents how

More information

Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions Page 1 of 14 Multiplying and Dividing Rational Expressions Attendance Problems. Simplify each expression. Assume all variables are nonzero. x 6 y 2 1. x 5 x 2 2. y 3 y 3 3. 4. x 2 y 5 Factor each expression.

More information

Section 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b.

Section 2.3 Rational Numbers. A rational number is a number that may be written in the form a b. for any integer a and any nonzero integer b. Section 2.3 Rational Numbers A rational number is a number that may be written in the form a b for any integer a and any nonzero integer b. Why is division by zero undefined? For example, we know that

More information

Mini-Lesson 1. Section 1.1: Order of Operations PEMDAS

Mini-Lesson 1. Section 1.1: Order of Operations PEMDAS Name: Date: 1 Section 1.1: Order of Operations PEMDAS If we are working with a mathematical expression that contains more than one operation, then we need to understand how to simplify. The acronym PEMDAS

More information

Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions Multiplying and Dividing Rational Expressions Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 Factor each expression. 2. y 3 y 3 y 6 x 4 4. y 2 1 y 5 y 3 5.

More information

Warm Up Simplify each expression. Assume all variables are nonzero.

Warm Up Simplify each expression. Assume all variables are nonzero. Warm Up Simplify each expression. Assume all variables are nonzero. 1. x 5 x 2 3. x 6 x 2 x 7 x 4 Factor each expression. 2. y 3 y 3 y 6 4. y 2 1 y 5 y 3 5. x 2 2x 8 (x 4)(x + 2) 6. x 2 5x x(x 5) 7. x

More information

Chapter 4 Section 2 Operations on Decimals

Chapter 4 Section 2 Operations on Decimals Chapter 4 Section 2 Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers.

More information

Lesson 1: Arithmetic Review

Lesson 1: Arithmetic Review In this lesson we step back and review several key arithmetic topics that are extremely relevant to this course. Before we work with algebraic expressions and equations, it is important to have a good

More information

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties

Learning Log Title: CHAPTER 3: ARITHMETIC PROPERTIES. Date: Lesson: Chapter 3: Arithmetic Properties Chapter 3: Arithmetic Properties CHAPTER 3: ARITHMETIC PROPERTIES Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Arithmetic Properties Date: Lesson: Learning Log Title:

More information

1-3 Multiplying and Dividing Real Numbers

1-3 Multiplying and Dividing Real Numbers Multiplying and Dividing 1-3 Multiplying and Dividing Real Numbers Real Numbers Warm Up Lesson Presentation Lesson Quiz 1 2 pts Bell Quiz 1-3 Add or Subtract 1. 3 8 2 pts 2. - 8 + 12 2 pts 3. 4 (-4) 2

More information

Name: Date: Review Packet: Unit 1 The Number System

Name: Date: Review Packet: Unit 1 The Number System Name: Date: Math 7 Ms. Conway Review Packet: Unit 1 The Number System Key Concepts Module 1: Adding and Subtracting Integers 7.NS.1, 7.NS.1a, 7.NS.1b, 7.NS.1c, 7.NS.1d, 7.NS.3, 7.EE.3 To add integers with

More information

1. To add (or subtract) fractions, the denominators must be equal! a. Build each fraction (if needed) so that both denominators are equal.

1. To add (or subtract) fractions, the denominators must be equal! a. Build each fraction (if needed) so that both denominators are equal. MAT000- Fractions Purpose One of the areas most frustrating for teachers and students alike is the study of fractions, specifically operations with fractions. Year after year, students learn and forget

More information

50 MATHCOUNTS LECTURES (6) OPERATIONS WITH DECIMALS

50 MATHCOUNTS LECTURES (6) OPERATIONS WITH DECIMALS BASIC KNOWLEDGE 1. Decimal representation: A decimal is used to represent a portion of whole. It contains three parts: an integer (which indicates the number of wholes), a decimal point (which separates

More information

Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE:

Rational number operations can often be simplified by converting mixed numbers to improper fractions Add EXAMPLE: Rational number operations can often be simplified by converting mixed numbers to improper fractions Add ( 2) EXAMPLE: 2 Multiply 1 Negative fractions can be written with the negative number in the numerator

More information

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole

What is a Fraction? Fractions. One Way To Remember Numerator = North / 16. Example. What Fraction is Shaded? 9/16/16. Fraction = Part of a Whole // Fractions Pages What is a Fraction? Fraction Part of a Whole Top Number? Bottom Number? Page Numerator tells how many parts you have Denominator tells how many parts are in the whole Note: the fraction

More information

Study Guide For use with pages

Study Guide For use with pages . GOAL For use with pages Write fractions as decimals and vice versa. VOCABULARY A rational number is a number that can be written as a quotient of two integers. In a terminating decimal, the division

More information

CW Middle School. Math RtI 7 A. 4 Pro cient I can add and subtract positive fractions with unlike denominators and simplify the result.

CW Middle School. Math RtI 7 A. 4 Pro cient I can add and subtract positive fractions with unlike denominators and simplify the result. 1. Foundations (14.29%) 1.1 I can add and subtract positive fractions with unlike denominators and simplify the result. 4 Pro cient I can add and subtract positive fractions with unlike denominators and

More information

The Bracket Strategy

The Bracket Strategy The Bracket Strategy This strategy will show students how common denominators are actually found. This strategy should be done with fraction bars. Step Create a bracket X Step Fill in the bracket with

More information

Lesson 1: Arithmetic Review

Lesson 1: Arithmetic Review Lesson 1: Arithmetic Review Topics and Objectives: Order of Operations Fractions o Improper fractions and mixed numbers o Equivalent fractions o Fractions in simplest form o One and zero Operations on

More information

Multiply the dividend by the reciprocal of the divisor.

Multiply the dividend by the reciprocal of the divisor. Domain Lesson 6 Complex Fractions Common Core Standards: 7.RP., 7.RP. Getting the Idea To divide fractions, first find the reciprocal of the divisor. Then multiply the dividend by the reciprocal of the

More information

Revision on fractions and decimals

Revision on fractions and decimals Revision on fractions and decimals Fractions 1. Addition and subtraction of fractions (i) For same denominator, only need to add the numerators, then simplify the fraction Example 1: " + $ " = &$ " (they

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts

More information

CHAPTER 4: DECIMALS. Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS

CHAPTER 4: DECIMALS. Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS CHAPTER 4: DECIMALS Image from Microsoft Office Clip Art CHAPTER 4 CONTENTS 4.1 Introduction to Decimals 4.2 Converting between Decimals and Fractions 4.3 Addition and Subtraction of Decimals 4.4 Multiplication

More information

Reteaching. Comparing and Ordering Integers

Reteaching. Comparing and Ordering Integers - Comparing and Ordering Integers The numbers and - are opposites. The numbers 7 and -7 are opposites. Integers are the set of positive whole numbers, their opposites, and zero. 7 6 4 0 negative zero You

More information

Rules of Exponents Part 1[Algebra 1](In Class Version).notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION.

Rules of Exponents Part 1[Algebra 1](In Class Version).notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION. WARM UP Simplify using order of operations. Aug 22 3:22 PM 1 Aug 22 4:09 PM 2 WARM UP a) The equation 3(4x) = (4x)3 illustrates which property? b) Which property of real numbers is illustrated by the equation

More information

CIV Module Unit Session Learning Objectives

CIV Module Unit Session Learning Objectives CIV Module Unit Session Learning Objectives C IV Module: Essentials of Recognizing a Fraction 1. Learning that a fraction is a part of a whole through the use of area models C IV Module: Essentials of

More information

Unit 3: Multiplication and Division Reference Guide pages x 7 = 392 factors: 56, 7 product 392

Unit 3: Multiplication and Division Reference Guide pages x 7 = 392 factors: 56, 7 product 392 Lesson 1: Multiplying Integers and Decimals, part 1 factor: any two or more numbers multiplied to form a product 56 x 7 = 392 factors: 56, 7 product 392 Integers: all positive and negative whole numbers

More information

Fractions. Dividing the numerator and denominator by the highest common element (or number) in them, we get the fraction in its lowest form.

Fractions. Dividing the numerator and denominator by the highest common element (or number) in them, we get the fraction in its lowest form. Fractions A fraction is a part of the whole (object, thing, region). It forms the part of basic aptitude of a person to have and idea of the parts of a population, group or territory. Civil servants must

More information

Adding Integers with the Same Sign

Adding Integers with the Same Sign Name Date Class - Adding Integers with the Same Sign How do you add integers with the same sign? Add 4 5. Add 4. Step Check the signs. Are the integers both positive or negative? 4 and 5 are both positive.

More information

Student Success Center Arithmetic Study Guide for the ACCUPLACER (CPT)

Student Success Center Arithmetic Study Guide for the ACCUPLACER (CPT) Fractions Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) is parts have a dot out of Proper fraction:

More information

Sail into Summer with Math!

Sail into Summer with Math! Sail into Summer with Math! For Students Entering Math C This summer math booklet was developed to provide students in kindergarten through the eighth grade an opportunity to review grade level math objectives

More information

Multiplying and Dividing Fractions 2

Multiplying and Dividing Fractions 2 Unit : Linear Equations Name Directions: Solve. Multiplying and Dividing Fractions 7 Appendix B: Answer Keys Transparency/Guided Practice Book Answers 4 Unit : Linear Equations Name Directions: Calculate.

More information

WHOLE NUMBER AND DECIMAL OPERATIONS

WHOLE NUMBER AND DECIMAL OPERATIONS WHOLE NUMBER AND DECIMAL OPERATIONS Whole Number Place Value : 5,854,902 = Ten thousands thousands millions Hundred thousands Ten thousands Adding & Subtracting Decimals : Line up the decimals vertically.

More information

SUMMER REVIEW PACKET 2 FOR STUDENTS ENTERING ALGEBRA 1

SUMMER REVIEW PACKET 2 FOR STUDENTS ENTERING ALGEBRA 1 SUMMER REVIEW PACKET FOR STUDENTS ENTERING ALGEBRA Dear Students, Welcome to Ma ayanot. We are very happy that you will be with us in the Fall. The Math department is looking forward to working with you

More information

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.)

Place Value. Verbal Form: 30,542 = Thirty thousand, five hundred forty-two. (Notice we don t use the word and.) WHOLE NUMBERS REVIEW A set is a collection of objects. The set of natural numbers is {1,2,3,4,5,.} The set of whole numbers is {0,1,2,3,4,5, } Whole numbers are used for counting objects (such as money,

More information

Math 085 Final Exam Review

Math 085 Final Exam Review Math 08 Final Exam Review Objective : Use the rules of signed number arithmetic to perform operations on integers. These operations include, but are not limited to, addition, subtraction, multiplication,

More information

8 th Grade Math Reference Sheet

8 th Grade Math Reference Sheet 8 th Grade Math Reference Sheet Number Sense DECIMALS NS 1 To change a DECIMAL FRACTION, use the place value of the decimal as the denominator of the fraction; simplify if. 1. Line up decimal points 2.

More information

A. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum.

A. Incorrect! To simplify this expression you need to find the product of 7 and 4, not the sum. Problem Solving Drill 05: Exponents and Radicals Question No. 1 of 10 Question 1. Simplify: 7u v 4u 3 v 6 Question #01 (A) 11u 5 v 7 (B) 8u 6 v 6 (C) 8u 5 v 7 (D) 8u 3 v 9 To simplify this expression you

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Math 24 - Study Guide - Chapter 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Give one number between -8 and 8 that is a negative real

More information

Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions

Algebra 1 Review. Properties of Real Numbers. Algebraic Expressions Algebra 1 Review Properties of Real Numbers Algebraic Expressions Real Numbers Natural Numbers: 1, 2, 3, 4,.. Numbers used for counting Whole Numbers: 0, 1, 2, 3, 4,.. Natural Numbers and 0 Integers:,

More information

CCBC Math 081 Order of Operations Section 1.7. Step 2: Exponents and Roots Simplify any numbers being raised to a power and any numbers under the

CCBC Math 081 Order of Operations Section 1.7. Step 2: Exponents and Roots Simplify any numbers being raised to a power and any numbers under the CCBC Math 081 Order of Operations 1.7 1.7 Order of Operations Now you know how to perform all the operations addition, subtraction, multiplication, division, exponents, and roots. But what if we have a

More information

Fractions Decimals Percents

Fractions Decimals Percents 1 Fractions Decimals Percents Name TAG 2 Fractions to Decimals There are ways to convert fractions to decimals. 1. Use place value 2. Using equivalent fractions with denominators of,, 0, etc.. Use long

More information

Addition with Unlike Denominators

Addition with Unlike Denominators Lesson. Addition with Unlike Denominators Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on 0of the string. How much of the string does Karen cover with

More information

Distributive Property Order of Operations

Distributive Property Order of Operations Distributive Property Order of Operations Distributive Property a(b + c) = a b + a c a(b + c + d) = a b + a c + a d a(b c) = a b a c Reteaching 21 Math Course 3, Lesson 21 We expand 2(a + b) and get 2a

More information

Pre-Algebra Notes Unit Five: Rational Numbers and Equations

Pre-Algebra Notes Unit Five: Rational Numbers and Equations Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the

More information

Part 1: Dividing Fractions Using Visual Representations

Part 1: Dividing Fractions Using Visual Representations Part : Dividing Fractions Using Visual Representations To divide fractions, remember that division can be represented by repeated subtraction, just like multiplication can be represented by repeated addition.

More information

Objective Simplify expressions using the properties of exponents.

Objective Simplify expressions using the properties of exponents. Pre-Algebra: Exponent Properties Objective Simplify expressions using the properties of exponents. Exponents are used to simplify expressions. For example, a*a*a*a*a*a*a is the expanded expression of a

More information

Equations and Problem Solving with Fractions. Variable. Expression. Equation. A variable is a letter used to represent a number.

Equations and Problem Solving with Fractions. Variable. Expression. Equation. A variable is a letter used to represent a number. MAT 040: Basic Math Equations and Problem Solving with Fractions Variable A variable is a letter used to represent a number. Expression An algebraic expression is a combination of variables and/or numbers

More information

6 th Grade Math Reference Sheet

6 th Grade Math Reference Sheet 6 th Grade Math Reference Sheet Data Analysis, Statistics, and Probability DATA ANALYSIS DSP 1 GRAPHS DSP 2 PROBABILITY DSP 3 Mean: Average Median: 1 middle number or average of 2 middle number Mode: Most

More information

6.2 Adding and Subtracting Rational Expressions

6.2 Adding and Subtracting Rational Expressions 8 CHAPTER 6 Rational Epressions Simplify. Assume that no denominator is 0. 99. p - - p 00. + q n q n + n + k - 9 0. n 0. - 6 + k Perform the indicated operation. Write all answers in lowest terms. 0. 0.

More information

I can statements for NBT 1-7 1st attempt 2nd attempt mastered

I can statements for NBT 1-7 1st attempt 2nd attempt mastered MATH NAME: I can statements for OA1-3 1st attempt Date 2nd attempt Date Mastered statement I can write expressions using parenthesis, brackets and braces based on wording such as add 5 and then divide

More information

TOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3

TOPIC 2 DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 TOPIC DECIMALS (and INTRODUCTION TO FRACTIONS) WEEK 3 Association between Fractions and Decimals is a fraction. It means divided by. If we divide by the result is not a whole number. It is a half of whole

More information

Algebra2go: Working with Fractions and Mixed Numbers

Algebra2go: Working with Fractions and Mixed Numbers Algebrago: Working with Fractions and Mixed Numbers Algebrago Review of Fractions. Understand Fractions on a Number Line Fractions are used to represent quantities between the whole numbers on a number

More information

- 0.8.00-0.8. 7 ANSWERS: ) : ) : ) : ) : 8 RATIO WORD PROBLEM EXAMPLES: Ratio Compares two amounts or values; they can be written in ways. As a fraction With a colon : With words to A classroom has girls

More information

MAFS.5.NF.2.5. Interpret multiplication as rescaling.

MAFS.5.NF.2.5. Interpret multiplication as rescaling. MAFS.5.NF.2.5 Interpret multiplication as rescaling. Understand that multiplying a fraction > 1 and a given number results in a product > either factor. Examples: 2 x 5/4 = 10/4 or 2½; 10/4 > 2 or 2½ >

More information

Adding and Subtracting Integers

Adding and Subtracting Integers Quarterly 1 Review Sheet (NOTE: This may not include everything you need to know for tomorrow about every topic. It is student created and I am just sharing it in case you find it helpful) Page 1: Adding

More information

Decimals. Chapter Five

Decimals. Chapter Five Chapter Five Decimals 5.1 Introductions to Decimals 5.2 Adding & Subtracting Decimals 5.3 Multiplying Decimals & Circumference of a Circle 5.4 Dividing Decimals 5.5 Fractions, Decimals, & Order of Operations

More information

Rational Numbers: Multiply and Divide

Rational Numbers: Multiply and Divide Rational Numbers: Multiply and Divide Multiplying Positive and Negative Numbers You know that when you multiply a positive number by a positive number, the result is positive. Multiplication with negative

More information

6th Grade Arithmetic (with QuickTables)

6th Grade Arithmetic (with QuickTables) 6th Grade Arithmetic (with QuickTables) This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence

More information

Pre-Algebra Notes Unit Five: Rational Numbers and Equations

Pre-Algebra Notes Unit Five: Rational Numbers and Equations Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the

More information

Name Student ID Number. Group Name. Group Members. Fractions

Name Student ID Number. Group Name. Group Members. Fractions Name Student ID Number Group Name Group Members Fractions Many people struggle with and even fear working with fractions. Part of the reason people struggle is because they do not know what a fraction

More information

Pre-Algebra Notes Unit Five: Rational Numbers; Solving Equations & Inequalities

Pre-Algebra Notes Unit Five: Rational Numbers; Solving Equations & Inequalities Pre-Algebra Notes Unit Five: Rational Numbers; Solving Equations & Inequalities Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special

More information

Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 10.

Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 10. PA Ch 5 Rational Expressions Rational Number is a number that can be written as a quotient of two integers. DECIMALS are special fractions whose denominators are powers of 0. Since decimals are special

More information

Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework

Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period) Day Date In-Class Homework 1 T 8/30 Introductions Operations on Decimals Converting Decimals

More information

Math 6 Pre-assessment

Math 6 Pre-assessment Name: lass: ate: I: Math 6 Pre-assessment Multiple hoice Identify the choice that best completes the statement or answers the question. Use the four-step plan to solve each problem.. omplete the pattern:,,

More information

Lesson 2: Generating Equivalent Expressions

Lesson 2: Generating Equivalent Expressions Lesson 2: Generating Equivalent Expressions Classwork Opening Exercise Additive inverses have a sum of zero. Multiplicative inverses have a product of 1. Fill in the center column of the table with the

More information

Summer Packet 7 th into 8 th grade. Name. Integer Operations = 2. (-7)(6)(-4) = = = = 6.

Summer Packet 7 th into 8 th grade. Name. Integer Operations = 2. (-7)(6)(-4) = = = = 6. Integer Operations Name Adding Integers If the signs are the same, add the numbers and keep the sign. 7 + 9 = 16 - + -6 = -8 If the signs are different, find the difference between the numbers and keep

More information

Fractions / 8 / / 10 1 ½ / 12

Fractions / 8 / / 10 1 ½ / 12 Fractions / 8 / 60 / ½ / 0 / What is a fraction? Loosely speaking, a fraction is a quantity that cannot be represented by a whole number. Why do we need fractions? Consider the following scenario. Can

More information

Algebra II Chapter 6: Rational Exponents and Radical Functions

Algebra II Chapter 6: Rational Exponents and Radical Functions Algebra II Chapter 6: Rational Exponents and Radical Functions Chapter 6 Lesson 1 Evaluate nth Roots and Use Rational Exponents Vocabulary 1 Example 1: Find nth Roots Note: and Example 2: Evaluate Expressions

More information

MATH REVIEW SUPPLEMENT. For The ARITHMETIC SECTION. of the. ACCUPLACER Entry Assessment

MATH REVIEW SUPPLEMENT. For The ARITHMETIC SECTION. of the. ACCUPLACER Entry Assessment Assessment Center MATH REVIEW SUPPLEMENT For The ARITHMETIC SECTION of the ACCUPLACER Entry Assessment Visit The Assessment Center At http://www.stlcc.cc.mo.us/mc/services/assess/index.html This document

More information

Math 6 Notes Unit 03 Notes: Decimals

Math 6 Notes Unit 03 Notes: Decimals Math 6 Notes Unit 03 Notes: Decimals Reading and Writing Decimals Syllabus Objective: (3.2) The student will translate written forms of fractions, decimals, and percents to numerical form. Decimals are

More information

Diocese of Boise Math Curriculum 6 th grade

Diocese of Boise Math Curriculum 6 th grade Diocese of Boise Math Curriculum 6 th grade compute fractions? When do we use Roman Numerals? Numbers, Operations Algebraic Thinking Know use number names the count sequence Use properties of multiplicatio

More information

Pre-Algebra Notes Unit Five: Rational Numbers and Equations

Pre-Algebra Notes Unit Five: Rational Numbers and Equations Pre-Algebra Notes Unit Five: Rational Numbers and Equations Rational Numbers Rational numbers are numbers that can be written as a quotient of two integers. Since decimals are special fractions, all the

More information

Integer Operations. Summer Packet 7 th into 8 th grade 1. Name = = = = = 6.

Integer Operations. Summer Packet 7 th into 8 th grade 1. Name = = = = = 6. Summer Packet 7 th into 8 th grade 1 Integer Operations Name Adding Integers If the signs are the same, add the numbers and keep the sign. 7 + 9 = 16-2 + -6 = -8 If the signs are different, find the difference

More information

MS RtI Tier 3. Curriculum (107 topics + 91 additional topics)

MS RtI Tier 3. Curriculum (107 topics + 91 additional topics) MS RtI Tier 3 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

Lesson 1: THE DECIMAL SYSTEM

Lesson 1: THE DECIMAL SYSTEM Lesson 1: THE DECIMAL SYSTEM The word DECIMAL comes from a Latin word, which means "ten. The Decimal system uses the following ten digits to write a number: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each time

More information

Math Glossary Numbers and Arithmetic

Math Glossary Numbers and Arithmetic Math Glossary Numbers and Arithmetic Version 0.1.1 September 1, 200 Next release: On or before September 0, 200. E-mail edu@ezlink.com for the latest version. Copyright 200 by Brad Jolly All Rights Reserved

More information

Fraction Arithmetic. A proper fraction is a fraction with a smaller numerator than denominator.

Fraction Arithmetic. A proper fraction is a fraction with a smaller numerator than denominator. Fraction Arithmetic FRAX is a game that is designed to help you and your student/child master fractions, but it does not teach them the basics. I ve put together this document to help remind you about

More information

Course Learning Outcomes for Unit I. Reading Assignment. Unit Lesson. UNIT I STUDY GUIDE Number Theory and the Real Number System

Course Learning Outcomes for Unit I. Reading Assignment. Unit Lesson. UNIT I STUDY GUIDE Number Theory and the Real Number System UNIT I STUDY GUIDE Number Theory and the Real Number System Course Learning Outcomes for Unit I Upon completion of this unit, students should be able to: 2. Relate number theory, integer computation, and

More information

Mini-Lectures by Section

Mini-Lectures by Section Mini-Lectures by Section BEGINNING AND INTERMEDIATE ALGEBRA, Mini-Lecture 1.1 1. Learn the definition of factor.. Write fractions in lowest terms.. Multiply and divide fractions.. Add and subtract fractions..

More information

MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP Subject: Mathematics Grade: 6. Quarter 1 Content (What Students Should Know) Vocabulary Integer

MARLBORO CENTRAL SCHOOL DISTRICT CURRICULUM MAP Subject: Mathematics Grade: 6. Quarter 1 Content (What Students Should Know) Vocabulary Integer Instructional Days September (10 days) Essential Questions How do you locate rational numbers on a number line? How are integers and absolute value used in real world situations? How are decimals and fractions

More information

Unit 2: Accentuate the Negative Name:

Unit 2: Accentuate the Negative Name: Unit 2: Accentuate the Negative Name: 1.1 Using Positive & Negative Numbers Number Sentence A mathematical statement that gives the relationship between two expressions that are composed of numbers and

More information

Iron County Schools. Yes! Less than 90 No! 90 No! More than 90. angle: an angle is made where two straight lines cross or meet each other at a point.

Iron County Schools. Yes! Less than 90 No! 90 No! More than 90. angle: an angle is made where two straight lines cross or meet each other at a point. Iron County Schools 1 acute angle: any angle that is less than 90. Yes! Less than 90 No! 90 No! More than 90 acute triangle: a triangle where all the angles are less than 90 angle: an angle is made where

More information

Example 2: Simplify each of the following. Round your answer to the nearest hundredth. a

Example 2: Simplify each of the following. Round your answer to the nearest hundredth. a Section 5.4 Division with Decimals 1. Dividing by a Whole Number: To divide a decimal number by a whole number Divide as you would if the decimal point was not there. If the decimal number has digits after

More information

DECIMAL FRACTIONS. Thus, 0.25=25/100=1/4;2.008=2008/1000=251/125.

DECIMAL FRACTIONS. Thus, 0.25=25/100=1/4;2.008=2008/1000=251/125. DECIMAL FRACTIONS I. Decimal Fractions : Fractions in which denominators are powers of 10 are known as decimal fractions. Thus,1/10=1 tenth=.1;1/100=1 hundredth =.01; 99/100=99 hundreths=.99;7/1000=7 thousandths=.007,etc

More information

Section 1.2 Fractions

Section 1.2 Fractions Objectives Section 1.2 Fractions Factor and prime factor natural numbers Recognize special fraction forms Multiply and divide fractions Build equivalent fractions Simplify fractions Add and subtract fractions

More information

CLASSIFICATION OF FRACTIONS 1. Proper Fraction : A Proper fraction is one whose numerator is less than its denominator. 1 eg., 3

CLASSIFICATION OF FRACTIONS 1. Proper Fraction : A Proper fraction is one whose numerator is less than its denominator. 1 eg., 3 CLASSIFICATION OF FRACTIONS. Proper Fraction : A Proper fraction is one whose numerator is less than its denominator. eg.,. Improper Fraction : An improper fraction is one whose numerator is equal to or

More information

Grade 4 Fractions. Answer the questions. For more such worksheets visit (1) Convert into a mixed fraction. (2) Convert

Grade 4 Fractions. Answer the questions. For more such worksheets visit   (1) Convert into a mixed fraction. (2) Convert ID : aefractions [1] Grade Fractions For more such worksheets visit www.edugain.com Answer the questions (1) Convert 63 13 (2) Convert 6 7 12 into a mixed fraction. to improper fraction. (3) Aleser had

More information

NFC ACADEMY MATH 600 COURSE OVERVIEW

NFC ACADEMY MATH 600 COURSE OVERVIEW NFC ACADEMY MATH 600 COURSE OVERVIEW Math 600 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to rational numbers and the skills needed for

More information

Concept Fourth Grade: Second Nine Weeks Readiness Standards Time Key Content Key Vocabulary

Concept Fourth Grade: Second Nine Weeks Readiness Standards Time Key Content Key Vocabulary Multiplication by 2-Digit Numbers Concept Fourth Grade: Second Nine Weeks 14-15 Time Key Content Key Vocabulary 4.4C represent the product of 2 two-digit numbers using arrays, area models, or equations,

More information

Digits Interventions. Part 1/ Got It 1 (Journal Page) Part 2/ Got It 2 (Journal Page) Part 3/ Got It 3 (Journal Page) Lesson Check

Digits Interventions. Part 1/ Got It 1 (Journal Page) Part 2/ Got It 2 (Journal Page) Part 3/ Got It 3 (Journal Page) Lesson Check Quarter 1 Core Content Process Skills/ Activities Unit A: Expressions & Interventions Equations Rocket Math Intervention Lessons: i1-1 Place Value i1-2 Comparing & Ordering Whole Numbers i2-1 Additional

More information

( 3) ( 4 ) 1. Exponents and Radicals ( ) ( xy) 1. MATH 102 College Algebra. still holds when m = n, we are led to the result

( 3) ( 4 ) 1. Exponents and Radicals ( ) ( xy) 1. MATH 102 College Algebra. still holds when m = n, we are led to the result Exponents and Radicals ZERO & NEGATIVE EXPONENTS If we assume that the relation still holds when m = n, we are led to the result m m a m n 0 a = a = a. Consequently, = 1, a 0 n n a a a 0 = 1, a 0. Then

More information

Math 7 Notes Unit Three: Applying Rational Numbers

Math 7 Notes Unit Three: Applying Rational Numbers Math 7 Notes Unit Three: Applying Rational Numbers Strategy note to teachers: Typically students need more practice doing computations with fractions. You may want to consider teaching the sections on

More information

GTPS Curriculum 5 th Grade Math. Topic: Topic 1 - Understand Place Value

GTPS Curriculum 5 th Grade Math. Topic: Topic 1 - Understand Place Value Topic: Topic 1 - Understand Place Value Understand the place value system. 5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place

More information

Tantasqua/Union 61 Math Alignment GRADE 5

Tantasqua/Union 61 Math Alignment GRADE 5 Tantasqua/Union 61 Math Alignment GRADE 5 Massachusetts Frameworks Domain Massachusetts Standard GO Math Operations and Algebraic Thinking A. Write and interpret numerical expressions. B. Analyze patterns

More information

Unit 1 Integers, Fractions & Order of Operations

Unit 1 Integers, Fractions & Order of Operations Unit 1 Integers, Fractions & Order of Operations In this unit I will learn Date: I have finished this work! I can do this on the test! Operations with positive and negative numbers The order of operations

More information

6.3. Complex Fractions

6.3. Complex Fractions 6. Comple Fractions 1. Simplify comple fractions by simplifying the numerator and denominator (Method 1).. Simplify comple fractions by multiplying by a common denominator (Method ).. Compare the two methods

More information

Sand Creek Zone Curriculum Map

Sand Creek Zone Curriculum Map Quarter 1 Concept: Add and subtract 0. 3.NBT.2 Fluently add and subtract 0 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

More information

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number

More information

EXAMPLE 1. Change each of the following fractions into decimals.

EXAMPLE 1. Change each of the following fractions into decimals. CHAPTER 1. THE ARITHMETIC OF NUMBERS 1.4 Decimal Notation Every rational number can be expressed using decimal notation. To change a fraction into its decimal equivalent, divide the numerator of the fraction

More information