Math: Fractions & Decimals Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Fractions & decimals Fractions & decimals Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-3005 \|xiBAHBDy01264rzu Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Place Value – Understanding Numbers Understanding Fractions All About Fractions All About Decimals Adding & Subtracting Decimals Fraction Concepts Adding & Subtracting Fractions Multiplying & Dividing Decimals Multiplying & Dividing Fractions Operations with Mixed Numbers

This pizza is cut into 2 equal parts. Each part is one half or of the whole. This pizza is cut into 3 equal parts. Each part is one third or of the whole. This pizza is cut into 4 equal parts. Each part is one fourth or of the whole. 1 4 1 4 1 3 1 3 1 2 1 2 Equal Parts Fractions of a Set Halves Thirds Fourths A fraction is used to name equal parts of a whole. 1 green tomato 2 tomatoes in all of the tomatoes are green 1 green banana 3 bananas in all of the bananas are green 1 green apple 4 apples in all of the apples are green 1 out of 2 is green 1 out of 3 is green 1 out of 4 is green © Copyright NewPath Learning. All Rights Reserved. 93-4205 www.newpathlearning.com Understanding Fractions

Key Vocabulary Terms • fourths • one half • fraction • one third • halves • thirds • one fourth • whole This pizza is cut into parts. Each part is or of the whole. Equal Parts Fractions of a Set Halves Thirds Fourths A frac tion is used to name equal parts of a whole. 1 green tomato 2 tomatoes in all of the tomatoes are green 1 green banana 3 bananas in all of the bananas are green 1 green apple 4 apples in all of the apples are green 1 out of 2 is green 1 out of 3 is green 1 out of 4 is green This pizza is cut into parts. Each part is or of the whole. This pizza is cut into parts. Each part is or of the whole. © Copyright N ewPath Learning. All Rights Reserved. 93-4205 www.newpathlearning.com Understanding Fractions \|xiBAHBDy01632ozX

• Mixed numbers have a whole number and a fraction. • A number line can be used to compare fractions. • Fractions that represent the same amount of a whole are called equivalent fractions. – One and one half tomatoes Equal Parts of a Whole Equivalent Fractions Mixed Numbers Fractions on a Number Line 2 equal parts Halves 3 equal parts Thirds 4 equal parts Fourths 5 equal parts Fifths 6 equal parts Sixths represents the same amount as example: 8 equal parts Eighths 10 equal parts Tenths 12 equal parts Twelfths Subtracting Fractions Adding Fractions 1. Only add the numerators 2. Write the total over the same denominator. 1. Only subtract the numerators 2. Write the difference over the same denominator. To add fractions with the same denominator: To subtract fractions with the same denominator: + = – = © Copyright NewPath Learning. All Rights Reserved. 93-4307 www.newpathlearning.com All About Fractions 1 5 1 4 1 3 1 6 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 2 8 3 8 4 8 4 8 5 8 6 8 7 8 8 8 1 10 1 12 1 1 2 1 1 2 0 1 4 2 4 3 4 4 4 0 1 2 1 2 2 2 0 0 1 1 4 1 2 1 2 1 4 1 4 1 4 1 3 6 2 6 5 6 = + 3 6 2 6 5 6 = + 3 8 2 8 1 8 = – 3 8 2 8 1 8 = – 1 2 Denominator Numerator

Equal Parts of a Whole © Copyright NewPath Learning. All Rights Reserved. 93-4307 www.newpathlearning.com \|xiBAHBDy01638qzZ All About Fractions 1 5 1 4 1 3 1 6 1 8 1 10 1 12 1 2 Key Vocabulary Terms • denominator • difference • eighths • equal parts • equivalent fraction • fifths • fourths • fraction • halves • mixed number • number line • numerator • sixths • tenths • thirds • total • twelfths equal parts equal parts equal parts equal parts • A number li can be used to fractions. Fractions on a Number Line 0 0 0 0 1 • Fractions that represent the same amount of a whole are called . Equivalent Fractions represents the same amount as example: 4 8 1 2 equal parts equal parts equal parts equal parts Adding Fractions 1. Only add the numerators 2. Write the total over the same denominat . To add fractions with the same denominator: + = 3 6 2 6 5 6 = + 3 6 2 6 5 6 = + Subtracting Fractions 1. Only subtract the numerators 2. Write the difference over the same denominator . To subtract fractions with the same denominator: – = 3 8 2 8 1 8 = – 3 8 2 8 1 8 = –

Adding Decimals Add 2.74 + 1.52 2.74 + 1.52 Subtract 2.74 – 1.52 Subtracting Decimals Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 2.7 4 + 1.5 2 6 2.74 + 1.52 26 2.74 + 1.52 4.26 1 1 2.74 – 1.52 2.74 – 1.52 2 2.74 – 1.52 22 2.74 – 1.52 1.22 ones tens tenths hundr eds hundr edths ones tens tenths hundr eds hundr edths 1 2 1. 2 0 1 1. 3 2 1. 4 0 1. 0 4 0. 7 8 0. 7 0 7 10 7 10 1.04 1.04 0.78 0.78 1.4 0.7 1.4 0.7 4 100 4 100 100 78 78 100 1 2 1. 2 0 1 1. 3 2 1. 4 0 1. 0 4 0. 7 8 0. 7 0 Decimals & Fr actions: Place Value Ordering & Comparing Decimals Decimal numbers are another way of writing fractions or mixed numbers. seven tenths one and four tenths seventy - eight hundredths one and four hundredths • The numbers to the left of the decimal point are whole numbers. • The numbers to the right of the decimal point are parts or fractions of whole numbers. • Line up the decimal points. • Compare the digits in each column, starting on the left. One hundr ed twenty-one and two tenths Eleven and thirty-two hundr endths One and four tenths One and four hundr endths Seven tenths Seventy-eight hundr endths Hundredths Tenths 4 10 4 10 Base Blocks Fraction Decimal Word Form Base Blocks Fraction Decimal Word Form Line up the decimal points. Add the hundredths and regroup if needed. Add the tenths and regroup if needed. Add the ones. Place the decimal point in the sum. Line up the decimal points. Subtract the hundredths and regroup if needed. Subtract the tenths and regroup if needed. Subtract the ones. Place the decimal point in the difference. © Copyright NewPath Learning. All Rights Reserved. 93-4308 www.newpathlearning.com All About Decimals

Adding Decimals Add 2.74 + 1.52 2.74 + 1.52 Subtract 2.74 – 1.52 Subtracting Decimals Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 2.7 4 + 1.5 2 6 2.74 + 1.52 2 2.74 + 1.52 4 . 1 1 2.74 – 1.52 2.74 – 1.52 2 2.74 – 1.52 2 2.74 – 1.52 1. ones tens tenths hund reds hund redths ones tens tenths hund reds hund redths Decimals & Fr actions: Place Value Decimal numbers are another way of writing fractions or mixed numbers. seven tenths one and four tenths seventy - eight hundredths one and four hundredths • The numbers to the left of the decimal point are . • The numbers to the right of the decimal point are parts or fractions of whole numbers. One hund red twenty-one and two tenths Eleven and thirty-two hundr endths One and four tenths One and four hundr endths Seven tenths Seventy-eight hundr endths Hundredths Tenths Base Blocks Fraction Decimal Word Form Base Blocks Fraction Decimal Word Form Line up the decimal points. Add the hundredths and regroup if needed. Add the tenths and regroup if needed. Add the ones. Place the decimal point in the sum. Line up the decimal points. Subtract the hundredths and regroup if needed. Subtract the tenths and regroup if needed. Subtract the ones. Place the decimal point in the difference. Key Vocabulary Terms • decimal • ones • decimal point • regroup • difference • sum • fraction • tens • hundreds • tenths • hundredths © Copyright NewPath Learning. All Rights Reserved. 93-4308 www.newpathlearning.com All About Decimals \|xiBAHBDy01637tz]

Thousands 10 hundreds make up 1 thousand Hundreds 10 tens make up 1 hundred Tens 10 ones make up 1 ten Ones 1 Standard Form Expanded Form Number Word 372,512,489 300,000,000 + 70,000,000 + 2,000,000 + 500,000 + 10,000 + 2,000 + 400 + 80 + 9 three hundred seventy-two million, five hundred twelve thousand, four hundred eighty-nine 11 2 2 6 6 . hundredths tenths ones tens 1 one 2 tenths 6 hundredths 3 7 2 5 1 2 4 8 9 3 7 2 5 1 2 4 8 9 ones tens hundr eds ones tens hundr eds thousands thousands ten thousands ten thousands millions millions ten millions ten millions hundr ed millions hundr ed millions hundr ed thousands hundr ed thousands Ones Period Thousands Period Millions Period • Place value is the value assigned to the position of a digit in a written number. • A digit is a symbol used to write a number 0 to 9. • A period is a group of three digits separated by a comma. Base–ten Place Value Decimal Place Value • Our place value system is based on groups of ten. • Each place represents ten times the value of the place to the right. 1.1 1.2 1.21 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.22 1.24 1.26 1.28 1.23 1.25 1.27 1.29 1.3 1.4 0 1.0 2.0 © Copyright NewPath Learning. All Rights Reserved. 93-4401 www.newpathlearning.com Place Value - Understanding Numbers

\|xiBAHBDy01658ozX 10 hundreds make up 10 tens make up 10 ones make up Standard Form Expanded Form Number Word 372,512,489 11 2 2 6 6 . hundredths tenths ones tens 1.26 Key Vocabulary Terms • base-ten • decimal • expanded form • hundreds • hundredths • millions • millions period • number word • ones • ones period • place value • standard form • tens • tenths • thousands • thousands period 3 7 2 5 1 2 4 8 9 3 7 2 5 1 2 4 8 9 Ones Period Thousands Period Millions Period • Place value is the value assigned to the position of a digit in a written number. • A digit is a symbol used to write a number 0 to 9. • A period is a group of three digits separated by a comma. Base–ten Place Value Decimal Place Value • Our place value system is based on groups of . • Each place represents the value of the place to the right. 1.1 1.2 1.21 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.22 1.24 1.26 1.28 1.23 1.25 1.27 1.29 1.3 1.4 0 1.0 2.0 ___________ + _________ + ________ + ______ + _____ + _____ + ____ + ___ + __ © Copyright NewPath Learning. All Rights Reserved. 93-4401 www.newpathlearning.com Place Value - Understanding Numbers

16.58 + 27.8 27.8 – 16.58 Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 • Line up the decimal points. • Write zeros as place holders, if needed. • Add the hundredths. • Carry (regroup) if needed. • Add the tenths. • Carry (regroup) if needed. 0.62 + 0.34 = 0.96 1.8 – 1.2 = 0.6 Decimal Models Adding Decimals with Grids Adding Decimals Subtracting Decimals Subtracting Decimals with Grids 1.0 one whole (1) 0.1 . 01 1 10 hundredths 1 100 thousandths 1 1000 + + ones tens tenthshundr edths ones tens tenthshundr edths 1 1 1 6 5 8 . 2 7 8 0 4 4 3 8 . + 1 1 6 5 8 . 2 7 8 0 . 3 8 + 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . 8 • Line up the decimal points. • Write zeros as place holders, if needed. • Regroup if needed. • Subtract the hundredths. • Regroup if needed. • Subtract the tenths. • Regroup if needed. • Subtract the ones, then the tens. • Drag the decimal point straight down. – – ones tens tenthshundr edths ones tens tenthshundr edths 1 7 10 7 10 7 10 6 5 8 . 2 7 8 0 1 1 2 2 . – 1 6 5 8 . 2 7 8 0 . 2 2 – 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . 2 . . © Copyright NewPath Learning. All Rights Reserved. 93-4404 www.newpathlearning.com Adding & Subtracting Decimals 0.001

16.58 + 27.8 27.8 – 16.58 Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 • Line up the decimal points. • Write zeros as place holders, if needed. • Add the hundredths. • Carry (regroup) if needed. • Add the tenths. • Carry (regroup) if needed. 0.62 + 0.34 = 0.96 1.8 – 1.2 = 0.6 Decimal Models Adding Decimals with Grids Adding Decimals Subtracting Decimals Subtracting Decimals with Grids 1.0 one whole (1) 0.1 . 01 1 10 hundredths 1 100 thousandths 1 1000 + + ones tens tenthshund redths ones tens tenthshund redths 1 6 5 8 . 2 7 8 0 . + 1 6 5 8 . 2 7 8 0 . + 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . • Line up the decimal points. • Write zeros as place holders, if needed. • Regroup if needed. • Subtract the hundredths. • Regroup if needed. • Subtract the tenths. • Regroup if needed. • Subtract the ones, then the tens. • Drag the decimal point straight down. – – ones tens tenthshund redths ones tens tenthshund redths 1 6 5 8 . 2 7 8 0 . – 1 6 5 8 . 2 7 8 0 . – 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . . . © Copyright NewPath Learning. All Rights Reserved. 93-4404 www.newpathlearning.com Adding & Subtracting Decimals 0.001 Key Vocabulary Terms • add • decimal • decimal point • hundredth • regroup • subtract • tenth • thousandth \|xiBAHBDy01634sz\

Mixed Numbers & Impr oper Fractions Fractions in Simplest Form To subtract fractions with the same denominator: + = – = 3 6 2 6 5 6 = + 2 6 5 6 + 3 8 2 8 1 8 = – 3 8 2 8 1 8 = – Parts of a Whole Part of a Group A fraction is used to describe a part of a whole. A fraction can also describe part of a group or set. Equivalent fractions are fractions with different numerators and denominators but have the same value. To find an equivalent fraction, multiply or divide the numerator and denominator of a fraction by the same number. Equivalent Fractions To find the simplest form of a fraction, keep dividing until 1 is the only number that divides both the numerator and denominator. Fractions in Simplest Form Improper Fractions & Mixed Numbers 8 16 4 8 2 4 1 2 = = = = = = ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 6 16 6 16 3 8 3 8 = = 2 4 2 4 1 2 1 2 = = 10 3 1 3 6 16 6 16 3 8 3 8 = = x2 x2 x2 x2 2 4 2 4 1 2 1 2 = = ÷2 ÷2 ÷2 ÷2 2 6 green sections (numerator) total number of sections (denominator) 5 12 apples (numerator) total number of fruit (denominator) • divide the numerator by the denominator • write the remainder as the numerator of the mixed number To change an improper fraction to a mixed number: improper fraction mixed number = 3 1 whole 3 3 ( ) 1 whole 3 3 ( ) 1 whole 3 3 ( ) of a whole 1 3 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 1 2 1 2 1 4 1 4 1 4 1 © Copyright NewPath Learning. All Rights Reserved. 93-4408 www.newpathlearning.com Fraction Concepts

Parts of a Whole Part of a Group A fraction is used to describe a part of a whole. A fraction can also describe part of a group or set. Equivalent fractions are fractions with different numerators and denominators but have the same value. To find an equivalent fraction, multiply or divide the numerator and denominator of a fraction by the same number. Equivalent Fractions To find the simplest form of a fraction, keep dividing until 1 is the only number that divides both the numerator and denominator. Fractions in Simplest Form Improper Fractions & Mixed Numbers 8 16 4 8 2 4 1 2 = = = = = = ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 6 16 6 16 3 8 3 8 = = 2 4 2 4 1 2 1 2 = = 10 3 1 3 6 16 6 16 3 8 3 8 = = x2 x2 x2 x2 2 4 2 4 1 2 1 2 = = ÷2 ÷2 ÷2 ÷2 2 6 green sections (numerator) total number of sections (denominator) 5 12 apples (numerator) total number of fruit (denominator) • divide the numerator by the denominator • write the remainder as the numerator of the mixed number To change an improper fraction to a mixed number: improper fraction mixed number = 3 1 whole 3 3 ( ) 1 whole 3 3 ( ) 1 whole 3 3 ( ) of a whole 1 3 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 1 2 1 2 1 4 1 4 1 4 1 Key Vocabulary Terms • denominator • equivalent fraction • fraction • improper fraction • mixed number • numerator • remainder • simplest form © Copyright NewPath Learning. All Rights Reserved. 93-4408 www.newpathlearning.com Fraction Concepts \|xiBAHBDy01646lz[

2 8 2 8 6 8 6 8 4 8 4 8 + + + + = = = = = = = = = = = = 1 8 1 8 7 8 7 8 3 4 3 4 = = 1 4 1 4 1 8 1 8 3 8 3 8 = = 1 8 1 8 1 8 1 8 = = 3 12 3 12 6 12 6 12 9 12 9 12 - - - - + + + + - - - - 2 8 2 8 3 4 3 4 4 8 4 8 + + = = 1 8 1 8 7 8 7 8 6 8 6 8 + + = = 3 4 3 4 6 8 6 8 ÷2 ÷2 ÷2 ÷2 6 8 6 8 3 4 3 4 x2 x2 x2 x2 3 12 3 12 1 2 1 2 9 12 9 12 = = 1 2 1 2 6 12 6 12 ÷6 ÷6 ÷6 ÷6 -- 3 8 3 8 3 8 3 8 = = 2 8 2 8 1 8 1 8 3 8 3 8 -- = = 2 8 2 8 1 4 1 4 x2 x2 x2 x2 Adding Fractions with Like Denominators Subtracting Fractions with Like Denominators • Add the numerators. • Keep the denominators the same. • Simplify, if needed. • Subtract the numerators. • Keep the denominators the same. • Simplify, if needed. Adding Fractions with Unlike Denominators • Find equivalent fractions with the same denominator. • Add the numerators and place the sum over the same denominator. • Simplify, if needed. • Find equivalent fractions with the same denominator. • Subtract the numerators and place the difference over the same denominator. • Simplify, if needed. Subtracting Fractions with Unlike Denominators © Copyright NewPath Learning. All Rights Reserved. 93-4409 www.newpathlearning.com Adding & Subtracting Fractions

\|xiBAHBDy01635pzY 2 8 2 8 6 8 6 8 4 8 4 8 + + + + = = = = = = = = = = = = 1 8 1 8 7 8 7 8 3 4 3 4 = = 1 4 1 4 1 8 1 8 3 8 3 8 = = 1 8 1 8 1 8 1 8 = = 3 12 3 12 6 12 6 12 9 12 9 12 - - - - + + + + - - - - 2 8 2 8 3 4 3 4 4 8 4 8 + + = = 1 8 1 8 7 8 7 8 6 8 6 8 + + = = 3 4 3 4 6 8 6 8 6 8 6 8 3 4 3 4 3 12 3 12 1 2 1 2 9 12 9 12 = = 1 2 1 2 6 12 6 12 ÷6 ÷6 ÷6 ÷6 -- 3 8 3 8 3 8 3 8 = = 2 8 2 8 1 8 1 8 3 8 3 8 -- = = 2 8 2 8 1 4 1 4 Adding Fractions with Like Denominators Subtracting Fractions with Like Denominators • Add the numerators. • Keep the denominators the same. • Simplify, if needed. • Subtract the numerators. • Keep the denominators the same. • Simplify, if needed. Adding Fractions with Unlike Denominators • Find equivalent fractions with the same denominator. • Add the numerators and place the sum over the same denominator. • Simplify, if needed. • Find equivalent fractions with the same denominator. • Subtract the numerators and place the difference over the same denominator. • Simplify, if needed. Subtracting Fractions with Unlike Denominators Key Vocabulary Terms • add • fraction • denominator • numerator • difference • subtract • equivalent fraction • sum ÷2 ÷2 ÷2 ÷2 x2 x2 x2 x2 x2 x2 x2 x2 © Copyright NewPath Learning. All Rights Reserved. 93-4409 www.newpathlearning.com Adding & Subtracting Fractions

Therefore, 3 ÷ 0.2 = 15 Therefore, 0.6 x 0.3 = 0.18 or Therefore, 0.59 x 4.8 = 2.832 m = 32.22 n = 6.75 18 100 Multiplying Whole Numbers by Decimals Using Grids to Multiply Multiplying Decimals by Decimals Dividing Decimals by Whole Numbers Dividing a Decimal by a Decimal • Multiply as you would with whole numbers. How many 2 tenths are there in 3 wholes? There are 15 sets of 2 tenths. • Add the number of decimal places in each factor. • Place the decimal point in the product. • The 18 overlapping squares (green) that are shaded twice show the product of 0.6 x 0.3. • Multiply as you would with whole numbers. • Add the number of decimal places in each factor. • Place the decimal point in the product. • Shade 0.6 of the grid. • Shade 0.3 of the grid with a different color or pattern in the other direction. • Change the divisor and the dividend to a whole number by multiplying each by the same power of 10. • Divide as you would divide whole numbers. Add zeros as needed. • Place the decimal point in the quotient directly above the decimal point in the dividend. Bring down the ones and divide. Step 2 The answer checks if the product is the same as the dividend Multiply: 6 x 5.37 = m Multiply: 0.6 x 0.3 = n Divide: 3 ÷ 0.2 = p Divide: 5.4 ÷ 0.8 = n • multiply: 1 x 6 • subtract: 8 – 6 • compare: 2 < 4 5.37 x 6 32.22 2 decimal places 0 decimal places move decimal point 2 places + 2 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 0.5 9 4.8 4 7 2 2 3 6 0 2 8 3 2 2 decimal places 1 decimal places move decimal point 3 places + 3 2 1 7 3 x . = 5.4 0.8 54 8 x10 x10 x10 x10 54.00 6.75 6 0 5 6 – – 40 40 0 – 48 08. 5.4 0.8 54. 8. © Copyright NewPath Learning. All Rights Reserved. 93-4502 www.newpathlearning.com Multiplying & Dividing Decimals

\|xiBAHBDy01654qzZ Therefore, 3 ÷ 0.2 = 15 Therefore, 0.6 x 0.3 = 0.18 or Therefore 0.59 x 4.8 = 2.832 m = 32.22 n = 6.75 18 100 Multiplying Whole Numbers by Decimals Using Grids to Multiply Dividing Decimals by Whole Numbers • Multiply as you would with whole numbers. How many 2 tenths are there in 3 wholes? There are 15 sets of 2 tenths. • Add the number of decimal places in each factor. • Place the decimal point in the product. • The 18 overlapping squares (green) that are shaded twice show the product of 0.6 x 0.3. • Multiply as you would with whole numbers. • Add the number of decimal places in each factor. • Place the decimal point in the product. • Shade 0.6 of the grid. • Shade 0.3 of the grid with a different color or pattern in the other direction. • Change the divisor and the dividend to a whole number by multiplying each by the same power of 10. • Divide as you would divide whole numbers. Add zeros as needed. • Place the decimal point in the quotient directly above the decimal point in the dividend. Multiply: 6 x 5.37 = m Multiply: 0.6 x 0.3 = n Divide: 3 ÷ 0.2 = p Divide: 5.4 ÷ 0.8 = n 5.37 x 6 2 decimal places 0 decimal places move decimal point 2 places + 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 0.5 9 4.8 + 7 3 x = 5.4 0.8 54.00 08. 5.4 0.8 54. 8. Key Vocabulary Terms • decimal • decimal place • decimal point • divide • dividend • divisor • multiply • power of 10 • product • quotient • tenth • whole number 2 decimal places 0 decimal places move decimal point 2 places Multiplying Decimals by Decimals Dividing a Decimal by a Decimal © Copyright NewPath Learning. All Rights Reserved. 93-4502 www.newpathlearning.com Multiplying & Dividing Decimals

Modeling Multiplication Multiplying Fractions Modeling Division Dividing Fractions 2 3 3 4 = = 1 2 6 12 ÷6 ÷6 ÷6 ÷6 6 12 x 2 3 2 3 3 4 3 4 x x x = = Multiply 2 3 3 4 x Multiply 3 16 9 16 ÷ Divide 2 3 6 ÷ Divide • Shade of the rectangle. • Divide rectangle into thirds. • Shade of the rectangle with a different color or pattern in the other direction. Step 1 3 4 Therefore, X = or 3 4 The answer of is in simplest form. 1 2 2 3 2 3 2 3 2 3 3 4 2 3 • The overlapping sections (green) that are shaded twice show the product of x . • There are 3 groups of in . Multiply the numerators. How many sets of are there in ? Step 2 Multiply the denominators. Step 3 Use the greatest common factor (GCF) to simplify the product, if necessary. The GCF of 6 & 12 is 6. 2 3 6 1 2 3 ÷ ÷ 6 1 3 2 x = Step 1 Write the whole number as a fraction. Step Dividend Divisor 2 Flip the divisor upside down to find the reciprocal. The reciprocal of is . Rewrite as multiplication using the reciprocal. Simplify before multiplying. Step 4 Step 3 6 12 3 16 3 16 3 16 3 16 9 16 9 16 3 16 9 16 6 12 1 2 Therefore, ÷ = 9 16 3 3 9 16 6 3 1 9 1 3 1 x = = 3 3 1 2 © Copyright NewPath Learning. All Rights Reserved. 93-4504 www.newpathlearning.com Multiplying & Dividing Fractions

Modeling Multiplication Multiplying Fractions Modeling Division Dividing Fractions 2 3 3 4 = = 6 12 x 2 3 3 4 x x x = = Multiply 2 3 3 4 x Multiply 3 16 9 16 ÷ Divide 2 3 6 ÷ Divide • Shade of the rectangle. • Divide rectangle into thirds. • Shade of the rectangle with a different color or pattern in the other direction. Step 1 3 4 Therefore, X = or 3 4 The answer of is in simplest form. 1 2 2 3 2 3 2 3 2 3 3 4 2 3 • The overlapping sections (green) that are shaded twice show the product of x . • There are 3 groups of in . Multiply the numerators. How many sets of are there in ? Step 2 Multiply the denominators. Step 3 Use the greatest common factor (GCF) to simplify the product, if necessary. The GCF of 6 & 12 is 6. 2 3 ÷ ÷ x = Step 1 Write the whole number as a fraction. Step Dividend Divisor 2 Flip the divisor upside down to find the reciprocal. The reciprocal of is . Rewrite as multiplication using the reciprocal. Simplify before multiplying. Step 4 Step 3 3 16 9 16 9 16 3 16 9 16 Therefore, ÷ = 9 16 3 3 16 6 x = = Key Vocabulary Terms • denominator • divide • divisor • fraction • greatest common factor (GCF) • multiply • numerator • product • reciprocal • whole number © Copyright NewPath Learning. All Rights Reserved. 93-4504 www.newpathlearning.com Multiplying & Dividing Fractions \|xiBAHBDy01655nzW

Addition Subtraction Multiplication Division + + Add Step 1 2 3 2 1 6 3 Multiply 1 4 2 1 4 2 9 4 2 3 – – Subtract 3 4 4 5 8 2 Find the least common denominator (LCD) of and . 2 3 1 6 Step 1 Find the LCD and write equivalent fractions. LCD of and is 8. Step 2 Subtract the fractions first, then the whole numbers. Simplify the difference, if necessary. 3 4 5 8 Step 2 Write equivalent fractions with a denominator of 6. Step 1 Write the mixed number as an improper fraction. Step 1 Write the mixed number as improper fractions. Step 2 Rewrite as multiplication using the reciprocal of the divisor. Step 3 Multiply the numerators and denominators and simplify. Step 4 Write as a mixed number. Step 2 Multiply the numerators and denominators of the two factors. Step 3 Simplify the product. Step 4 Write the product as a mixed number, if it is an improper fraction. Step 3 Add the fractions. Then add the whole numbers. Simplify the sum, if necessary. 2 3 1 6 2 3 2 = 4 6 2 x2 x2 3 4 4 = 6 8 4 – 5 8 2 1 8 2 x2 x2 1 6 3 + 5 6 5 x = m Divide 3 7 1 2 3 1 ÷ = n = = factor factor product quotient divisor dividend multiples of 3: 3,6,9,12,15... multiples of 6: 6,12,18,24... © Copyright NewPath Learning. All Rights Reserved. 93-4506 www.newpathlearning.com Operations with Mixed Numbers 1 4 2 = x 2 3 x 2 3 9 4 = 18 12 18 12 = 3 2 ÷6 ÷6 35 30 = 7 6 ÷5 ÷5 3 2 = 1 2 1 5 3 = 2 3 1 10 7 = 3 7 1 improper fraction mixed number 7 6 = 1 6 1 improper fraction mixed number 5 3 7 10 35 30 x =

Addition Subtraction Multiplication Division + + Add Step 1 2 3 2 1 6 3 Multiply 1 4 2 1 4 2 9 4 2 3 – – Subtract 3 4 4 5 8 2 Find the least common denominator (LCD) of and . 2 3 1 6 Step 1 Find the LCD and write equivalent fractions. LCD of and is . Step 2 Subtract the fractions first, then the whole numbers. Simplify the difference, if necessary. 3 4 5 8 Step 2 Write equivalent fractions with a denominator of 6. Step 1 Write the mixed number as an improper fraction. Step 1 Write the mixed number as improper fractions. Step 2 Rewrite as multiplication using the reciprocal of the divisor. Step 3 Multiply the numerators and denominators and simplify. Step 4 Write as a mixed number. Step 2 Multiply the numerators and denominators of the two factors. Step 3 Simplify the product. Step 4 Write the product as a mixed number, if it is an improper fraction. Step 3 Add the fractions. Then add the whole numbers. Simplify the sum, if necessary. 2 3 1 6 2 3 2 = 3 4 4 = – 5 8 2 1 6 3 + x = m Divide 3 7 1 2 3 1 ÷ = n = = factor factor product quotient divisor dividend multiples of 3: , , , , ... multiples of 6: , , , ... © Copyright NewPath Learning. All Rights Reserved. 93-4506 www.newpathlearning.com Operations with Mixed Numbers 1 4 2 = x 2 3 x = = = = 2 3 1 = 3 7 1 improper fraction mixed number 7 6 = improper fraction mixed number 5 3 7 10 x = Key Vocabulary Terms • addition • dividend • division • divisor • equivalent fraction • factor • fraction • improper fraction • least common denominator (LCD) • mixed number • multiplication • numerator • product • quotient • reciprocal • subtraction 35 30 = \|xiBAHBDy01657rzu

Math: Fractions & Decimals

Mathematics, Grade 6

Need Help?

NewPath Learning

Solutions

Shop By Product

Shop By Grade

Shop By Subject