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Home Explore 84913_CO - 62_222310144-COMPASS-STUDENT-TEXTBOOK-MATHEMATICS-G05-PART2

84913_CO - 62_222310144-COMPASS-STUDENT-TEXTBOOK-MATHEMATICS-G05-PART2

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Description: 84913_CO - 62_222310144-COMPASS-STUDENT-TEXTBOOK-MATHEMATICS-G05-PART2

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CO MPASS SERIES mathematics textbook part -2 3 Name: Learn@Home Sec�on: Roll No.: School:

Preface C ass ap partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. C ass ap presents the Compass s s s sp a o m ms o the new curriculum released in November 2016 by the Council for the Indian School C a am a o s C C Guiding principles: CC m s a s o o as a o s p p so Mathematics teaching:  Develop mathematical thinking and problem-solving skills and apply these skills to formulate and solve problems.  ssa ma ma a o p s a s s o a and for continuous learning in Mathematics and related disciplines.  Recognise and use connections among mathematical ideas and between Mathematics and other disciplines.  Reason logically, communicate mathematically and learn cooperatively and independently. a o s p p s so a s sp C ass ap oo s workbooks and teacher companion books have been designed. The C ass ap team o p a o p s as a o a s mapp so a a am o as o CC mo m Key features of C ass ap Compass series:  Theme-based content that holistically addresses all the learning outcomes sp CC m  oo s a o oo s a s as p oom s a o om o help organise the learning process according to the different levels involved.  Student engagement through simple, age-appropriate content with a p a a o o s ps  Learning is supported through visually appealing images, especially for Grades 1 and 2.  as s soso so  p a o a s p o as p C C m All in all, the Compass Mathematics books aim to develop problem-solving and aso s s as as om a p a ma ma a skills as appropriate to the primary level. – The Authors

Textbook Features I Will Learn About I Think Contains the list of concepts to be covered oss s s in the chapter along with the learning objectives curiosity before introducing the concept I Recall I RUenmdeermsbtearndand Pin-Up-Note Recapitulates the as as Highlights the key points or os p so o elements that form the the concept learnt previously basis of the concept ? Train My Brain I Apply I Explore(H.O.T.S.) Checks for learning to gauge Connects the concept oa s s o the understanding level of the to real-life situations by op a student providing an opportunity a os to apply what the student o mo omp s has learnt Maths Munchies Connect the Dots Drill Time Aims at improving speed of Aims at integrating Revises the concepts with calculation and problem Mathematical concepts pa s o sa solving with interesting facts, with other subjects end of the chapter tips or tricks A Note to Parent a s pa oo classroom learning of their child

Contents 7 Integers 7.1 Introduction to Negative Numbers ............................................................................ 1 8 Fractions C ass a o o a o s ........................................................................................ 14 8.2 Comparison of Fractions .......................................................................................... 20 9 Fraction Operations 9.1 Add and Subtract Fractions .................................................................................... 28 9.2 Multiply and Divide Fractions.................................................................................. 34 10 Money 10.1 Unitary Method in Money ....................................................................................... 46 11 Decimals 11.1 Introduction to Decimals ........................................................................................ 52 11.2 Compare and Order Decimals............................................................................... 61 12 Decimal Operations 12.1 Add and Subtract Decimals ................................................................................... 71 12.2 Multiply Decimals.................................................................................................... 75 13 Percentages 13.1 Introduction to Percentage .................................................................................... 82 14 Measurement 14.1 Conversion of Units of Measurement ..................................................................... 90 14.2 Area and Perimeter................................................................................................. 94 15 Data Handling 15.1 Line Graphs and Pie Charts .................................................................................. 104

Integers7Chapter I Will Learn About a ms ompa ss a m oo s a oo oa s so a s 7.1 Introduction to Negative Numbers I Think oo a s am s aa a o aa s oo am a s a o ao mo m o sa a o ps s ma a o oo oo a a I Recall a aa a oma m a s aa a o a s s ms o m ao so ps a ompa m m 1

s mo om oo m ms as s mo om o o m ms as s s s o p as oo a m s as as os a a s a omp s s a I Remember and Understand a a ssa o as a so o Co om om s a a o s as o oo natural numbers o m ssa om a a amp a so o aa m sao om o o o m s a whole numbers o sma s o ms as sma s a a ms am as mo o o a as s decreases a m a moving o left o mo o o o ms a so o a sa as o as a as a os o a a positive a o ma sa ms s ms am ss sa o numbers negative mo pos as oppos o om aa numbers s mo pos a so o o oa a so o a m o oa am s as s o oa mo s a o spo o Negative numbers Positive numbers 2

os ms a ms a o oma so m sa om sa a ss a integers o os s o m Z so ss o os o aa aa a mo m s o s m o oa m s ss a m o amp a pos m sa a a so o oa a m s a ss a a a sam a as o a a pos sma s s o spo a Predecessor and successor of a given integer as a a om s o s sa p sso o am the integer just before the given integer (that is, to its left) is called its predecessor. ma as a a om s a s s a s sso o am the integer just after the given integer (that is, to its right) is called its successor. m as a p sso o a sa om a a s sso a oa a o o sma s a a s pos ao m sso sso o o sso o sso o Uses of integers o p o oppos s s a pos a a ms oo os s o p s oppos s s as a o forward s ps o o backward s ps o o` ` Integers 3

Loss o ` ` ` Saving o ` ` Expenditure o ` o m above sea level: m p o m below sea level: m C above 0° C C C below 0° C C Example 1: p s oo o a m a Solution: aa m ma s a a as m m a ao o po C s a s om s a m Example 2: oo ss a pos o ` o a sa s a o a ao ` om a sa s a o mo a s ma o s a o op s a s a a p o m o s a Solution: a ` ` m m s Example 3: p sso s a s sso s o oo a 4

Solution: Given Predecessor Successor a integer (Just before the given (Just after the given integer) integer) ? Train My Brain sso o a o p sso a s s s a I Apply Compare and order integers p o s ass s a a o ompa a o o m s ma s a ompa a o oa a o oa s sma a a o oa sa a a pos sa a a a a s s ss a a pos sa a a a a s Co s o o amp s Example 4: ao s ao o o pa s a Solution: a Compa o pos s s ompa oo ms s o ao a pos s a a a a o ao as am am ss so o a sma m am ss o s sma a sma m am s so ao a s Integers 5

Example 5: as o s ao oo a Solution: a Compa pos s s ompa o m so sma s o s a s sma a a pos o as o s am am ss so o a sma m am ss o s sma a sma m o as o s Example 6: s as as os a Solution: a Compa s so so Compa s so so Compa s so so Example 7: mp a s o ma o a s a as oa C sa C sa C os a as Solution: mp a s o m a o o a sa a sa C Ca C sp Compa mp a s a CCC C so sa s a as os Absolute value of an integer aa a pos o o as a o spo a o s a sam s a om s m o s 6

o so o s pos o so os a 4 units 4 units ma o so o sa o so o s a so o sa o a om o o s so os a s absolute value o a so a o a ss s m aa sp o s s p s o m s s a so a o a pos oa a o s pos Note: a so a oa m s a a so a oa m s as a s a as a so a o o amp a so ao s as as ao os ao a so ao a so a as as a s s as ao Example 8: a so a so s a Solution: a so a o a pos oa a sa a s pos o a so a sa a I Explore (H.O.T.S.) Addition and subtraction of integers aa o a oa a o m oa o mo as ma pa s as m oa o o o smo m o amp o mo p a s o oo m as s m Integers 7

ma os a ao m om a o mo as ma p a s o o m as m osa o amp o mo pa s o oo m o as ma aa a s a s am s as o a o a s a o o a positive integer o a as s a opposite as o a o a s a o o a negative integer o a Rules of addition and subtraction Rule 1: o a s a o o o a om a s s sam o amp as s o o oo m Rule 2: o add a positive integer mo as ma p a s o right o s as o a o amp as s o o m Rule 3: o add a negative integer mo as ma pa s o left o s as o a o amp 8

a as s o as s o o oo m Rule 4: o subtract a positive integer mo as ma p a s o left o s as osa o amp as s o o m Rule 5: o subtract a negative integer mo as ma p a s o right o s as osa o amp a as s o o oo m as s o Integers 9

s o so a amp s as o s s Example 9: o s a m a Solution: a om om Example 10: o s am a Solution: a om Train My Brain om 10

Maths Munchies a ma p a a a as o om a ma ma a o o po a ms sm as s a so p s s a pos m s as o s a a m s as s a so a s o op a o s o a m sa o Connect the Dots Science Fun o mp a o a po a a s a o Cs a ma a oa a o ao s a aa p o mo ao s ao ps a po a a a m a mp a s op o C Social Studies Fun o o o a s s o sa o s po ao m s o sa a s po s a o a o sa ao sa Integers 11

Drill Time 7.1 Introduction to Negative Numbers 1) Represent the following on a number line. a 2) Write the following using integers. a a ao ` om a sa s a o pos o ` o a sa s a o a op a aa o ma o s a s ma a a p o m o s a mp a o a p a s C o C 3) Write the predecessors and successors of the following integers. a 4) Write the smaller of the given integers in each of the following pairs. a 5) Write the greatest of the given integers in each of the following. a 6) Write the given integers in the ascending and descending orders. a 7) Write the absolute values of the given integers. a 8) Add the following using a number line. a 9) Subtract the following using a number line. a 12

10) Word problem a mp a s o aao a s a as oa C sa C sa C a as os 11) Write the following using integers. a mp a o sC o C p o a ma ma a s m o o s aa o ma o s a oa oa p o m o s a 12) The following are the temperatures recorded in four places on a particular day of a year. Place Temperature a Co C aa Ca o C o a Co C Ca o C om a as oo so s a mp a s o pa s s s p a as o so a a p a as o so a a am s o p a s as o o mp a s A Note to Parent oo o sa s a pass oo s m o o s pos s a a as o a mo s s as m o o a aa a Integers 13

8Chapter Fractions I Will Learn About p op mp op a m a os a os ompa so o o mo 8.1 Classification of Fractions I Think oo a s a o a sp so s o s mo sa a a sa s s oo a a a amo a p mo sa s om s sa a o ` a o oo oo a o a a s sa s p mo I Recall ass a a o o a o oa o o p sa s so a o a a as a a oa o a a as oo s a oo s ao oo s o a oo s 14

a o app s app s a op s ps I Remember and Understand a a ao a a os s o a ao o p so a o s Proper, Improper and Mixed Fractions Co s 1+ 5 =6 s mo o a o s sa ao s 888 m a o less than its denominator. a o s a a proper fractions. om m s s poss a sm s m ao a a om a o o a o s sa ao 7 5 12 s mo a o sa a improper o amp 8 8 8 s numerator greater than its denominator. fractions. Note: som as s s mo m aoso a o s ma equal to the denominator. a o s sa o a mp op a o o amp 3 4 73 5 a so o 7 7 78 8 7 a a so as a o a s a o s s as 7 12 s mo 8+4   a 8 as 12 a o s as 88 s as a whole   a a proper fraction  4 as 8 4 14 a o s a a mixed fractions.  8  88 mixed fraction s a so a a mixed number. o amp m a o 12 3 12 s whole a 3 proper fraction. 8 8s Example 1: s o p op a o s mp op a o s a m a o s om oo 13 ,15 7 , 11 , 37 , 9 , 65 13 , 143 , 75 3 ,107 27 , 72 , 68 2 , 29 , 50 23 , 69 , 53 18 9 34 6 14 17 98 4 49 59 5 32 35 32 30 Fractions 15

Solution: om a os 13 11 9 29 op a o s 18 34 14 32 mp op a o s 37 143 72 69 53 6 98 59 32 30 a os 15 7 6513 75 3 107 27 68 2 50 23 9 17 4 49 5 35 sa a o s as p op o m a os o o a oo mp op a o s o m a o sa m a o s o mp op a o s Conversion of improper fractions to mixed fractions Co s a amp Example 2: Co 37 o s m a o om 6 Solution: oo mp op a o s o m a o s oo s s ps Steps Solved 143 Solve these 53 98 30 37 72 69 6 59 32 Step 1: )6 37(6 m ao om a o − 36 1 Step 2: oa o ma ma Step 3: o as o ma m as m a o a o omo a so as 37 1 6 6 om a o o s 6 p op a o s s m ao Conversion of mixed fractions to improper fractions Co s a amp Example 3: Co 15 7 o a mp op a o 9 a o s o mp op Solution: o o m a o s oo s s ps 16

Steps Solved 65 13 Solve these 107 27 15 7 17 75 3 49 9 4 Step 1: p o om a o Step 2: m ao o p op a o o p o oa sp Step 3: s m as m ao o m ao mp op a o omo om a o o s o a ss mp op 15 7 s 142 ao 9 9 ? Train My Brain C ass oo o p op mp op a m a os 5 6 5 5 a6 6 I Apply s o s som a amp s a o oa m Example 4: o a a s o a a oo s o s s o oo s a p o as a a o ma a s oo s as a m a o a as a mp op a o Solution: m o oo s o a a s o a a m o oo s a a aa oa a m o a s aa 48 13 48 mp op a o a o 48 13 13 60 mp op 13 Example 5: o as a a o po s s p pa so oa ao p ss a o oa as a Fractions 17

Solution: a o oa p pa 1 s mp op a o ao 2 1 12×2+1 25 2 2 2 Example 6: s oo a o m as as a a a 1o a o m as o p o ma as 10 op Solution: oa m o as ao m a oo a so p 1 10 4× 2500 mo a so p 1 5 10 10000 5 o as a om op I Explore (H.O.T.S.) Co s o o a o s s o oa a s a a os a aa a a oa s a oo p op a os s s som a amp s o a o a s a o o mp op am a os Example 7: o 5 11 12 12 Solution: aa a os oo p s aos + sa 5 + 11 o oo 12 a os a 12 a oo pa 18

a o om 11 o o a o s om 5 12 12 4 12 4 sa a o a a a o o 12 o s mo 5 11 s 4 Example 8: o 12 12 12 13 11 Solution: as a a os oo p s aos o om a o as 1121 13 a 11 m s as o a ps a 12 s pa s o o ao 11 a om a o pa oo o pa s o as pa o o s ao a ps o o 13 s 11 Fractions 19

8.2 Comparison of Fractions I Think oo a a s o p s o a a a as o o a p s a a as p s o a a o sam s a as os a p s o a sam amo o a I Recall ass a a ao a a os ss m ppos a p a s as s o p op a oa as 2 o pa s s 8 a as 1 o pa p op a ss 4 s a p so p a a oao sam s o sa a a o s2a 1a a 8 4 m as 2 1 84 a oo m p so a m a o a mp a so o o amp s s m p so a a m sa a m a aa s a os o amp a oso a a a a o sa o a mp o m ao a m om a o o ao sam a os o amp 1 3 5 2 a so o a a 7 21 35 14 20

I Remember and Understand a a oo a a o s s p s s s som mo amp s o a a os Example 9: o a os ao a os Solution: a 24 33 a os 46 66 a o sam o a os a o om a o m po m o m ao a om sam a 24 p o m ao a 46 sm m s sa a 24×2 48 46×2 92 24×3 72 46×3 138 s 48 a 72 a a os a o 24 92 138 46 33 66 s aa a ommo a o s a o o o 33 o m ao a om a o a os 66 ao a o 33 66 33 ÷ 3 = 11 33 ÷11= 3 o 33 ÷ 33 = 1 66 ÷ 3 22 66 ÷11 6 66 ÷ 33 2 o 11 3a 1 a os a 22 6 2a om a o Example 10: 4 a a o o 10 Solution: a 4 om a o mp ao a a o o 10 om a o a m ao 12 4×3 30 10 × 3 Fractions 21

o 4 mp a a o o 10 om a o om a o a m ao 4×6 24 10×6 60 a a o ompa a os s o a o ompa o mo a a os Example 11: Compa s a os 5 13 a 7 2 4 888 9 9 9 a os Solution: o ompa ompa m aos a Compa m aoso a os o 247 Compa 999 o m aoso a os a ompa 135 Note: 888 m aos s o oo m Example12: Compa s a os o compare unlike 2 11 135 fractions s a2 4 8 339 convert a o s to Solution: a13 5 like fractions 248 a oo o ompa a os s o mo C a o s o o so om a o s C oa s a a oo1 1×4 4 2 2×4 8 a a o o 3 3×2 6 4 4×2 8 s a o sa 4 6 a 5 8 8 8 Compa m aos 61 5 3 s 4 5 82 8 4 8 8 2 11 s 339 C oa 22

a 2 2×3 6 a oo3 3×3 9 a 1 1× 3 3 a oo3 3×3 9 s a o sa 63 1 9 9a 9 Compa m aos as o 1 12 a s o as 1 3 6 933 s9 9 9 ps s o Note: Compa a os o a os ? Train My Brain Compa s a os 123 a12 4 439 864 235 16 16 16 I Apply s s som a s a o s ompa a os 1 2 Example 13: s a a 4 o a app mo a 3 o app Solution: a oo s a aa pa o TraainppMy Brain app s a a 1 mo 4 a o o app s a 2 3 o s a a a pa m s ompa oa os as 12 Step 1: a os a o4a 3 C oa om a o s C oa s o a o sa 1 2 2×4 = 8 4 1×3 = 3 a 3 3×4 12 4×3 12 Compa Step 2: m aoso a a os Fractions 23

8 3 12 12 21 34 Example 14: o s aa a a pa o app a s sa a a a os 1 2 ma sa s 4 o mo a a sa s 6 o s sa a sam amo o sa s a ss amo Solution: o o sa s ss ms ss o C oa s 123 4 a a o s o 4 a 6 a 12 a 12 34 aa 12 12 2 o 1 4 6 o ma sa s a ss amo a I Explore (H.O.T.S.) s s som mo amp s s ompa so o a os o Example 15: Co o a o ps ao a ompa m 2 2 9 7 Solution: 2 pa o 9 2 2 9 ps 2s a aa 7 2 7 o 7s a Ca 2 a9 ps 24

s ompa so o a os a a a som a os as s Co s as o 2 12 s amp s Example 16: a 325 3 a 1 as o 4 6 a os Solution: a a o so Co om a o s as o a os a o 2 1 2 3 a 1 C as om a o a 3 2 5 4 6 3 = 3 ×15 = 45 4 4 ×15 60 2 = 2 × 20 = 40 1 = 1 × 30 = 30 2 = 2 ×12 = 24 3 3 × 20 60 2 2 × 30 60 5 5 ×12 60 a 1 = 1×10 = 10 6 6 ×10 60 Compa m aos 10 24 30 40 45 12 12 3 o 60 60 60 60 60 o s6 5 2 3 4 o as so Example 17: a 2 , 1 1 5 a 3 7 4 8 14 16 Solution: a a o so a os Co om a o s as o a os a o 2 , 1 1 5 a 3 C as 7 4 8 14 16 om a o a 40 112 2 = 2×16 32 , 1 = 1×28 28 , 1 = 1×14 14 5 = 5×8 7 713×6 1=61361××1727 4 4×28 112 8 8×14 112 14 14×8 21 a 112 Compa m aos o 40 32 28 21 14 112 112 112 112 112 os 5 21 3 1 o s 14 7 , 4 16 8 Fractions 25

Maths Munchies Comparing unit fractions ompa a os ao as om a o s sa sma ao sma s om a o s as a 1 1 a 1 1 s as 1 s sma s o s 12 7 10 7 12 Connect the Dots English Fun o am a mo s a o s os o o o am mo s ao o am a o o Social Studies Fun o 3 o a so a sa 97 s 4 s os a o 100 sa a a Drill Time 8.1 Classification of Fractions 1) Convert the following improper fractions to mixed fractions: a 35 121 93 100 115 4 12 12 26 20 2) Convert the following mixed fractions to improper fractions: a 15 6 2 7 125190 40 3 8 3 13 5 26

3) Word Problems a s a pa a sa so sa a sa amo a pa o sa o a s as a m ao 4 so 3 s o m pa s o 6 s o pa 2 m 8.2 Comparison of Fractions 4) Compare these fractions. 5 91 4 23 143 a 16 4 8 21 3 7 555 521 7 42 999 12 15 3 5) Word problems oa o 7 o a oa s om o o 5 o a pa 30 12 ao sp sam amo o m o o a s aa 3 o a o oa aa a sa 1 o asm a o oa 16 4 a a a amo o o oa o o a ss A Note to Parent o so o s mo o som o m a o s o som o so os ao o o o amp ` s o o` Fractions 27

CHAPTER 9 FOrpaecrtaitoinons9Chapter I Will Learn About a as a a m a os o ms sa a o s mp a os a a os o m a os 9.1 Add and Subtract Fractions I Think oo a as a o a oa som o s po o s o o os a ao a os a p s o o po o s a a os oo a o o pa s o a oa o oo oo a a a I Recall a a ao p so a o s sa m ao os m a o s a a s om a o s a a improper ao a o os m a o s ss a s om a o s a a proper a o ao a om a o o a o m a a p op a o s a a mixed a o 28

I Remember and Understand Addition and Subtraction of Unlike Fractions s sa a oa s a oo a os a a o s o som amp s added or subtracted s Example 1: 3 1 72 a o a 15 10 13 39 a o sa ao 22 7 100 10 sa m aos Solution: 31 C oa s a 15 10 3×2 1×3 15×2 10×3 63 30 30 6+3 9 3 C oa s 30 30 10 7 2 21 2 21+ 2 23 Co a s 13 39 39 39 39 39 22 7 22 70 22 + 70 92 23 100 10 100 100 100 100 25 Co a sa Co a s Example 2: o 84 17 5 14 17 a 9 11 30 24 25 50 8 4 88 36 C oa s Solution: a 9 11 99 99 88 36 52 99 99 17 5 68 25 Co a s 30 24 120 120 68 25 43 120 120 Fraction Operations 29

14 17 28 17 Coa s 25 50 50 50 28 17 11 50 50 Addition and Subtraction of Mixed, Improper and Proper Fractions a oa s a o om a o sa sm a o a o a os s sa som amp s sam o Solve this Example 3: 12 1 15 1 2 3 3 2 5 7 43 Steps Solved 23 32 57 Step 1: Co am 3 2 5+3 13 5 5 5 a o s o mp op a o s 2 32 3 7+2 23 7 7 7 Step 2: C aa 23 32 13 23 5 7 5 7 mp op a o s s C oa 7 13 + 5 23 35 91+115 206 35 35 Step 3: Co Co a s m ao a om a o o ao 31 35 o sm a oa mp op a o o s s mp s om Step 4: Co mp op 206 31 35 35 a o oam ao o 23 5 32 7 30

Example 4: a 2 3 om 3 2 57 Steps Solve Solve this 2 3 om 3 2 12 1 om 15 1 57 43 Step 1: Co am 32 3 7 + 2 23 7 77 a o s o mp op a os 2 3 2 5 + 3 13 55 5 Step 2: C 32 23 23 13 as a mp op 7 5 75 a os C oa s 5 23 - 7 13 115 - 91 24 35 35 35 Step 3: C Co a so ao ao o m ao a a om a o o p op a o o s s mp s om Step 4: sa 24 s a p op ao o mp op 35 oam ao o aoo oam ao ao o 32 23 24 7 5 35 ? Train My Brain o oo a 13 + 1 41 21 25 2 1 46 4 8 9 3 Fraction Operations 31

I Apply som a s a o s s a o os a o o a os s so a s amp s Example 5: so s oo po o o o s ps o pap o s ps a pa o s ps s o o a pa a s o o oo Solution: o a m o pa s o ss p som a ao p oo 2 Example 6: sp 9 o a m o pa s o s o s p a o oa 4 oo s p 7 o a oo pa o 24 s ps 9 7 14 36 C oa s 63 63 14 + 36 50 63 63 ao s p a s o oo s 50 9 + 7 = 1+1= 2 63 97 2 - 50 126 - 50 76 1 63 63 63 s aos s a o os a o om a os a 3 s sa a 1s s o ma ss 5 s 4 a a o ma s ma oa ss Solution: oa m o s s o m o s sa 3 5 32

m o s sa 1 oa m o s s a 4 oa 3 1 28 33 112 +165 277 17 5 45 4 20 20 20 m o s s ma 17 20 277 400 - 277 20 1 20 20 C oa s 123 3 20 20 oa a 17 s s3 s sa ma 20 20 Example 7: ao 2m o sa o 1m o Solution: 3 3m 4 sa m s s s as o a a oa o 5 m mo o 3m oa sa o o a 5 sa o s os 2m sa o 3 oa sa s a o 1m 4 2m 1m 3 4 104 65 416 +195 611 11 3 m 4m 12 m 12 m 12 m sa o o 3 11 5m 12 328 611 oa s 5 m 12 m 3936 - 3055 60 m C 881 41 60 m 60 m o sa 41 a as o o s 60 m Fraction Operations 33

I Explore (H.O.T.S.) s s som mo amp s o a o a s a o o m a os Example 8: om s 411 a a 39 2 6 5 Solution: m 4161 39 2 247 197 1235 - 1182 5 6 5 30 53 123 30 30 o 411 s a a 39 2 123 6 5 30 Example 9: om s 22 3 ss a 50 1 Solution: 4 7 o m 50 1 22 3 351 91 1404 - 637 7 4 74 9.2 28 767 27 11 28 28 22 3 s ss a 50 1 27 11 4 7 28 Multiply and Divide Fractions I Think oo a a a o s a a ao o oa a o ma 5 o o oa a 12 o o a oo a a s o o o m o aa o oo oo a a s I Recall aa a o oa m mp m o so s ms m a ao m p ao s mp po a m p a a o ao a o oo 34

Fraction in the simplest terms: a o s sa o s s mp s o m s m ao a om a o o o a a ommo a o o a Reducing or simplifying fractions: aa o s a a as sa m ao a om a o a o ommo a o o a o s mp a o o s o s ms Methods used to reduce a fraction: a o a o so s ms s so C I Remember and Understand Multiply fractions by whole numbers so ao a o oa m ppos a s sa oa os s s so a so s 1 o m o a a po m m 5 as op om a o a o ps a m ao s s o ps s s a op o a sa a 1 o s 3 5 10 a sss 3 s s os s ss o m a a s o s 10 o m o s om a o a o ps a a s o ps m ao s s s s a op a a s s os 1 o as 1 20 5 5 5 3 3 × 20 m a 10 o 10 Example 10: oo 2 m 1 a 5 o am 22 10 o a o am 5 m5 2 2 × 100 200 Solution: a 5 o am m 5 m 5m m 1 o a o am 1 10 10 Fraction Operations 35

1 1000 10 10 Example 11: oo 2 ms 1oa a os a 3oa o 4 120 m Solution: a 2 o a o 22 m 2 × 60 3 3 33 3 a oo 1oa a 1 a 1 24 s os s 4 4 4 aa o 4 p om am s s sam as Example 12: oo a 23 o 15 o 45 32 Solution: a 23 o 23 23 90 45 45 45 2070 45 p ms m ao a sp a so m sa a o sa ao ms m ao a om a o a a ommo a o sa Co ms m so a ommo a o s a o o s o s ms 23 23 a 45 o 45 a Co a so oa C 23 s Co ms 23 2 o 45 451 90 15 o 15 Co a s 32 32 a a s mp m p ao 15 32 1 36

Multiply fractions by fractions p a o o o a o s s s mp aa da oa os a ao ao o a a os o a× d× po o o o m aos o o om a o s om p m ms a po m o mp op a o s a s omp ms m ao a s os ms s sp a so m sa a o sa ao m ao a om a o a a ommo a o a os o o s ms a mp m Co s a amp o sa op a o s oo Example 13: o 23 15 45 46 Solution: om p s s ps Step 1: C m ao a om a o a a ommo a o s s a os s a aa o o a a ommo a o s o a a ommo a o s Step 2: Co m ao a om a o a a ommo a o s Co a s Co a s Step 3: m ao a om a o a a ommo a o s C s 1 23 1 3 45 15 = 1 1 = 1 46 2 3 2 6 o 23 15 1 45 46 6 Fraction Operations 37

Example 14: o a 2 5 7 70 84 45 5 6 35 63 54 60 11 2 9 Solution: 2 5 1 1 1 1=1 a5 6 1 3 13 3 13 12 1 2 12 1 9 19 7 70 35 63 1 84 45 7 5 7 5 = 35 = 7 1 54 60 6 5 6 5 30 6 6 Reciprocal of a fraction o po a o a a o m oa a o a s m ao a om a o mp a ms po a o a m sa a o as p o sa o amp po a o 1 reciprocal o s 20 multiplicative inverse o po a o a a o sa m m o amp 1 po a o 7 s p o a o a p op a o s a mp op a o a as s o o oam ao o amp 37 1 po a o 7 s 3 o 3 p o a o a mp op a o s a p op a o o amp 95 po a o 5 s 9 po a o am a o s a p op a o o amp po a o 3 s8 8 19 Note: po a o s p o a o o s o s as s o os o 38

m s s as a so o a o o mp op a os o s m as 4 , 6 , 9 p o as 111 o a o sa o ms poss o p o as s p o a s o som a o s Example 15: p o aso s a o s 43 a 8 19 11 4 17 5 Solution: o po a o a a o a s m ao a om a o o p o aso a o sa 17 19 11 5 a8 4 3 4 Example 16: m pa s so s a o s a 7 5 33 1 9 3 Solution: o m p a s oa a o as m ao a om a o m pa s so a o sa 1 9 om p a s 3 a5 68 100 Note: as o p o a o m p a s as a om p a ms oo s o mo om p a s m a o s o a am p a ? Train My Brain o oo 14 94 2 14 43 7 21 15 12 a 54 7 Fraction Operations 39

I Apply Divide a number by a fraction so o a m ao maso o ma o so s a ps 1 5m aso o amp maso m oos ma m oo s s sa so a os o som amp s Example 17: a1 3 ps 5 Solution: o 3 a oo s s 1 3 Steps Solved Solve this 1 3 3 5 Step 1: m as a 15 ao 1 Step 2: po a o 13 so po a o 3 s 1 Step 3: p 1 15 3 45 3 11 1 po a o so Step 4: p o o s 45 o s ms 1 o 1 3 Note: o am a a o s om p po a o so Divide a fraction by a number so o a a o a m ssm a o so o a m a ao s sa so o a o s m s o som amp s Example 18: o 1 3 40

Solution: o o o s s ps Steps Solved Solve this 1 3 3 5 67 Step 1: m 1 as a a o Step 2: po a 67 1 o so p o a o 1 s 67 Step 3: p 1 11 1 po a 3 o so 3 67 3 67 Step 4: 11 po o s o s ms 3 67 201 1 1 o3 201 Divide a fraction by another fraction so o a a o a o a o ssm a o so o a m a ao s s a s o som amp s Example 19: o 11 3 21 Solution: o so s ms o o s s ps Steps Solved Solve this 11 3 210 3 21 25 75 1 21 Step 1: po a p o a o 21 s 1 o so 1 1 1 21 Step 2: p 3 21 3 1 po a o so 1 217 Step 3: po 31 s ms o so 1 o3 1 21 Fraction Operations 41

I Explore (H.O.T.S.) s s som a amp s s so o a o s Example 20: a s a app s m o a s o ma p s s Solution: o m op s a as o ms mo as a s ms p oa m o app s s oa p o app 1 1 o os moa s4 po a o 4 o a s o p s o app 3 po a Example 21: a a 5 o a o am o s a o o ma ams o s a s a Solution: oa a 3 os a 5 m o os 33 a o s a a o 5 5 po a o 3 13 3 1000 50g = 3 50 g = 150 5 4 20 os a 20 1 oao as Example 22: 16 so oa 8 s po s 25 a o 25 s o Solution: a ass o ma ass s a s oa a o oa 16 25 ao po 8 a ass 25 s m o ass s 16 8 s 25 s 25 16 8 16 2 25 1 = 2 25 p o a o 25 25 1 81 o ass s a 42

Maths Munchies om oo s mo om a os aa m ao a a pa s a p op a os as a 23 32 Step 1: 5 7 Step 2: a pa s o m a os sC p op a o pa s 31 35 C 3 2 7 3+5 2 21+ 10 o 35 57 35 Step 3: a mp op ao o oam ao Step 4: sm s ms o a s ps a o o 23 32 31 35 57 Connect the Dots Social Studies Fun 1 n s4 s ooa oo oo s 1 o o a so o ao a aa ao o oo English Fun s ap a as s o s 5a o s 26 p ss m o o so a s omo a a o Fraction Operations 43

Drill Time 9.1 Add and Subtract Fractions 1) Add: a 3 5 43 12 1 + 13 2 4 13 14 12 75 10 1 +12 4 26 13 14 33 16 30 30 60 2) Subtract: 14 3 a4 3 30 24 9 11 72 41 12 3 112 84 89 3) Word problems a sa s ` p mo om s sa a o ` a sa s ` p mo om s sa a o ` sa a a oo sa a o a o m aa s m o sa o om a o ma a oo sa o ss 9.2 Multiply and Divide Fractions 4) Multiply fractions by a whole number 12 3 4 a 32 8 20 34 79 5) Multiply fractions by fractions a 22 × 26 4 ×16 3 × 51 13 44 12 24 17 21 7 × 45 5×4 15 49 20 25 44

6) Find the reciprocal of the following: 51 50 a2 2 23 53 1 7) Divide: 42 a 1 2 4 7 11 1 7 49 15 A Note to Parent a m as a o o p o a o s as o s oo ms s as apa a so o mm o mp as s a a a os a a pa s Fraction Operations 45

Money10Chapter I Will Learn About s o op a o s o m s o a a mo 10.1 Unitary Method in Money I Think oo a oa o so o a pa s o o oa s o a pa aa as o o a s os o o oa s Ca o os I Recall a aa a a o ma ma a op a o s s as a os ao m p ao a mo so a a so a a o ma s sa s oo o a op a o s o a` ` `` ` ` ` 46


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