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

I Remember and Understand s m p ao o a o ma s o a m om a oa s s so o o ma a o as o a m om a s a a so s o s ps ao m o s oo Step 1: a o as o a m om ao s s so oo a sam Step 2: s a oa p a o ma ss m p ao so s a amp s o sa am o Example 1: os o as s Solution: os o as s s ` as Step 1: os o as s ` Step 2: os o as ` m oo a oo ` a a o ma s s a os o as s ` Unitary Method. ` o as s os ` Example 2: p s os ` om o s a o p s os Solution: Step 1: os o p s ` os o p ` ` Step 2: o ms os o a o p s Cos o p s` ` o a o p s os s ` Example 3: os o o oo s s ` o ma o oo s a o Solution: o` ` os o o oo s ` os o o oo ` Money 47

amo o oo s a o o ` m o o oo s a ao o oo ` o a amo Cos o a ` o o` o o oo s a ? Train My Brain os a os o ma o s s ` os o ma o s os o aps s ` os o aps os o a s s` os o as I Apply am o a s o ompa o o mo ms Co s s amp s Example 4: p op sp ` oa s oa sa o a s p op sp sam p om o Solution: o sp p op ` o sp p so ` ` m o p op a o o sp p op o sam p ` ` o p op sp ` o a sam p Example 5: os a o oo oso` as ` m Ca Solution: oo os os o oo os ` os o oo os ` ` os o oo os ` ` os a as ` m s o a os o o o o s s` os o a o mo o oo os 48

I Explore (H.O.T.S.) as am o o o as mo o ss amo o m p as s mo o ss p s Example 6: o ao s a a pa o o soaps a o os s ` pa s o o pa o s soaps a o os s ` o a so a s sp s a ss amo Solution: o soaps a o os o soaps ` os o o soap ` `1 1 pa s pa s 10 10 o soaps a o os o soaps ` os o soap ` pa s `9 9 pa s pa s a o sp 100 100 pa s o a as o pa o soaps o a ss amo Example 7: s o p as s a p s os s ` s os s s ap s os s ` s o s ap s s p s Solution: os o p as s a p s ` ` 6.10 ` 8.10 os o p as s a p ` ) )8 ` 48.80 6 ` 48.60 os o s s ap s` 48 48 os o s s ap ` 86 `` s os 86 s ap s s p s 00 00 00 Money 49

Example 8: os o o a as s ` 32.50 Solution: as os o o a as )17 552.50 os o o a as ` os o o a as ` 51 os o o ` 42 a as ` 34 o o ` 85 a as os ` 85 00 00 00 Maths Munchies so ` o o` s s om a o as p s a a` ` a o os ao oo a mo s` a` os mo s o so ` a` a mo s ` as o os ` a` Connect the Dots Social Studies Fun po s s p a a sa s aa s as sa om s a as o s C sa o o as o o Science Fun a pap s a ma o o o a o o a so pap ao a s oo a o pap 50

Drill Time 10.1 Unitary Method in Money Word problems os o app s s ` a s os o app s pa s o s pp s os ` om o s a o pa o s pp s os os o oo s s ` o ma oo s a o o` a ma o s a a pa o a ams a o os s ` a a o pa s` pa s o a ma os a ams a o so a sp s a ss amo os o o po a o s s ` a s os o o po a o s A Note to Parent a m o s a mpo a s s a oa po o mo o pa s am o Money 51

11Chapter Decimals I Will Learn About o so o a o s o ma s a sa p oa p s ao o ma s pa a aa pa o ms o ma s p so ma a o s ompa a o ma m s 11.1 Introduction to Decimals I Think oo a a s pa pa o mp oo a m sa a m am s p o spo s a o mp a m m as m m o a p o pap as s o oo a o m s a a po as o mo o o o a po m a s I Recall a a a a ao a ao a ap s s a o p s so o o p o ms a a a oo3 as m a o 4 52

o a a o so 7 10 a a oo 3 as om a o 10 as m a o a a o o 4 5 a a o o 21 as om a o 25 I Remember and Understand a aa a ao a os ma s a a o s s om a o s ma s p ss o om a o a mo a o Conversion of fractions to decimals oo a a oo po o o as 3 s a p ss 10 s a o as as om a o s m as ma s omo a ao ma o o pa a p ss as 7 a as 10 ma o m m s s as a so o a a decimal numbers or simply decimals. as o mp op a o s a so o as om a o s o a o pa m a o as ma m om a o sa o po a po om s pa o amp 13 1 3 10 10 Co s o o amp Example 1: Co o o p op a o s o ma o ms Solution: 73 9 23 a 4 10 100 100 1000 a o s as ma s o o s s ps o Step 1: m ao Step 2: Co m o s om a o m o s a mo a mo s m ao p so o m o ma oo s ao m os a ma po o Decimals 53

Step 3: aa o o ma po a Example 2: p ss s mp op a m a o s as ma s Solution: 43 a 18 2 10 26 1 4 9 10 10 10 a o s as o ma s o o s s ps Step 1: Co mp op a o o m a o s Step 2: a pa as s Step 3: a a po o s Step 4: ma o m o p op a o pa o 43 a 18 2 10 10 26 1 49 a o sa 10 10 Note: s m o s s om a o s o a so o Shortcut method: o a os om a o s o as ma s o o s s ps Step 1: m ao Step 2: o m o os om a o Step 3: a ma po a sam m o s om as Note: o a as a pa o m o os o amp ma omo 232 = 2.32 100 ma a o a p op a o p a ma m Pictorial representation a ps ma s p o a as o o s 2 tenths 2 0.2 10 5 tenths 5 0.5 10 54

8 tenths 8 0.8 10 10 tenths 10 1 10 a s o pa s o sam s a o a pa s s 1 s a as one-tenth. ma o m o a a pa s 10 ms ma pa a a as s pa a s a m s s as as o po o o po o o po a so o o a s oa pa o om a o a omo a 1 s pa a ma po m pa s 10 sa tenths place s 1 s 9 s 33 100 100 100 s s 57 100 100 100 s o pa a ma po m s a hundredths place m ma pa a ma po sa thousandths place Decimals 55

Equivalent decimals ss m sa ma po a sam a s ma s a aa ma s ma s a sa a oso o am a po o s o a ao m Example 3: oa ma s o oo ms a Solution: oa ma s o m s a a Place value chart for decimals m a o pa a ao m s a apa a ao ma s oo sa pa a ao m s Thousands Hundreds Tens Ones 1 ms ma po as mo om o a oa om s 10 pa a o om s o a as a sa 56

s a as o po o m a mo o p a o om o o sa 1 o o 1a a pa 100 as o o s 1000 ao a Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths point 1 1 1396 10 100 1000 m s a as o o sa o s po o po p a m sa decimal point. s s mo m s s a ma po s a decimal system. Note: a a a mas Expansion of decimal numbers s pa a a a pa ma m s ss a amp s Example 4: pa o o m s a Solution: o pa ma m s s m pa aa Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths point 1 11 1000 100 10 1 ( . ) 10 100 1000 a Expansions: 11 1 a 10 100 1000 Decimals 57

11 10 100 1 1 100 1000 Conversion of decimals to fractions oo a ma o a a o o o s s ps Step 1: mo ma Step 2: Co mo ma p a s a s m o pa s o o ma m Step 3: om a o oo as ma os as mo s a ma po Example 5: s ma s as a o s Solution: a 23 13107 a 10 1000 10543 52 100 100 Alternate method: ma s a a a pa a as m a os o amp a so o s 2 3 ; 10 a o sa s 13 107 ; 1000 a s 105 43 a 100 ? Train My Brain o oo a pa as a a o ma p ss 37 as a 100 58

I Apply ss a a amp s o ma s Example 6: amo o mo aa sa a aa ma a ` a ` oa ` a ` ao amo s o s Solution: o ma s o s s pa a pa s s a Amount In words ` ` p so o a pa s ` ps o ` ps a pa s p ss a s pa s sa pa s Example 7: s ams o som a a Name Weight (in grams) a a s o o ams o am Solution: oo ams o o ams Co a o oa o s o ams a as o o s Decimals 59

Name Weight (in grams) Weight (in kilograms) a a o am Example 8: p ss a o 1 as a ma 5 Solution: ao ao oa a ao a as om a o mp m ao a om a o s 1× 2 2 5×2 10 Co a a o o a ma 2 10 I Explore (H.O.T.S.) Example 9: ma s a p s s a pa a 60

Solution: a sa pa p s sa o o ma a ps s s ma s a ms ma s 10 + 43 = 143 = 1 43 10 100 100 100 100 + 100 + 29 = 212021209090 100 100 100 Example 10: s pa s a a Solution: a as s s as s s as s o s as s s 11.2 Compare and Order Decimals I Think oo a o p as a a o mo o as o as a` o p a ss o ` ps o a s as mo a sa o o ps Ca o ss p Decimals 61

I Recall a a oo a o s o ma s s so oo a o s o ma s 56 a2 100 71 81 321 1000 100 100 1000 I Remember and Understand s a ao a ma s ma s a ma s Decimal places: s ma pa a a decimal places. o amp as o ma p a s as o o ma p a Equivalent decimals: ma m s a aa a a equivalent decimals. o amp aa ma s Like decimals: ma m s a a sam m o ma p a s a a like decimals. o amp aa aa ma s Unlike decimals: ma m s a a mo ma p a s a a unlike decimals. o amp Adding a mo a s o right side o aa ma s ma po o s o ao Example 11 s a sa a ma s Unlike decimals a a o o ma s adding zeros a a a Solution a a o ompa o ma s o o s s ps 62

Step 1 Co ma m s o ma s Step 2: Compa a pa s ma a a pa s Step 3 a s s a pa s a sam a o ompa a o ma a ompa spa s s a so s s s a a so sam 69.20 69.02 6=6 9=9 o Note: a s s a ompa om a s p a a a pa ma s ma m s a ma s Step 1 Co ma s o pa s o Step 2: Compa a pa s Step 3: Compa ss o a Step 1: Co ma s o Step 2: Compa a pa s Step 3: Compa ss o Example 12: s sma o a o aa a a Decimals 63

Solution: a a Co ma s o ma s Compa a pa s o s sma a ma s a ma s Compa a pa s Compa ss ss o sa s s o a ma s a ma s Compa a pa s Compa ss ss o sa s s o s sma Compa ma m s ps s a a m as a s o os ss a amp s Example 13: a oo ma m s as a Solution: a p ss ma s as ma s a o as o s 64

p ss ma s as ma s a o as os p ss ma s as ma s a o as os Example 14: a s ma m s s o a Solution: a p ss ma s as ma s o s os p ss ma s as ma s o s os a p ss ma s as ma s o s os Decimals 65

? Train My Brain Compa s ma s aa a a I Apply s o s a a amp s o ompa so o ma s Example 15: am sa s ` a sa s ` o sa s mo mo Solution: oo o sa s mo mo ao ma s a o` a` 361.80 351.90 o am sa s mo mo Example 16: as o ma s s a ma s a Solution: a oa ma s s s s so ma m m ma s s a ma s p ss ma s as ma s s a s o o as m as o ma m m ma s a ma s 66

Example 17: a o o a m os om s a o s a mo s a Solution: oo a m o o so a mo 12.352 12.365 o oo os o s o a mo s a a s I Explore (H.O.T.S.) ss o a amp s o ompa a o ma s Example 18: a s mm omp o a omp o s o o s mm s aa sm oo a s s s a s om omp o m ms as s mm omp sa o Solution: a m s as o os ma s o ma as s mm m s ss a s oo omp o Example 19: s s a pa pa a a m so s m m m aa m ma m oo a Solution: a s o s as o s oo s sa as m s a ms os o omp Decimals 67

Maths Munchies Faster method to convert a fraction to decimal 1 Co s s amp Co 5 os ma o m Step 1: p m ao a om a o o ao am o as om a o p m ao a om a o so a Step 2: a o o m as p s p o s s 1 2 Step 3: s 5 10 o ma o m ma o m o 1 5 Connect the Dots Social Studies Fun a a s os m sa s o s o omp a o a o o ma as o a a m a s as o s English Fun o o as so o a os a oo a o so a ma m o o so a s p ss om 68

Drill Time 11.1 Introduction to Decimals 1) Write the following numbers in the decimal place value chart. a 2) Write the expanded forms of the given decimals and then write them in words. a 3) Convert the given unlike decimals into like decimals. a 4) Convert the following decimals into fractions: a 5) Convert the following fractions into decimals: a2 23 45 73 834 10 100 1000 10 100 6) Write the following decimals in words: om m a 7) Word problems a m as s o som o s a a o a a po s m oa a m sa o m o apa m s m as s o s m oa oo pa s oa a pa a ma ao a o om Decimals 69

11.2 Compare and Order Decimals 8) Compare the decimals aa a aa a 9) Arrange the decimals in ascending and descending orders. a A Note to Parent o a s opp a ma m ma ms as m o ma m s as a o s a os a s m o a oo p a o ma s 70

12Chapter ODpeecrimatailons I Will Learn About a oa s a o ma a os m p ao o ma a o s a m p ao o ma m s oa ma m s 12.1 Add and Subtract Decimals I Think oo a oa am pa o o p as som ams sa o oa o o` a ao` a o` a` o s op p a oa a oa po s op p a ps as a o a ma s s a oo o oo o a os o ams a oo a o os om a I Recall oa s a oo ma m s a s m a o a o s a m s sa o so o ma s o ma s 71

Co ma s o ma s a I Remember and Understand oa s a oo ma m s o sa s p a s s m a o a o ma s s pa ma m s s a s sam p a s a a o oo Note: ma po s o m sm s ao o adding or subtracting oo ma s o ss a amp s unlike decimals o like Example 1: a s mo a decimals a om Solution: a) 1 / / // // + 0 1 1 –1 99 oa 9 1 Example 2: Solution: a) 1 1 1 11 9 / + 9 1 0 1 1/ 1/ 9/ 0/ 1 0 – 0 9 o ? Train My Brain a 72

I Apply ss a a amp s o a oa s a oo ma s Example 3: o o o oma o s s o o ma oma o p as o oma o s o Solution: a o oma o s o a o oma o s s o oma o p a o oma o s o o o oma o s a o Example 4: o p as a s o` a pa o o s s o ` aa pa o s o s o ` o a mo sp o Solution: amo sp o o as ` amo sp o a pa o o s s ` amo sp o a pa o s o s ` o a amo sp o` ` ` ` o o sp a o a o ` Example 5: o m so as o Solution: ms o 11 Example 6: a 1/ / // o so as // o 9 n s oopa o so m o m s so m o ma pa a ma Solution: a om o s oopa s a o m s o ma pa s a o m ma s s o s o m s ma Decimal Operations 73

Example 7: a a s mo o o as a m o o o a pa o s m ss a a os s sa a ap o o a a sa a as oo Solution: oo o as m o o o a pa o o s s m oa o m o mm o s mm o as s o m oo a a sa m I Explore (H.O.T.S.) ss a mo amp s o a o a s a o o ma s Example 8: a Solution: a s mo a om s m o Step 1: so a Step 2: + 10 00 1 1 0 a + 1 Step 3: a sm s p om sm s p 11 / 1/ 0 1 Example 9: oo a sa a o a o s op os o o as ` ao o m mo a s so o` oo a 74

Solution: os o o` 7 mo s so o ` // / 9 90 o a oo a a ` `` o oo a a ` 12.2 Multiply Decimals I Think oo a o s p so o s o ` a aa o a os a pa amo s op p os o o a os o oo o o o I Recall a aa a m p ao o m s a s oo sa sam H TO Th H T O H TO ×1 ×1 1 × I Remember and Understand p ao o ma s s s m a o m p a o o m s amp s Multiply decimals by 1-digit and 2-digit numbers s sa m p a o o ma s o a Decimal Operations 75

Example 10: o a Solution: a m s oo s s ps ma po Step 1: om p m s as s a o os p T Th Th H T O 11 Step 2: 1 9 ma p a s mm o Step 3: o so Co m ma p a s mo m Co om s po as m o ma p a s pa ma po os T Th Th H T O 11 1 11 1 1 + 0 90 os Multiply decimals by 10,100 and 1000 Example 11: o a Solution: o m p a ma m a o o s s ps as ma s as m o Step 1: ma m as s Step 2: ma po o os m p 76

o a ma po ss o o as m p s as o o o s as m p s ma po ss o as o os ma po s s o s as m p s as os Multiply a decimal number by another decimal number p ao oa ma m ao ma m s s m a o a m p ao oa ma m am s sa s o amp Example 12: o Solution: o ma m s a Step1: mp p m s as sa o os a count o a m o s ma po 1 a ma po o 1 m s a sn multiply o ma m s as s a a p a 11 ma po po after 9 ‘n’ digits om +1 0 Step 2: Co mo ma p a s o m pa a mp a a m mo ma p a s so mo ma p a s so oa m o ma p a s Step 3: Co as ma s po om as o a m o ma p a s pa ma po os om m s mo s p o s ss a s m o mo os o ma p a s m pa a mp s as s p a o ma mm a o ma po po s a m mp pa s s a o s mo ma p a s m pa a Decimal Operations 77

? Train My Brain o a I Apply s s a a amp s s m p ao o ma ms ` a Example 13: a a o o a a as a o os amo o s a a a o pa a o Solution: os o o a a as ` os o o a a as ` ` o a a as o pa a o a o ` Example 14: oa a o as os as Solution: oo a a os as o as I Explore (H.O.T.S.) s so a mo amp s o m p a o o ma m s Example 15: m ss m s a Solution: a 78

Example 16: oopa o a so` a a oo a o a so `a o pa ss o a sa om Solution: os o a a oopa o ` os o a s ` ` os o a a oo a o ` os o a s ` ` s` ` oopa pa ss o as amo a oopa pa ss ` ` ` o oopa pa ` ss a oo a o as Maths Munchies s ma o s a s m oo po o o Rounding ma m so amp o off o oo o ao Connect the Dots Social Studies Fun s a ma m as m s s as o mo a s po a as s a a so o a o s app o ma a s ss aa ma s o amp oo om s Decimal Operations 79

Science Fun ma o s os so m o so sa o Drill Time 12.1 Add and Subtract Decimals 1) Add: aa a a a 2) Subtract: a 3) Word problems a o m so as o s a ao so a s o a o as om a o a 12.2 Multiply Decimals 4) Multiply the following: a 80

5) Word problems a a a so a a o s` a a so ao s so a o s mp o o p o a s s o ma as p o os osm ao o A Note to Parent so oo so oo ma p a s o a mm s sa aa o o am o a as a o s a ompa s m as o Decimal Operations 81

13Chapter Percentages 25% 20% I Will Learn About Off Off .50 400.50 2250.50 aos p p as a ma s a a o s p oa p s ao op 13.1 Introduction to Percentage I Think oo a a mo o a s opp ma s sa a a as s o a as mo s ao s oo o as s I Recall a a a a o oo a ma oa a o oo ma s as a o s sa op a 82

I Remember and Understand s oo a os oo a ao o a4 72 82 100 100 14 a p a multiply the 100 100 fraction by 100% p ss oo ap a oa s a os a as a o divide p a om a o a os a by 100 and write the number as p a without the % symbol. Convert fraction into percentage s o s a amp Example 1: Co oo a o s op as Solution: a 76 34 100 43 5 3 100 50 10 5 S.No. Fraction Conversion Percent Read as a sp 76 76 100 100 34 34 op 100 100 sp p 43 43 p 50 50 55 10 10 33 55 Convert percentage into fraction s o s a amp Example 2: Co oo p a s o a os a Percentages 83

Solution: S.No. Percent Fraction a 73 100 1 100 6.5 = 65 100 1000 10 100 18.6 = 186 100 1000 Pictorial representation oo a oo s a o ss o pa s o o p oa ps s pa s a p as s sa ao o a os po s amp Circle Fraction Percentage a a o o a pa s a pa s o 1 4 s 3 4 pa s o o oa a 2 pa s a o o 5 ao pa s o a os 3 ma 1 5 ps a 3 sp 4 4 a pa s o a o p pa s a o o a pa s s pa s a o o p a pa s a o o oa o a os p s m a 2 a 3 sp 55 84

Circle Fraction Percentage a o pa s a pa s o 2 s m 10 a o o a pa s pa s a o o 8 a pa s a o o 10 oa o a os p s a 2 a 8 sp 10 10 Convert percentage into decimal oo ap a o a ma m op sm o a p a a ma po a o s om s s o s a amp Example 3: Co o ma s a Solution: S.No. Percent Decimal a ? Train My Brain s oo a Co 81 o p a 100 Co o a o Co o ma Percentages 85

I Apply s o s som a amp s o so o ma s a p a sa s Example 4: a ma o s a app s a as ap o s as a ma o s a app s Solution: oa m o s Example 5: a o o ma o s 40 100 a o ma o s 40 100 a o o app s 60 100 a o app s 60 100 as 9 a ma s a 46 10 50 s a p om Solution: a ma s s o s o o ma s a s o so o ma s o a o ompa o ao p a o ss o s os s o ompa m 9 as a p 9 10 a 10 46 as a p a 46 50 50 o a p om I Explore (H.O.T.S.) s so a mo amp s o p as Example 6: o a ass o s ss s o s mm ap o s s o o o s mm Solution: oa m o s s 86

m os s o o s mm m os s o o o o s mm a o os s o o o o s mm os 7 35 1 s o o o o s mm 5 7 35 Example 7: a a as ` sp o p oa ` o oo o m s p o o a amo Solution: a a s om ` o om sp o p o ` 20 mo sp o p o 100 mo sp o oo ` o a amo sp ` ` ` mo a a ` ` ` o amo aa ` 400 800 o o o a amo s Maths Munchies oo p a oa a o a om a o s mp o m ao a om a o om a o s mp o m ao a om a o om a o s mp o m ao a om a o Percentages 87

Connect the Dots English Fun op a om s om ap m maso Science Fun ooa ao a a as a s a o ssa o o o a a s ma p o a Drill Time 13.1 Introduction to Percentage 1) Convert these fractions into percentages: a 21 67 20 83 32 50 100 50 150 100 2) Convert these percentages into fractions: a 3) Identify the percentages of the green coloured parts in the following circles. a 88

4) Complete the table. Percent S.No Decimal Fraction a 8 10 18 100 5) Word problems aa o sa os a o ap o os os ap o oa a a o po ao a oo o s A Note to Parent so oo s p ao so a so o pa a oo s o a o pa a oo ao a sa p Percentages 89

14Chapter Measurement I Will Learn About the relation between different units of length, weight and capacity. converting larger units to smaller units and vice versa. applying the four operations in solving problems involving length, weight and capacity. computing the area and perimeter of simple geometrical shapes. 14.1 Conversion of Units of Measurement I Think Pooja uses 17.5 cm of wool to make a friendship bracelet. o a oo a o o m oo s o make 3 such friendship bracelets? I Recall We know the standard units of length are cm, m and km. The standard units of weight am a ma sa a s o apa a m a We can convert one unit of measurement into another using the relation between them, i.e., 1 m = 100 cm 1 cm = 10 mm 1 g = 1000 mg m 1 km = 1000 m 1 m = 1000 mm 1 kg = 1000 g To convert measures from a larger unit to a smaller unit, we multiply. To convert measures from a smaller unit to a larger unit, we divide. 90

Let us solve the following to recall the concept. a Co o Co m om m o ma m Co o a Co I Remember and Understand Let us understand the conversions of units through a few examples. Example 1: Convert the following: m m om mo a mo m o mm oa Solution: Solved Solve these 3640 g into kg a) 1800 mg into g o 1 g = 1000 mg o Therefore, 1800 mg = 1800 g = 1.800 g. 1000 b) 4 km 460 m into km 1 km = 1000 m Therefore, 460 m = 460 km = 0.46 km. 1000 4 km 460 m = 4 km + 0.46 km = 4.46 km mo m Therefore, m 70 1000 m d) 82.3 m into mm o m o ma m 1 m = 1000 mm Therefore, 82.3 m = 82.3 × 1000 mm = 82300 mm o a 1 kg = 1000 g o Measurement 91

Example 2: Compare the given measures using <, > or =. One has been done for you. a m For comparing m m m m m two different units of measurement, s convert them into the same ? Train My Brain unit. Answer the following: a Co oa Co m o Co m m o m I Apply We can apply different operations on length, weight or volume just as we do with numbers. Example 3: Solve the following: a) Add 42.628 g and 67.453 g. a m om m c) Multiply 254 m by 14 and covert into km. m ao o mm Solution: Solved Solve these a) Add 42.628 g + 67.453 g a 11 1 4 2.628 + 6 7.453 1 1 0.081 Therefore, 42.628 g + 67.453 g = 110.081 g. 92

Solved Solve these m mm a m om Multiply 41.8 kg by 26. 4 1/0 13 8 5/ . /0 3/ 3 Divide 208 cm by 4. –62 . 142 22 .8 1 Therefore, mm m c) 254 m × 14 21 2 54 × 14 1 0 16 2 5 40 3 5 56 Therefore, 254 m × 14 = 3556 m 1 km = 1000 m Therefore, 3556 m = 3556 km = 3.556 km 1000 m 2043 )3 6129 − 6↓ 01 − 00 012 − 12 09 − 09 00 om m 1 cm = 10 mm Therefore, 2043 × 10 = 20430 mm Measurement 93

I Explore (H.O.T.S.) Let us see a few real-life examples of operations on the units of measurement. Example 4: a s s o mo o a om o does she buy in a year? Solution: a oo o a s mo Number of months in a year = 12 a oo o as a a o as s o aa Example 5: Lohit has a piece of wood of length 117 m. He wants to cut it into 3 pieces of the same length. How long would each piece be in centimetres? Solution: Length of the piece of wood that Lohit has = 117 m Number of equal pieces Lohit wants to cut the wood into = 3 o a p o oo m m m o a p o oo o mo 14.2 Area and Perimeter I Think Pooja wanted to cut some handkerchiefs of different shapes from a piece of cloth. She also wanted to attach lace to their edges on all sides. But she did not know how much cloth she needed. She also wanted to know what length of lace is required. o oo sa o oa length of the lace needed for the same? I Recall a ap m s oo o a s ap o p m oa rectangle or square, we add the lengths of all its four sides. The units of perimeter of a shape is the same as the units of the lengths of its sides. 94

Area of a shape is the amount of surface or region covered by it. The area of a shape is expressed in square units (the unit of length of the side of the shape). ao a a a ss Area of a square = side × side = s × s sq. units Let us solve the following to recall the concept. Find the perimeter and area of each of the given shapes. a) 5 cm b) 8 cm 4 cm c) 5 cm 5 cm 7 cm I Remember and Understand We know that the perimeter is the length of the outline of a shape. We can also calculate it for shapes other than a square and a rectangle. Let us see a few examples. Example 6: Find the perimeter of each of the given shapes. 5 cm 6 cm a) 4.5 cm b) 3 cm 3 cm 2 cm 5.5 cm 3 cm 3 cm 3 cm 6 cm Solution: a) Perimeter = Sum of all the sides = (5 + 5.5 + 3 + 2 + 4.5) cm = 20 cm b) Perimeter = Sum of all the sides = (6 + 3 + 3 + 6 + 3 + 3) cm = 24 cm Example 7: p m a a ao a o s so each square is 1 cm. Measurement 95

a) b) c) Solution: a m o m = 24 cm Side of each square = 1 cm So, its area = 1 × 1 sq. cm = 1 sq. cm. The number of squares coloured = 16 o a ao ss m mo m = 22 cm The number of squares coloured = 26 The area of each square of side 1 cm = 1 sq. cm. o a ao ss m mo = (6 + 5 + 6 + 1 + 3 + 1 + 2 + 1 + 3 + 1 + 4 + 1) cm = 34 cm The number of squares coloured = 22 The area of each square of side 1 cm = 1 sq. cm. o a ao ss m Area of a triangle s a s om s s a o ao a a o as a divides it into two equal triangles. Thus, the surface or region covered by the triangle formed 1 cm = 1 of the total region covered by the rectangle or square. 1 cm 2 Therefore, the area of a triangle formed from a rectangle 1 = 2 × the area of the rectangle 96