1. Pick the right fraction represented by the shaded part of each shape. First one is done as an example:12 56 16 16 65 12 13 46 13 12 14 16 12 45 12 56 36 38 36 57 14 34 34 17 15 16 15 14 13 68 14 35 21 43 15 ActivityAcme Mathematics 5 101
16 35 33 54 23 34 13 46 25 45 Look at the number line Write the fractionShade the rectangle to show the fraction0 10 10 10 10 1Activity102 Acme Mathematics 5
a. Proper fraction Look at the given figure:One part is shaded.There are 3 parts.It is represented by 13.Similarly14 is shaded 12 is shaded 34 is shadedIt is numeratorIt is denominator34Part of a whole is called the fraction.The whole is shaded. Whole is denoted by 1.12 (half) is shaded12, 13, 34, and 57 are proper fraction, here numerators are less than denominators.b. Mixed fraction (mixed number)Consider the improper fractions 323 half is shaded. 12121222 = 1 122 half is whole.22 = 1 (whole)3 half = 1 (whole) and 12 = 1 and 12 = 112I know 12, 14, 34 all are fractions.12 is called half+ + = +Acme Mathematics 5 103
In 32 the numerator is greater than denominator. 32 in the number line:o 12223242112 is called mixed number. 1 is whole number. 12 is fraction.c. Conversion of mixed fraction into improper fractionConsider the following example.Example 1 : Convert 3 12 into an improper fraction.Solution : Here,7 half is shaded. 3 12 is shaded 72 is shadedHence, 3 12 = 72Second method3 12 = 3 + 12= 31 + 12= 3 × 21 × 2 + 12= 62 + 12= 6 + 12 = 72Hence, 3 12 = 72In short,3 12 = 3 × 2 + 12= 6 + 12 = 72d. Conversion of an improper fraction into mixed numberConsider the following example.Example 2 : Convert 52 into mixed number.3 12 contains 3 whole and 12 fractionIt is denominator of 12.Denominator is common (same)Denominator of 12.Whole number104 Acme Mathematics 5
Solution : Here, 52 an improper fraction.5 half is shaded1 whole 1 whole2 whole and 12Hence, 52 = 2 12Short cut method:In 52, Divide 5 by 2Now. 2) 5 (2 – 4 1Hence, 52 = 2 12remainderdivisorquotientIt is wholeIt is part of 2.Classwork1. Match the followings:22 143 342 12Acme Mathematics 5 105
2. Colour the followings.(a) 312(b) 52(c) 2Exercise 2.101. (a) List the proper fractions from the given fractions:12, 34, 128 , 1520, 32,53, 911, 76, 97, 17(b) Write the proper fraction, whose denomineter is the same as the given fractions.(i) 45 (ii) 37 (iii) 69 (iv) 232. (a) List the improper fractions from the given fractions:32, 13, 1110, 85, 83, 27, 34, 125(b) Write the improper fraction, whose denomineter is the same as the given fractions.(i) 54 (ii) 73 (iii) 96 (iv) 323. List the mixed number (fractions) from the given fractions:35, 234, 110, 314, 2030, 313, 1015, 179, 257, 5164. Convert the given mixed fraction into improper fraction:(a) 314 (b) 234 (c) 712 (d) 834Remember!Numerator and denominator106 Acme Mathematics 5
(e) 179 (f) 515 (g) 2 510 (h) 7135. Convert the given improper fraction into mixed fraction:(a) 83 (b) 104 (c) 32 (d) 74(e) 85 (f) 209 (g) 307 (h) 2566. Write the given fraction into increasing order.(a) 37 , 77 , 47 , 57 (b) 910 , 710 , 1010 , 2107. Write the given fraction into decreasing order:(a) 38 , 88 , 48 , 58 (b) 911 , 711 , 1011 , 11118. There are 4 red marbles, 6 blue marbles nad 11 yellow marbles in the box.(a) How many marbles are there in a box?(b) Write the number of red marbles in fraction.(c) Write blue and yellow marbles in fraction.(d) Compare the fractions.9. Draw a picture to represent the following and colour it.(a) 54 (b) 76 (c) 2 1310. Draw a number line to represent the following fractions.(a) 94 (b) 56 (c) 10511. There are 3 circles. Study the circles.(a) Write the fraction of the shaded parts?(b) Write the fraction of the unshaded parts?(c) Convert the fraction in (a) into improper fraction.Acme Mathematics 5 107
3.2 Like and Unlike FractionsStudy the given fractions carefully. 14243414, 24, 34 are the parts of the same whole. Denominator of the fractions 14, 24 and 34 are same.14, 24 and 34 are like fractions. 13, 24 and 35 are unlike fractions.Denominator of 13, 24 and 35 are not same.Exercise 2.111. Choose the like fractions from the given fractions.19342739110512297967892. Choose the unlike fractions from the given fractions.231748910141225673. Fill in the blanks 'like fraction' or 'unlike fractions'.(a) 14 and 34 .................... (b) 79 and 610 ....................(c) 37 and 27 .................... (d) 58 and 310 ....................132335108 Acme Mathematics 5
3.3 Addition and Subtraction of Like Fractions(a) AdditionLook at the following carefully.+13+ 13 = 2315+ 25+ 15 = 45Way of additionExample 1 : Add: 13 + 13 Solution : Here, 13 + 13 = 1 + 13= 23Addition of Like FractionsLook at the given examples carefully.Solved ExampleExample 1 : Add : 16 + 36Solution : Here, 16 + 36= 1 + 36= 46If the denominators are the same, we simply add the numerators.16 and 36 are like fractions.+ = 163646Example 1 : Add: 15 + 25 + 15Solution : Here, 15 + 25 + 15= 1 + 2 + 15= 452Acme Mathematics 5 109
+ =1. Add the fraction by colouring.+ =+ = + =+ = + =Example 2 : Simplify:213 + 313 + 23Solution : Here, 213 + 313 + 23= 2 × 3 + 13 + 3 × 3 + 13 + 23= 6 + 13 + 9 + 13 + 23= 73 + 103 + 23= 7 + 10 + 23= 17 + 23= 193= 6 13RemainderRough 3) 19 (6 – 181Quotient DivisorClasswork110 Acme Mathematics 5
+ =+ =+ = + =+ =+ = + =+ =+ = + =12 +14 +24 +12 =14 =14 =2. Complete the addition and colour.244Acme Mathematics 5 111
13 +23 +35 +15 +13 =13 =15 =15 =33551. Colour the sum of the shaded portion and write the fraction representation for each.___ ___ ___ ___ ___ ___+ ++ += == =___ ___ ___ ___ ___ ___+ ++ += == =Exercise 2.12112 Acme Mathematics 5
2. Sum the fractions and colour the sum.___ ___ ___ ___ ___ ___+ ++ += == =___ ___ ___ ___ ___ ___+ ++ += == =69 + 19 = 416 + 1216 = 312 + 212 = 112 + 212 = 624 + 1224 = 720 + 920 = 3. Add the followings :(a) 711 + 211 = 911 (b) 37 + 27 = _____ (c) 29 + 39 = _____(d) 67 + 27 = _____ (e) 1920 + 1920 = _____ (f) 2425 + 2025 = _____(g) 14 + 14 = _____ (h) 5100 + 9100 = _____ (i) 78 + 58 = _____(j) 1112 + 1112 = _____ (k) 26 + 56 = _____ (l) 12 + 12 = _____(m) 215 + 315 = _____ (n) 614 + 414 = _____ (o) 1113 + 1213 = _____Acme Mathematics 5 113
(p) 35 + 45 = _____ (q) 711 + 511 = _____ (r) 13 + 13 = _____(s) 1316 + 216 = _____ (t) 810 + 510 = _____ (u) 1550 + 650 = _____4. Simplify the following. (a) 28 + 18 + 48 (b) 110 + 310 + 210 (c) 312 + 212 + 512(d) 113 + 713 + 213 (e) 411 + 511 + 211 (f) 1115 + 115 + 215(g) 2025 + 325 + 125 (h) 78 + 28 + 18 (i) 23 + 13 + 135. Find the total shaded part in each of the figure.(a) Red = 14 partBlack = 14 partTotal shaded part = 14 + 14 = 24(b) (c)6. Complete the following magic square. 917141713171617? 817111710171517114 Acme Mathematics 5
(b) SubtractionStudy the given figure carefully.610610 – 310 = 310Way of subtraction:Example 1 : Subtract: 610 – 310Solution : Here, 610 – 310= 6 – 310It is common denominator.= 310Subtraction of fractionsLook at the following figures.1 2 3 1 2 3 4 4 5 57 7 6 6This shape has 10 equal parts. 710 are shaded. Let's take away 5 shaded parts from 7 parts, thenWe have 710 – 510 = 210The rule which we follow in addition works in subtraction also. If denominator is same subtract only numerators.Oh! Denominator is same.3 out of 10 is taken offAcme Mathematics 5 115
Subtraction of Like FractionsSubtraction of fractions is the same as the addition of fractions.Example 1 : Subtract: 36 – 16Solution : Here, denominators are same. So fractions are like fractions.So, 36 – 16 = 3 – 16= 26Classwork1. Subtract:(a) 45 – 35 = 15 (b) 86 – 26 = (c) 57 – 37 = (d) 58 – 38 = (e) 69 – 29 = (f) 910 – 510 = (g) 811 – 511 = (h) 412 – 112 = 2. Match the followings:79 – 191635 – 155926 – 1669 – 196925116 Acme Mathematics 5
Exercise 2.131. Subtract the following fractions.(a) 910 – 210 (b) 57 – 27 (c) 34 – 14(d) 317 – 217 (e) 68 – 48 (f) 1013 – 413(g) 59 – 29 (h) 518 – 118 (i) 811 – 3112. Subtract:(a) 274 – 54 (b) 8110 – 1110 (c) 476 – 76(d) 7312 – 1312 (e) 94 – 54 (f) 6410 – 5210(g) 438 – 178 (h) 15215 – 12215 (i) 9120 – 21203. Solve the followings:(a) 68 – 38 = (b) 1216 – 1016 = (c) 512 – 112 = (d) 43 – 13 = (e) 714 – 314 = (f) 1418 – 1218 = (g) 69 – 39 = (h) 615 – 315 = (i) 710 – 210 = (j) 820 – 420 = (k) 612 – 412 = (l) 37 – 27 = 4. Subtract:(a) 14 from 34 = 24 (b) 25 from 45 = (c) 36 from 86 = (d) 27 from 47 = (e) 38 from 68 = (f) 49 from 89 = Acme Mathematics 5 117
5. Simplify:(a) 516 + 116 + 216 (b) 712 + 212 – 412 (c) 813 + 213 – 513(d) 1015 + 215 – 615 (e) 17 + 27 – 37 (f) 14 + 34 – 24(g) 910 – 210 – 610 (h) 1516 – 216 – 316 (i) 1718 – 218 – 718(j) 1319 – 219 – 119 (k) 35 – 15 + 25 (l) 416 – 116 + 516(m) 1218 – 218 + 318 (n) 1119 – 119 + 3196. Solve the following problems.(a) Kashi did 15 of his homework in the evening and 25 in the morning. How much homework did he do in all?(b) Ram ate 57 of cake, Asha ate 17 of the same cake. How much cake did they eat?(c) Manju has 36 of a pizza. She gave 26 of the same pizza to Sanju. How much pizza is left with Manju?(d) Nani has 810 of a bread. She ate 410 of it. How much bread is left?(e) Out of 20 oranges 4 of them were rotten?(i) Write the fraction of rotten oranges.(ii) Write the fraction of good oranges.118 Acme Mathematics 5
(f) Aman ate 37 of a big cake and Amar ate 27 of the same cake.(i) Who ate more?(ii) Write fraction of the cake left?(g) Dhruba has 10 marbles. He divided his marbles among his 3 friends in the following way.(i) 210 to Arjun. (ii) 410 to Nilima.(iii) 210 to RamhariHow many marbles are left?(h) There is a bag with oranges. Gopal took 213 , Bishnu took 313 and Bishal took 513 of the oranges.(i) How many oranges did they take in total?(ii) How many oranges are left?(iii) Compare the amount of oranges that Bishal has and left in a bag.(iv) Who took fewer oranges?(i) Baburam spent 25 of his income for food and 15 of his income for busfair.(i) How much money did he spend?(ii) How much money is saved?(iii) If income is Rs. 50,000, how much money is saved?Acme Mathematics 5 119
Project WorkObjective: To know the subtraction fact.Methods : Take a long strong string. Make four knots and divide the string into 5 equal parts. Remove 15 and 25 parts respectively. How many parts of string do you have? Is there any relation of above activities with 1 – 15 – 25 ? Give your conclusion.120 Acme Mathematics 5
4.1 Conversion of Fraction and DecimalStudy the figures and complete the table. Fraction Decimal110 0.1Activity 14 DecimalAcme Mathematics 5 121
A. Tenths and HundredthTenthsIn the figure alongside2 parts out of 10 parts is shaded.It is written as 210. 210 is a fraction.It can also be written as 0.2. 0.2 is a decimal number.Similarly, 310 , 410 , 910 can be written as310 = 0.3, 410 = 0.4, 910 = 0.90.3 is read as three tenths. 0.4 is read as four tenths. 0.9 is read as nine tenths.HundredthIn the figure 4 parts out of 100 parts are shaded.It is written as 4100 . 4100 is a fraction. 4100 = 0.04, 0.04 is a decimal number.Similarly, 2100 = 0.02, 3100 = 0.03 12100 = 0.12, 55100 = 0.55 99100 = 0.99 0.02 is read as two hundredth.0.03 is read as three hundredth.0.12 is read as twelve hundredth.0.55 is read as fifty five hundredth.0.99 is read as ninety nine hundredth.I think decimal numbers are small numbers in valueInteresting210 = 0.22100 = 0.02122 Acme Mathematics 5
In general0.2 is read as zero point two.0.02 is read as zero point zero two.1Whole is shaded.1101 out of 10 is shaded.These numbers are written as 1 110In decimal, it is written as 1 110 = 1.1Similarly, 3 210 = 3.2, 2 3100 = 2.034 310 = 4.3, 1 7100 = 1.0712 610 = 12.6, 18 59100 = 18.59 B. Place Value Chart of Decimal NumberIn the figure, shaded part is 110 and unshaded part is 910.110 = 0.1 → it is a decimal number → one-tenth910 = 0.9 → it is a decimal number → nine-tenthNow, Read the following place value chart .Hundreds Tens Ones Tenths Hundredths4 5 6 7 8It is 456.78This is read as:Four hundred fifty six point seven eightNote: After decimal point we write the number name individually.decimal signTens Ones Tenths0 1Tens Ones Tenths0 9Acme Mathematics 5 123
In the expanded form: 456.78 = 400 + 50 + 6 + 710 + 8100 Hence,The number having its denominator as 10,100 or multiple of 10 are decimal numbers.C. Conversion of the decimal number into the fractionSolved ExampleExample 1 : Convert 0.2, 0.12 as fractions.Solution : Here, 0.2 = 0210 = 210 = 2 × 12 × 5 = 150.12 = 012100 = 12100 = 2 × 2 × 35 × 5 × 2 × 2 = 325Hence, 0.2 = 15 and 0.12 = 325• If number after decimal is 1, divide by 10.• If number after decimal is 2, divide by 100.RememberStudy the given examples,0.7 → seven – tenths → 7100.07 → seven – hundredths →7100Is there any relation between number of digits after decimal and number of zeros in the denominators?0.7 → one digit after decimal, 710 → one zero in the denominator 0.17 → two digits after decimal, 17100 → two zeros in the denominatordecimal numberOh!Point (.) is replaced by 1.124 Acme Mathematics 5
Example 2 : Convert 0.35 into fractions.Solution : 0.35 = 35100= 5 × 75 × 20= 720Thus, 0.35 = 720D. Conversion of the fraction into the decimal numberSolved ExampleExample 1 : Convert 710 , 18100 and 9100 as decimal number.Solution : Here, 710 = 0.718100 = 0.189100 = 0.09Example 2 : Convert 12 and 725 as decimal number.Solution : Here, 12 = 1 × 52 × 5 = 510 = 0.5725 = 7 × 425 × 4 = 28100 = 0.28Example 3 : Convert 4 12 into decimal.Solution : Here, 4 12=4+12=4+ 1 × 52 × 5=4+ 510= 4+0.5∴ 412 = 4.5Yes ! Number of Zeros is equal to number of digits after decimal.Now! I understand. If 10 is denominator, left one number after decimal. If 100 is denominator, left two numbers after decimal.Remember!Make denominator either 10 or 100 and count the zero then put the decimal.Acme Mathematics 5 125
Example 4 : Convert 178 into decimalSolution : Here, 178Now divide 17 by 8∴178 = 2.125Classwork1. Write the number name:(a) 0.2 = ............... (b) 0.8 = .............. (c) 0.7 = ...............(d) 0.75 = ............... (e) 0.98 = ...............2. Fill in the blanks:(a) 0.3 = ............... ones ............... tenths(b) 0.5 = ............... ones ............... tenths(c) 0.6 = ............... ones ............... tenths(d) 7.1 = ............... ones ............... tenths(e) 8.12 = ............... ones ............... tenths and ............... hundredths(f) 9.99 = ............... ones ............... tenths and ............... hundredths3. Fill in the blanks:(a) 2.34 = ................ ones ................ tenths and ................ hundredths(b) 12.07 = ................ ones ................ tenths and ................ hundredths(c) 53.99 = ................ ones ................ tenths and ................ hundredths(d) 9.80 = ................ ones ................ tenths and ................ hundredths(e) 123.45 = ................ ones ................ tenths and ................ hundredths8) 17(2.125 – 1610– 820– 1640– 40×When we put desimal (.) in the quotient, we put 0 in the reminder after last digit.126 Acme Mathematics 5
Exercise 2.141. Express the following decimal numbers in the place value chart:(a) 12.1 (b) 23.02 (c) 32.45 (d) 453.152. Write the number name of the following decimals:(a) 32.9 (b) 156.4 (c) 732.45(d) 521.85 (e) 351.52 (f) 3210.453. Write the place value for the underlined digit of the following decimals:(a) 0.8 (b) 5.64 (c) 32.48(d) 528.85 (e) 301.52 (f) 521.434. Expand the following decimal numbers:(a) 0.5 (b) 5.12 (c) 3.45(d) 23.7 (e) 56.14 (f) 81.125. Write the decimal number for the following:(a) 5 + 610 (b) 6 + 710 + 8100(c) 15 + 110 + 5100 (d) 7 + 210 + 31006. Convert the following fractions into decimals:(a) 410 (b) 510 (c) 425100 (d) 56100(e) 1225100 (f) 122100 (g) 12310 (h) 1241007. Convert the following fractions into decimals:(a) 12 (b) 25 (c) 75 (d) 85(e) 34 (f) 6025 (g) 124 (h) 15 925(i) 913 (j) 132350 (k) 4550 (j) 4525Acme Mathematics 5 127
8. Write in decimal number:(a) Zero point three (b) Zero point one eight(c) One point zero four (d) Seven point zero nine(e) Ten point one zero (f) Fifty point three eight9. Read the thermometer and write the Temperature:(a)35 3695 96 97 98.6 100 101 102 103 104 105 10637 38 39 40 41 42107 °F°C___________________(b)35 3695 96 97 98.6 100 101 102 103 104 105 10637 38 39 40 41 42107 °F°C___________________(c)35 3695 96 97 98.6 100 101 102 103 104 105 10637 38 39 40 41 42107 °F°C___________________(d)35 3695 96 97 98.6 100 101 102 103 104 105 10637 38 39 40 41 42107 °F°C___________________(e)35 3695 96 97 98.6 100 101 102 103 104 105 10637 38 39 40 41 42107 °F°C___________________128 Acme Mathematics 5
4.2 Addition and Subtraction of Decimal Numbers(a) Addition of decimal numbersAdding numbers with a decimal point is similar to adding whole numbers. Look at the given examples carefully.Solved ExampleExample 1 : Add: 0.2 and 0.7.Solution : Here,Example 2 : Add: 4.28 and 5.31Solution : Here,Example 3 : Add: 3 tenths 4 hundredth and 2 tenth 3 hundredth.Solution : Here, 3 tenths 4 hundredth2 tenths 3 hundredthThe sum is 5 tenths 7 hundredth.Example 4 : Add: 12.34 and 36.86Solution : Here,Example 5 : Add : 21.45 and 52.34Solution : Here,21.45 + 52.34 = 73.79Are you ready now?0 . 2+ 0 . 7 0 . 9Decimal point in the vertical line 4 . 28 + 5 . 31 9 . 59 0 . 34 + 0 . 23 0 . 57It is simple addition with decimal at one under another. 12 . 34 + 36 . 86 49 . 20Acme Mathematics 5 129
21.45 and 52.34 are like decimals 0 is added to make like decimalsExample 6 : Simplify : 23.732 + 20.14 + 30.5Solution : Here,Example 7 : A pen costs Rs. 9.50 and dozen of pencils cost Rs. 36.75. Find the total cost.Solution : Here, Cost of a pen = Rs. 9.50Cost of pencils = Rs. 36.75 Total cost = Rs. 9.50 + Rs. 36.75 = Rs. 46.25(b) Subtraction of decimal numbersLook at the example carefullySolved ExampleExample 1 : Subtract: 12.34 from 56.78Solution : Here,Example 2 : Subtract: 86.56 – 7.80Solution : Here,Example 3 : Simplify: 7.4 + 12.98 – 2.80Solution : Here, 7.40 + 12.98 – 2.80= 20.38 – 2.80= 17.5823.73220.140+ 30.50074.372Rs. 9+ 3646P507525 56 . 78 – 12 . 34 44 . 44Oh! After decimal there are 2 numbers. 86 . 56 – 7 . 80 78 . 767.8 and 7.80 are same. We add zero to make number of digit after decimal equal.Rough 7 . 40 + 12 . 98 20 . 38 20 . 38 – 2 . 80 17 . 58130 Acme Mathematics 5
Example 4 : Subtract 35.5 from 50.8Solution : Here, 50.8 – 35.5 = 15.3Example 5 : Simplify: 827.67 – 432.342Solution : Here,Classwork1. Drag and drop the numbers into the correct place and then fill in the fraction.0.5 0.7 0.3 0.9 0.2 0.1(a) (b) (c) 10 = 10 = 10 =(d) (e) (f) 10 = 10 = 10 =2. Fill in the box:(a) 0.1 + 0.3 = (b) 0.7 + 0.2 =(c) 0.8 + 0.1 = (d) 0.4 + 0.5 = (e) 1.3 + 2.3 = (f) 2.4 + 3.3 = '0' is added. 827.670– 432.342395.328Acme Mathematics 5 131
(g) 0.8 – 0.3 = (h) 0.9 – 0.5 = (i) 2.8 – 1.8 = (j) 9.9 – 6.6 = (k) 12.00 – 7.00 = (l) 20.80 – 8.20 = Exercise 2.151. Match the following:(a) 4 tenths + 5 tenths (i) 0.6(b) 9 tenths – 3 tenths (ii) 0.4(c) 13 tenths – 9 tenths (iii) 0.08(d) 9 tenths + 8 tenths (iv) 0.9(e) 3 hundredth + 5 hundredth (v) 1.72. Add the following:(a) 0.1 + 0.3(b) 0.7 + 0.4(c) 0.9 + 0.8(d) 0.2 + 0.3 + 0.4 (e) 0.7 + 0.2 + 0.6(f) 7.8 6.2 + 9.6(g) 2.3 4.9 + 6.7(h) 1.1 2.2 + 3.9(i) 0.54 + 0.78(j) 0.76 + 0.15(k) 4.29 + 3.66(l) 9.78 + 6.24(m) 12.12 + 13.69(n) 5.99 + 13.64(o) 2.64 3.78 +4. 4.2(p) 5.67 6.78 + 7.89(q) 12.21 13.32 + 15.633. Add the following decimal numbers:(a) 4.2, 2.7 and 0.9 (b) 23.4, 56.87 and 16.54(c) 12.28, 100.75 and 89.54 (d) 29.24, 321.29 and 14.975(e) 332.4, 876.67 and 37.13 (f) 223.23, 54.12 and 9.72132 Acme Mathematics 5
(g) 122.45, 560.65 and 37.13 (h) 31.002, 900.431 and 33.0034. Find the sum:(a) (b) (c)(d) (e) (f)5. Subtract:(a) 0.8 – 0.4(b) 0.9 – 0.2(c) 0.7 – 0.5(d) 0.8 – 6.1(e) 12.7 – 9.6(f) 15.2 – 10.4(g) 0.78 – 0.12(h) 0.98 – 0.67(i) 0.77 – 0.23(j) 1.62 – 0.34(k) 7.65 – 5.88(l) 4.32 – 2.67(m) 40.03 – 7.9(n) 60.82 – 42.84(o) 28.29 – 25.29(p) 100.00 – 79.226. Subtract the following decimals:(a) 0.4 from 0.67 (b) 9.55 from 14.89(c) 27.13 from 79.0 (d) 21.05 from 45.66(e) 46.59 from 93.80 (f) 281.12 from 298.07(g) 121.07 from 200 (h) 0.088 from 17. Subtract:(a) (b) (c)(d) (e) (f)14.976.48+ 10.203.4005.040 + 6.0012.12 9.12 + 8.146.070 6.83 +12.620.1236.90+ 1.11 6.008 16.080+15.80014.04– 9.646.42– 2.3848.32– 8.9729.493– 26.43615.31– 9.7642.00– 38.07Acme Mathematics 5 133
8. Simplify the following:(a) 5.73 + 8.29 + 1.27 (b) 13.2 + 30.06 + 6.85(c) 56.07 + 6.88 – 15.30 (d) 0.96 + 0.76 + 0.88(e) 1.69 – 2.68 + 4.55 (f) 0.9 – 0.78 + 0.99(g) 0.8 + 0.9 – 1.0 (h) 0.7 – .99 + 12.33(i) 3.5 – 2.4 + 5.6 (j) 6.9 + 4.7 – 2.59. Study the height of Khushi and Udesh and answer the following questions:(a) Calculate their total height.(b) Who is taller? By how much?(c) Who is shorter? By how much?10. Look at the following goods and their price list:Rs. 15.50 Rs. 50.60 Rs. 19.75 Rs. 26.95(a) Find the total cost of all goods.(b) Which one is the cheapest?(c) Which one is the most costly?(d) Find the difference between the cost of ball and ice-cream.(e) If you have only 100 rupees, to buy all the goods, how much more money is needed to you?11. (a) I travelled 110.25 km by bus, 9.32 km on bicycle, 20 km on motorcycle and 1.02 km on foot. Find the total distance that I travelled.(b) Sangita bought 12.5 kg of potatoes, 30.25 kg of rice and 2 kg of onions. How much did she buy altogether ?1.03 m 1.09 mKhushi Udesh134 Acme Mathematics 5
(c) Bhanu spent Rs. 112.25 on food, Rs. 60.50 on bus fair and Rs. 25.00 on cold drink. How much money did he spend altogether?12. (a) Your weight is 22.5 kg, your sister's weight is 36.125 kg. Find the difference in weight.(b) Teknath had Rs.352.25. He spent Rs. 150.75. How much money was left with him ?(c) A ribbon is 60 m long. If two pieces of length 45.6 m and 12.45 m is cut, what length of the ribbon is left now ?13. Measure the length of the following object.(a) (b)(c) (d)Now answer the following questions:(i) How long is the pencil(ii) Which is the longest among all?(iii) Which is the shortest among all?(iv) If we put pen and pencil together end to end, what is the length?Acme Mathematics 5 135
FractionFractionFractionFractionFractionFractionDecimalDecimalDecimalDecimalDecimalDecimalPercentPercentPercentPercentPercentPercent131000.1313%Study the given figures and fill in the box.Activity 15 Percentage136 Acme Mathematics 5
In our daily life we come across the different activities. One of them is buying the goods.Study the following advertisement :What is the meaning of 10% discount, 20% off? The symbol % is called the percentage. Its meaning is \"Out of a 100\"Out of a 100 small squares in the figure alongside 12 squares are shaded. The shaded parts are \"12 out of 100\"Or12100 as fraction or 12% as percentage.A. Changing Fraction to PercentageConsider the fractions :12 = 1 × 502 × 50 = 50100 = 50%325 = 3 × 425 × 4 = 12100 = 12%Again, 12 = 12 × 100% = 50%Similarly, 325 = 325 × 100% = 3 × 4% = 12 %Therefore, to convert fractions into percentages multiply the fraction by 100%.Percent is a fraction in hundredths.Remember1100 = 1%10% Discount 20% DiscountAcme Mathematics 5 137
50% shaded 12% shadedB. Changing percentage to fractionConsider 75%75% = 75 × 1100= 75100 = 5 × 5 × 35 × 5 × 4 = 34Therefore, 75% = 34To convert percentage into fraction, divide the percentage by 100 and remove the symbol %.C. Changing percentage to decimalConsider 25 %25% = 25 × 1100= 25100 = 0.25Therefore, 25% = 0.25To change percentages to decimals divide the number by 100 and remove the % sign.D. Changing decimal to percentageConsider 0.350.35 = 35100and 35100 = 35100 × 100% = 35%Therefore, 0.35 = 35%To change decimal to percentage, multiply the number by 100%fraction percentage× 100÷ 100Oh! 34 is shaded.138 Acme Mathematics 5
Classwork1. Complete the table:110 0.1 10%15 0.214 12 34 12. Study the given figure and write in percentage.1 _____ = _____100 = _____ 1%Acme Mathematics 5 139
_____ = _____ _____ = __________ = _____ _____ = _____3. Complete the table:Fraction Decimal Read as13100 0.13 zero point one-three23100 _________ ___________________________33100 _________ ___________________________44100 _________ ___________________________88100 _________ ___________________________99100 _________ ___________________________1. (a) Shade the figure as 25% (b) Shade the figure as 50%Exercise 2.14140 Acme Mathematics 5
3. Complete the followings:Percentage : Percentage : Fraction : Fraction : Decimal : Decimal : 21% 67%0.2121100Percentage : Percentage : Fraction : Fraction : Decimal : Decimal : 0.53481004. Convert to the percentage:(a) 24100 (b) 36100 (c) 2100 (d) 45100 (e) 69100(f) 81100 (g) 80100 (h) 100100 (i) 24 (j) 110(k) 325 (l) 850 (m) 1320 (n) 1725 (o) 3450Percentage : Percentage : Fraction : Fraction : Decimal : Decimal : 37%2. Match the followings : 12 25% 0.534 40% 0.7514 50% 0.2525 75% 0.4Acme Mathematics 5 141
5. Convert these percentages into fractions:(a) 12% (b) 5% (c) 20% (d) 70% (e) 80%(f) 10% (g) 50% (h) 22% (i) 90% (j) 15%6. Express the decimal numbers as percentage:(a) 0.02 (b) 0.13 (c) 0.19 (d) 0.25 (e) 0.30(f) 0.35 (g) 0.41 (h) 0.62 (i) 0.69 (j) 0.727. Convert the following percentages to decimal number:(a) 15% (b) 20% (c) 25% (d) 35% (e) 50%(f) 85% (g) 48% (h) 110% (i) 112 % (j) 234 %8. Fill up your marks in the blanks (use your mark sheet):Subjects Full marks Marks obtainedMathsEnglishNepaliScienceSocial studies(a) Find the total full marks.(b) Find the total obtained marks.(c) Express your marks in percentage.(d) Express marks obtained in maths as percent.(e) Express marks obtained in science as percent.9. Express the following shaded part, first as fraction and then as percentage: (Ifpossible.)(a) (b) (c)142 Acme Mathematics 5
10. Complete the given figures.(a)0.4 .......... %zero point fourtwo-fifth0 5(b)0.1 .......... %zero point oneone-tenth0 1(d) (e) (f)Acme Mathematics 5 143
1. Study the length and breadth of a play ground given alongside.(a) How many metres more length than its breadth?(b) How long is outer part of the play ground?2. Study the length of two sticks.(a) Which stick is shorter?(b) By how many cm the stick B is longer than stick A?(c) What is the total length of stick A and stick B?3. The cost of 35 chocolates is Rs 103.75, the cost of a biscuit is Rs. 50.80 and the cost of 15 pencils is Rs 75. Calculate the total cost.4. Study the given table and answer the questions given below:Subjects Full marks Marks obtainedMaths 80 40English 75 50Nepali 60 45Science 90 60Social Studies 50 40(a) Find the total full marks.(b) Find the total obtained marks.(c) Express your total marks in percentage.(d) Express marks obtained in Maths as percent.(e) Express marks obtained in Science as percent.108.82 m68.90 mStick B2 mStick A1.48 mMixed Exercise144 Acme Mathematics 5
5. Rasmi got 50 out of 100 in Math subject and 80 out of 100 in Science subject.(a) What percentage did she get in Maths?(b) What percentage did she get in Science?6. A basket contains 1000 apples. 8% of them are rotten.(a) How many apples are rotten?(b) Also find the number of good apples.7. Look at the picture and answer the following questions.(a) Express the given figure into fraction.(b) Convert the fraction into decimal.(c) Convert the fraction into percentage.8. (a) Write 15 in decimal.(b) Write the decimal 21.24 in word.(c) A rope is 25.72 m long and another rope is 12.15 m long. What is the total length of both ropes?9. (a) Express 'two tens seven ones five hundredth' in decimal number.(b) Bishal got 15 out of 20 in monthly test. Find his percentage.(c) Write any two equivalent fractions of 45.10. Amod divides a pizaa into 8 equal parts.(a) If he eats 6 parts from it, write the eaten pizza in fraction.(b) Express the fraction in the percentage.(c) Write the remaining pizza into the decimal.11. What is the value of 1510 in decimal.(a) 1.05 (b) 4.5 (c) 2.5 (d) 1.512. In the figure, the shaded parts are the pieces of roti that has been eaten byAnanya.(a) Write the shaded parts into fraction.(b) Convert the shaded parts into decimal.(c) Convert the shaded parts into percentage.Acme Mathematics 5 145
13. Mahima has 3 25 pencils. Her father gave 1 15 pencils to her.(a) How many pencils does Mahima has now?(b) Find the sum of 2.5 and 3.754.(c) Convert 225% into mixed fraction in the simplest form.14. (a) Add : 312 + 512 (b) Add : 4 79 + 2 39 + 1 1915. (a) Convert into decimal : 275100 (b) Convert into decimal : 34(c) Write 0.02 as fraction.(d) Write 0.15 in expanded form.16. (a) Study the decimal number 578.14 and answer the following questions.i. Write the place value of 4 of the given number.ii. Write the expanded form of the given number.iii. Write the given number in words.(b) Write in decimal number : i. 5610 ii. 3510017. A farmer divided his rectangular garden in 5 equal parts. He planted flowersin 3 parts.(a) What fraction of the land was used for flowers?(b) Express the fraction in decimal.(c) Convert the decimal into percent.(d) If the farmer built his house in the remaining parts of the land, what percent of the land was occupied by his house?18. There are 500 students in a school. 40% of them are in Secondary level and the rest are in Primary level.(a) How many students are there in Secondary level?(b) Find the percent of students in Primary level.(c) How many students are there in Primary level?19. (a) Express 13% into fraction.(b) Find the value of : 25% of 80(c) Add: 125 + 215146 Acme Mathematics 5
EvaluationTime: 55 minutes Full Marks: 231. (a) Convert into decimal : (i) 6100 (ii) 1510 [1] (b) Convert the improper fraction 254 into mixed fraction. [1] (c) Simplify: 5 36 + 3 26 − 2 16 [2]2. (a) Present 125.63 in place value chart . [2](b) Write 0.28 in words. [1] (c) Convert 2.25 into percentage. [1](d) There are 13 boys in a class of 20 students. (i) What is the percentage of boys ? [1] (ii) What is the percentage of girls? [1] (e) Write the expanded form of 25.68. [1]3. (a) There are two parcels. One of them weighs 210 kg. and the other weighs 710kg. Find the total weight. [2] (b) The figure shows Royce's marks secured inmathematics (i) Write Royce's markes in decimals number [1](ii) What percentage did Royce get in mathematics ? [1]4. There are 50 students in 5. Among them, 35 are present. (a) How many students are absent? [1](b) Write the number of both absent and present students in fraction. [2](c) Write the absent students number in percentage? [1](d) Write the present students number in percentage. [1]5. (a) Simplify: 55 ÷ 11 + 5 × 2 [1] (b) Add: 2 13 + 3 16 [2]Acme Mathematics 5 147
MEASUREMENT CHAPTER31. Put the correct answer in the blanks.(a) 24 hours = .................... day (b) 7 days = ..................... week(c) 30 days = ......... month (d) 1 year = ............... months2. Write 'True' or 'False'.(a) 70 days makes 10 weeks. (b) 2 minutes makes 60 hours.(c) year is larger unit than month. (d) 1 day equals 20 hours.3. Fill in the blanks:(a) 2 weeks = ............... days (b) 4 months = ............... days(c) .......... days = 1 year (d) 2 years = ............... days(e) 24 months = ............... years (f) 5 years = ............... months4. Fill in the blanks:(a) 2 days = .......... hours (b) 48 hours = .......... days(c) 6 minutes = .......... seconds (d) 60 minutes = .......... hours(e) 120 seconds = ........... minutes5. Fill in the blanks:(a) 3 minutes + 60 seconds = ......... minutes(b) 25 minutes + 55 minutes = ......... hours and ......... minutes(c) 5 hours + 60 minutes = ......... hours(d) 12 hours + 13 hours = ......... days and ......... hours(e) 40 hours + 13 days = ......... days and ......... hours6. Complete the following.(a) 6 days – 20 hours = ...... days and ...... hours(b) 1 hour – 45 minutes = ...... minutes (c) 1 month – 10 days = ......(d) 1 year – 8 months = ...... months (e) 1 week – 2 days = ...... days(f) 7 am – 2 hours = ...... (g) 11:30 am – 10 hours = ......Warm Up Test148 Acme Mathematics 5
1.1 Introduction of 24-Hours Time24-hour time shows the amount of hours and minutes since midnight.24 00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00AM 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:0024 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00PM 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00AMPMAnte MeridiemLatin for 'before midday'AMPost MeridiemLatin for 'after midday'PMStudy the time table of Buddha Air.Flight No. Departure Time Arrival TimeU4-B852 Kathmandu 07:15 Bhairahawa 07:45U4-B855 Kathmandu 08:05 Biratnagar 08:40U4-B803 Kathmandu 09:00 Bhadrapur 09:40U4-B851 Kathmandu 10:20 Bharatpur 10:40U4-B854 Kathmandu 12:30 Simara 12:50U4-B850 Kathmandu 15:25 Dhangadi 15:00U4-B856 Kathmandu 18:15 Pokhara 18:451 TimeAcme Mathematics 5 149
School Time 10 am to 4 pmBus Time TableDeparture Time Arrival Time5:15 am 12:30 noon6:15 am 1:00 am How many hours do you watch the Television? How old are you? How old is your grandfather now?These all answers are related to time. The smallest unit of time is second.1.2. Relation among the different units of timeStudy the following relations :60 seconds = 1 minute60 minutes = 1 hour24 hours = 1 day7 days = 1 week30 days = 1 month365 days = 1 year10 years = 1 Decade100 years = 1 CenturySolved ExampleExample 1 : Convert 2 hours 23 minutes into seconds.Solution : We have, 23 minutes = 23 × 60 seconds = 1380 seconds2 hours = 2 × 60 minute = 120 minute = 120 × 60 seconds= 7200 seconds∴ 2 hours 32 minutes = 1380 secs + 7200 secs = 8580 secondshour second× 60÷ 60× 60÷ 60minuteweek hour× 7÷ 7× 24÷ 24day150 Acme Mathematics 5