B. Conversion of fractions into decimal numbersStudy the given examples carefully.Solved ExampleExample 1 : Convert 310 into decimal number.Solution: Here, 310 = 3 ÷ 10 10) 3.0 (0.3 – 0 30 – 30 ×Hence, 310 = 0.3 3 is one place after decimal.Example 2 : Convert 235 into decimal number.Solution: Here, 235 = 135 = 13 ÷ 5 5) 13 (2.6 – 10 30 – 30 ×Hence, 235 = 2.6C. Conversion of decimal into fractionExample 3 : Convert 0.7 into fraction.Solution: 0.7 = 0710 = 710Example 4 : Convert 0.75 into fraction.Solution: 0.75 = 075100= 75100 = 5 × 5 × 35 × 5 × 4 = 34Hence, 0.75 = 343 can be written as 3.0 also.5 755 1535 1005 204Acme Mathematics 6 101
Classwork1. Express as the percentage:(a) The red coloured part.(b) The blue coloured part(c) The green coloured part.(d) The white coloured part.2. Change to decimal:(a) 3100 = (b) 7100 = (c) 11100 =(d) 9100 = (e) 20100 = (f) 25100 =3. Change to fractions:(a) 0.2 = (b) 0.3 = (c) 0.13 = (e) 0.07 = (e) 0.67 = (f) 0.99 = Exercise 2.161. Covert into decimal numbers.(a) 210 (b) 13100 (c) 1231000 (d) 120(e) 150 (f) 325 (g) 75 (h) 1025(i) 1820 (j) 34 (k) 12 (l) 38(m) 140 (n) 916 (o) 52 (p) 1142. Change into decimal numbers.(a) 134 (b) 358 (c) 3 425 (d) 645(e) 188 (f) 11270 (g) 15060 (h) 12 912102 Acme Mathematics 6
3. Fill in the blanks with decimal numbers.(a) 110 = ................ (b) 210 = ................ (c) 1410 = ................(d) 3100 = ................ (e) 188 = ................ (f) 1225 = ................(g) 15060 = ................ (h) 142 1000 = ................ (i) 506 1000 = ................4. Fill in the blanks with fractional numbers.(a) 0.6 = ................ (b) 0.8 = ................ (c) 0.18 = ..............(d) 1.3 = ................ (e) 1.03 = ................ (f) 1.22 = ................(g) 24.5 = ................ (h) 20.55 = ................ (i) 50.562 = ...............5. Convert to the fraction with lowest term.(a) 0.6 (b) 1.5 (c) 2.54 (d) 0.005(e) 12.5 (f) 12.25 (g) 12.125 (h) 0.225D. Addition and subtraction of decimalsAddition and subtraction of decimal numbers is similar to addition and subtraction of whole numbers. Now study the following examples.Solved ExampleExample 1 : Add: 12.49 and 5.23Solution: Here, Example 2 : Add: 3.456, 4.76 and 12.8Solution: Here, Example 3 : Subtract 10.63 from 12.75Solution: Here, Example 4 : Subtract 34.3 from 40.004.Solution: Here,12.49+ 5.2317.72Number of digits after decimal is same3.4564.760+ 12.80021.016Adding zeros, to make number of digits after decimal same.12.75– 10.632.1240.004– 34.3005.704Number of digits after decimal is sameAcme Mathematics 6 103
1. 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 = (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 = 2. 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) 1.7Exercise 2.171. Add or subtract and fill in the blanks.(a) 1.2 + 0.9 = ............. (b) 0.9 + 0.3 = ............. (c) 2.9 – 0.03 = .............(d) 5 – 2.5 = ............. (e) 0.7 – 0.07 = ............. (f) 5 – 0.5 = .............(g) 0.9 – 0.2 = ............. (h) 2.5 – 0.9 = ............. (i) 34.3 – 7.0 = .............2. Add the following decimals.(a) 17.345, 18. 278 and 19.59(b) 20.0124, 36.918 and 0.793(c) 1.505, 2.606 and 3.707(d) 5.363 (e) (f)+ 8.4691.406+ 0.0096.347+ 9.62104 Acme Mathematics 6
(g) (h)3. Subtract the following.(a) (b) (c)(d) (e) (f)4. Simplify:(a) 16.97 – 13.234 + 8.667(b) 8.12 + 9.002 – 12.03(c) 426 – 28.43 + 6.246(d) 29.36 + 26.436 – 2.953(e) 9.9 – 20.123 + 31. 735. A water tank holds 112.7 liters of water. If 50.92 liters of water is used up, how much water is left in the tank ?6. What should be added to 13.45 to get 20 ?7. What should be subtracted from 55.17 to get 32.0 ?8. My car can hold 35.65 liters of petrol. I filled it with 25.00 liters. How much more petrol can it hold ?13.5402.123+ 4.56021.5423.89+ 9.226.67– 3.0922.082– 9.17788.072– 69.19920.000– 17.03292.000– 88.97313.070– 6.094Acme Mathematics 6 105
E. Multiplication of Decimals(a) Multiplication of decimal number by 10, 100, 1000 and 10,000.Look at the examples.Decimal numberMultiplying by 10Multiplying by 100Multiplying by 1000Multiplying by 10,0007.5434 75.434 754.34 7543.4 75434.00.345 3.45 34.5 345.0 3450.0 When multiplied by 10, decimal point shift to one digit right. When multiplied by 100, decimal point shift to two digits right. When multiplied by 1000, decimal point shift to three digits right. When multiplied by 10,000, decimal point shift to four digits right.Shift of Decimal PointSolved ExampleExample 1 : The length of a square book is 0.24 m. Find its perimeter.Solution: Length of the book = 0.24 mPerimeter of the book = ?Now, Perimeter of the book = 4 × length= 4 × 0.24 m = 0.96 mHence, perimeter of the book is 0.96 m.Example 2 : A rectangular garden has length 30.5 m and breadth 20.7 m. Calculate its area.Solution: Length of the garden = 30.5 mBreadth of the garden = 20.7 mNow, Area of the garden = l × b= 30.5 × 20.7 m= 631.35 m2Hence, area of the garden is 631.35 m2.(b) Multiplication of decimal numbers by other numbersStudy the following examples.Solved ExampleExample 1 : Multiply 2.5 by 15Solution: Here, Product of 2.5 and 15 = 2.5 × 15 = 2510 × 15 = 37510 = 37.5Oh! I remembered. Count the zero and shift the decimal point right to the digit according to number of zero.30.5× 20.72135 000061000631.35106 Acme Mathematics 6
Method II:25 × 15 = 375But after decimal there is one digit. So, 2.5 × 15 = 37.5Example 2 : Multiply 2.9 by 1.2Solution: Here, Product of 2.9 by 1.2 = 2.9 × 1.2= 2910 × 1210= 29 × 12100 = 348100 = 3.48Hence, 2.9 × 1.2 = 3.48Here, the product has 2 decimal places. Sum of decimal places 2.9 × 1.2 has also 2 decimal places.Example 3 : Find the product of 1.23 and 2.45.Solution: The product of 1.23 and 2.45Method I: 1.23 × 2.45 = 123100 × 245100= 123 × 245100 × 100 = 3013510000 = 3.0135Method II: No. of digits after decimal = 2, in 1.23No. of digit after decimal = 2, in 2.45Total No. of digits after decimal = 4Now,Hence, the product 1.23 × 2.45 is 3.013525× 15125 250375The product 37.5 has 1 decimal place which is the sum of the number of decimal place in 2.5 × 15.Number of decimal places123× 245615 4920 + 2460030135Acme Mathematics 6 107
Example 4 : The weight of 1 book is 1.640 kg. Calculate the weight of 8 such book.Solution: Here, number of book = 8Weight of 1 book = 1.640 kg.Now, weight of 8 book = 1.640 x 8 kg.= 16401000 x 8 kg.= 131201000 kg.= 13.120 kg.Hence, weight of 8 book is 13.120 kg.Classwork1. Match the following:(a) 0.4 × 2 (i) 0.9(b) 0.3 × 3 (ii) 1.2(c) 1.2 × 1 (iii) 7.2(d) 0.9 × 8 (iv) 0.8(e) 1.4 × 4 (v) 5.62. Fill in the blanks:(a) 0.2 × 10 = ............. (b) 0.3 × 10 = .............(c) 0.34 × 10 = ............. (d) 0.49 × 10 = .............(e) 0.92 × 100 = ............. (f) 0.88 × 100 = .............(g) 1.75 × 100 = ............. (h) 0.7 × 100 = .............3. Multiply the given numbers by 10 and 100:(a) 0.9 (b) 0.72 (c) 1.23(d) 8.7 (e) 18.2 (f) 9.11Exercise 2.181. Fill in the blanks.(a) 0.12 × 10 = .................... (b) 0.12 × 100 = ....................(c) 0.12 × 1000 = .................... (d) 0.03 × 7 = ....................(e) 0.01 × 4 = .................... (f) 0.02 × 3 = ....................108 Acme Mathematics 6
(g) 0.8 × 5 = .................... (h) 0.7 × 6 = ....................2. Multiply:(a) 2.4 × 6 (b) 18 × 0.4 (c) 20 × 1.5 (d) 0.07 × 12(e) 0.09 × 19 (f) 1.12 × 20 (g) 16.3 × 1.3 (h) 39.2 × 2.02(i) 56.1 × 1.5 (j) 72.18 × 1.6 (k) 27.34 × 0.8 (l) 50.02 × 0.73. Find the products:(a) 1.7 × 0.8 × 1.2 (b) 2.7 × 0.9 × 1.5 (c) 13.09 × 1.4 × 0.9(d) 123.4 × 0.5 × 0.17 (e) 0.4 × 2.1 × 1.68 (f) 15.1 × 0.11 × 10.14. The cost of a pair of eye glasses is Rs. 405.50. Find the cost of 25 such eye glasses.5. The monthly salary of a man is Rs. 9732.75. Find his annual salary.6. Calculate the area of the given figures.(a)120.7 cm5.6 cm(b)0.9 cm3.79 cm(c)3.34 cm3.3 cmF. Division of Decimals(a) Division of decimal number by 10, 100,1000 and 10,000Look at the examples.Decimal number Dividing by 10 Dividing by 100 Dividing by 1000 Dividing by 10,0007543.4 754.34 75.434 7.5434 0.754340.3 0.03 0.003 0.0003 0.00003Decimal point is shifted to left according to number of zero. If there is one zero (i.e. 10)decimal point shifted to 1 digit left i.e. 7543.4 ÷10 = 754.34 Shift of Decimal NumberAcme Mathematics 6 109
(b) Division of decimal numbers by other numbersStudy the following examples.Solved ExampleExample 1 : Divide 0.6 by 2.Solution: Method I0.6 ÷ 2 = 610 ÷ 2= 610 × 12= 2 × 310 × 2 = 310 = 0.3Example 2 : Divide 38.48 by 8.Solution: Here, 38.48 ÷ 8Thus, 38.48 ÷ 8 = 4.81Example 3 : Divide 28.272 by 1.2Solution: Here, 28.272 ÷ 1.2In this case both are decimal numbers. So we should make the divisor free of decimals as,28.272 ÷ 1.2 = 282721000 ÷ 1210= 282721000 × 1012= 28272100 × 12= 282.7212= 23.56Thus, 28.272 ÷ 1.2 = 23.56 Method III 0.6 ÷ 2 = 0.3 2) 0.6 (0.3 – 0 6 – 6 ×Method II0.6 ÷ 2= 6 tenths ÷ 2= 6 tenths2 = 3 tenths = 0.3 8) 38.48 (4.81 – 32 64 – 64 8 – 8 0Division is done in the normal way except that after the division of the whole number is completed, the decimal point is put in the quotient and division is continued. 12) 282.72 (23.56 – 24 42 – 36 67 – 60 72 – 72 ×It is from 1.2 = 1210110 Acme Mathematics 6
Classwork1. Write the quotient in the blanks:(a) 12.3 ÷ 10 = ............... (b) 9.7 ÷ 10 = ...............(c) 65.6 ÷ 10 = ............... (d) 16.9 ÷ 10 = ...............(e) 213.2 ÷ 100 = ............... (f) 0.7 ÷ 100 = ...............2. Divide:(a) 0.9 ÷ 3 (b) 0.92 ÷ 2 (c) 1.62 ÷ 3(d) 9.65 ÷ 5 (e) 0.64 ÷ 4 (f) 2.48 ÷ 4 3. Find the quotient (use the method used in question number 2):(a) 0.74 ÷ 10 (b) 0.99 ÷ 10 (c) 1.23 ÷ 10(d) 7.89 ÷ 10 (e) 12.3 ÷ 100 (f) 90.11 ÷ 100(g) 139.7 ÷ 100 (h) 120.6 ÷ 100 (i) 729.62 ÷ 100Exercise 2.191. Write the quotient in the blanks.(a) 4.7 ÷ 10 = .................... (b) 2.35 ÷ 10 = ....................(c) 24.3 ÷ 100 = .................... (d) 67.12 ÷ 100 = ....................(e) 123.4 ÷ 1000 = .................... (f) 4567 ÷ 1000 = ....................(g) 0.8 ÷ 2 = .................... (h) 0.25 ÷ 5 = ....................(i) 0.81 ÷ 9 = .................... (j) 056 ÷ 8 = ....................(k) 0.77 ÷ 7 = .................... (l) 0.48 ÷ 3 = ....................2. Find the quotient:(a) 15.6 ÷ 3 (b) 16.4 ÷ 4 (c) 30.5 ÷ 5(d) 24.6 ÷ 6 (e) 28.7 ÷ 7 (f) 48.8 ÷ 8(g) 81.9 ÷ 9 (h) 4.59 ÷ 9 (i) 4.32 ÷ 8(j) 10.78 ÷ 7 (k) 7.68 ÷ 6 (l) 4.85 ÷ 5(m) 140.58 ÷ 11 (n) 89.64 ÷ 12 (o) 253.95 ÷ 15Acme Mathematics 6 111
3. Divide and find the quotient.(a) 0.288 ÷ 0.6 (b) 47.999 ÷ 0.7 (c) 0. 576 ÷ 0.8(d) 0.747 ÷ 0.9 (e) 25.415 ÷ 11.5 (f) 5.728 ÷ 1.6(g) 0.4165 ÷ 1.7 (h) 2.214 ÷ 1.8 (i) 8.075 ÷1.9(j) 12.978 ÷ 2.14. Simplify:(a) (2.3 + 0.9) ÷ 0.3 (b) 9.2 ÷ ( 9.4 – 2.7)(c) 0.3 ÷ ( 0.7 + 0.12) (d) (6.5 – 3.1 ) ÷ 1.3(e) 4.5 ÷ ( 2.9 – 0.72) (f) (2.2 × 7.2 ) ÷ 0.9(g) 6.2 ÷ 0.2 × 0.73 + 0.9 (h) 2.7 × 0.5 ÷ (7.5 × 0.4 – 2.9)5. If 8 trousers cost Rs. 3404.80, find the cost of 1 trouser.6. A car travels 334.840 kilometers in 6 hours. Find the distance travelled in 1 hour.7. The perimeter of the rectangular garden is 97.5 m. If length is double its breadth, (a) Find its length and breadth.(b) Find its area.8. The cost of 2.75 kg cauliflower is Rs. 96.25.(a) Calculate the cost of 1 kg cauliflower.(b) How much cauliflower can be bought in Rs. 129.5?9. A rectangular field has length 16.5 ft and area 209.55 sq. feet.(a) How long is its breadth?(b) Calculate its perimeter.(c) If breadth is increased by 3.8 ft, calculate the change in its area.112 Acme Mathematics 6
G. Rounding the decimalsHow long is your pencil? My pencil is 14.6 cm longIt is 13.3 cm long.The length of one pencil is 14.6 cm.The length of other pencil is 13.3 cm.If we want to express the length in round figure, 14.6 cm changes to 15 cm and13.3 cm changes to 13 cm. We write it as 14.6 cm ≈ 15 cm13.3 cm ≈ 13 cm.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1514.613 14 1513.3 14.6 14.6 is nearer to 15 than 14. So it is rounded to 15. 13.3 cm is nearer to 13 than 14. So, it is rounded to 13. Hence,14.6 to 15 is called the round up process.13.3 to 13 is called the round down process.If the digits in the place is 5, 6, 7, 8, 9 then we round up and if the digits in the place is 0, 1, 2, 3 & 4 then we round down.Expressing the numbers in the nearest unit is called the rounding off.Now, Consider 4.49, 3.54 and 3.194.49 is near to 4.5 than to 4.4 so 4.49 ≈ 4.53.54 is near to 3.5 than to 3.6 so 3.54 ≈ 3.53.19 is near to 3.2 than to 3.1 so 3.19 ≈ 3.2Acme Mathematics 6 113
Solved ExampleExample 1 : Express 227 correct to:(a) Three decimal places(b) Two decimal places(c) One decimal placeSolution: Here, 227 = 3.14283.1428 has 4 decimal places.So, (a) 3.1428 ≈ 3.143(b) 3.1428 ≈ 3.14(c) 3.1428 ≈ 3.1Exercise 2.201. Round the decimal part to 1 decimal place.(a) 3.63 (b) 4.51 (c) 12.29 (d) 50.642. Round the decimal part to 2 decimal places.(a) 6.253 (b) 4.098 (c) 1.628 (d) 7.0093. Express the following fractions nearest to 3 decimal places.(a) 37 (b) 18 (c) 23 (d) 313(e) 11123 (f) 21219 (g) 1 121 (h) 3 4134. Round off 6.4687 to the following places.(a) Nearest ones (b) Nearest tenth(c) Nearest hundredth (d) One decimal place5. Round off the nearest unit given in the bracket.(a) 2.3 cm (cm) (b) 98 cm (m) (c) 1817 m (km)(d) Rs. 2.87 (Rs) (e) Rs 10.07 (Rs) (f) Rs. 9.50 (Rs)(g) 3.453 l (l) (h) 4.568 ml (l) (i) 5.670 g (kg) 7 ) 22 ( 3.1428... – 21 10 – 7 30 – 28 20 – 14 60 – 56 4114 Acme Mathematics 6
1. Aayesha is enrolled in a private school as a teacher: (a) If she spent 14 of her income in her pocket money and 12 of income in children's education, find out on which heading more money is invested?(b) If her monthly income is Rs. 40,000, find the total money spent on her children's education.(c) Write the monthly expenditure done on children's education in nearest thousand. 2. (a) Add : 23 + 56 (b) Subtract : 1124 – 38(c) Find the product : 27 × 14 (d) Divide : 30 ÷ 583. Manju works in a hospital as a nurse.(a) If she spends 13 of her income on food and 25 on house rent, find on which heading more money is invested?(b) If her monthly income is Rs. 30,000, find the total money spend on her house rent?(c) Find the total money spend on her food.4. (a) Write any two equivalent fractions of 13.(b) Multiply : 1210 × 56 (c) Divide : 9 ÷ 375. Manoj buys a milky bar and divides it into 8 equal pieces. he gives 2 pieces to Jiwan and 3 pieces to Suresh.(a) What fractions of the bar do Jiwan and Suresh get?(b) Show these fractions by shading a rectangle.(c) Find the sum of these two fractions.(d) Is the sum proper or improper fraction? Give reason.6. (a) Write the equivalent fractions of 23.(b) Which is greater? 58 or 112 (c) Divide : 45 ÷ 23(d) If 1 13 kg is a weight of a book, find the total weight of 18 such books.Mixed ExerciseAcme Mathematics 6 115
Project Work1. Objective: To verify multiplication of fraction by paper folding.2. Materials required : A-4 size papers Glue to stick the papers A pair of scissors A sheet of paper A sheet of paper each with multiplication problemExample:12 × 14 , 13 × 12 , 14 × 13 , etc.3. Activity : Take a rectangle. (It is whole, 1) Fold a rectangle vertically into halves and colour 12 of it. Fold it horizontally into 4 equal parts and colour 14 of it.The double shaded area is 18. Hence the product 12 × 14 = 18116 Acme Mathematics 6
Project Work1. Objective: To verify division by paper folding.2. Materials required : Strep of paper, string or rope A pair of scissors Glue to stick A sheet of paper each with division problemExample: Divide 15 cm by 3.3. Activity : Take a 15 cm long strep of paper. Fold it into 3 equal parts and cut it. Name each parts. Let they are A, B and CA B C Measure the length of each parts A, B and C. How long is your each pieces? Now work out the Division method.3 15 cm Does your answer tally with length of pieces you got?Acme Mathematics 6 117
EvaluationTime: 43 minutes Full Marks: 181. Binaya's Family went to ‘Dhading Bensi‘ last week. To reach Dhading Bensi they had to travel 14 part in Bolero, 34 part in Bus.(a) Which means of transportation did they use more to reach Dhading Bensi. [1](b) If the distance from home to Dhading Bensi is 32 km , Find how many distance did they travel in Bolero . [2](c) Convert the distance 34 that travel in bus in decimal. [1]2. Kumar is enrolled in a school.(a) He spent 35 part of his income in education and saves 14 of his income, find on which topic he investing more money? [2] (b) If Kumar's monthly income is Rs 60,000, find the total money he is saving. (c) Write the two places of decimal 3.572. [1]3. (a) Simplify: 34+ 56 - 78 [2] (b) There is 38 of a pizza in one box and 14 of a pizza in another box. How much pizza is there altogether ? [2](c) Write the reciprocal of: 45 [1] 4. (a) Which number should be filled in the blank space ? Write it : 37 = 49 [1](b) What is 15 part of 25? Calculate. [1](c) If the area of a rectangular field is 248.64m2 and it's length is 21 m find it's breadth. [2](d) Divide: 30 ÷ 58 [2] 118 Acme Mathematics 6
2.5 PercentageA. RevisionHaris got 90% marks in mathematics. It means he got 90 marks out of 100 full mark.2% = 2 out of 100 = 210011% = 11 out of 100 = 11100Hence, percentage is a fraction with denominator 100.If we compare any number in terms of 100, then it is percentage.2% = 2100 = 0.0211% = 11100 = 0.11Percentage is decimal number. It is hundredth of the number.B. Expressing fraction and decimal as percentageConsider the fractions 25 and 110.25 = 2 × 205 × 20 = 40100 = 40%110 = 1 × 1010 × 10 = 10100 = 10%Hence, 25 = 40% and 110 = 10%Now, Consider 0.13 and 0.070.13 = 13100 = 13% 0.07 = 7100 = 7%Hence, 0.13 = 13% and 0.07 = 7%C. Expressing percentage into fraction and decimalsConsider 80%.80% = 80 × 1100 = 0.80= 0.8Hence, 80% = 0.8I got 90% marks in Maths40% is shaded60%% is replaced by 1100Acme Mathematics 6 119
To covert fraction into percentage multiply the fraction by 100%. To covert decimal into percentage multiply the decimal by 100%. Remember:Classwork1. Express as the percentage:(a) The red colored part.(b) The blue colored part(c) The green colored part.(d) The white colored part.2. Change to percentage:(a) 3100 = (b) 7100 = (c) 11100 =(d) 9100 = (e) 20100 = (f) 25100 =3. Colour the correct one:3100 = 50%7100 = 17% 5% = 1201% = 1100 3% = 30100100100 = 100%Exercise 2.211. Write the fractions into percentage:(a) 2100 = .................. (b) 7100 = .................. (c) 50100 = ..................2. Express as percentage.(a) 0.12 = .................. (b) 0.40 = .................. (c) 0.75 = ..................3. Express as fractions.(a) 34% = .................. (b) 75% = .................. (c) 80% = ..................4. Express as decimals.(a) 18% = .................. (b) 24% = .................. (c) 4% = ..................120 Acme Mathematics 6
5. Change the following fractions as percentage.(a) 25 (b) 320 (c) 1850 (d) 14(e) 110 (f) 425 (g) 45 (h) 346. Change the following decimals as percentage.(a) 0.11 (b) 0.70 (c) 0.02 (d) 0.36(e) 0.62 (f) 0.91 (g) 0.01 (h) 0.97. Change the following percentages as fractions.(a) 20% (b) 2% (c) 60% (d) 58%(e) 64% (f) 6% (g) 90% (h) 100%8. Change the following percentages as decimals.(a) 11% (b) 33% (c) 37% (d) 1%(e) 3% (f) 99% (g) 65% (h) 100%D. Finding as Percentage(a) Expressing a given quantity as the percentage of whole quantityLook at the given examples carefully.Solved ExampleExample 1 : Express as percentage : 34 . Solution: Here, 34 = 34 × 100%= 3 × 1004 % = 3 × 25 % = 75%Hence, 34 = 75%Example 2 : Express 20 as the percent of 40.Solution: Here, 20 as the percent of 40 = 2040 × 100% = 50%Acme Mathematics 6 121
Example 3 : If 14 of the box is red, what percent of the box is red ?Solution: Here, 14 as the percent = 14 × 100%= 25%25% of the box is red.Example 4 : In the mixture of 10 litre milk, only 7 litre is pure milk. Find the percentage of water in the mixture.Solution: Here, 7 litre as the percent of 10 litre = 710 × 100%= 70%Now, percentage of water = 100% – 70% = 30%Hence, 30% of water was mixed. Total quantity is always taken as 100%. To express a given quantity as the percentage of whole quantity, convert the statement as fraction. (b) Finding the value of the given percentageLook at the given examples:Solved ExampleExample 1 : Anjali scored 90% in science. The full marks was 75. How many marks did she score ?Solution: Here, Anjali scored 90% out of 75.= 90% of 75= 90100 × 75= 67.5.Hence, Anjali scored 67.5 marks in Science.Example 2 : Calculate 25% of 200.Solution: Here, 25% of 200 = 25% × 200= 25100 × 200 = 50 25% of 200 = 50'of ' is replaced by 'x'Total amount = 100%122 Acme Mathematics 6
Example 3 : Calculate the selling price of the given ball.Solution: 15% of Rs. 600 = 15100 × Rs. 600= Rs. 90Rs. 90 is off.Now, selling price, = Rs. 600 – Rs. 90= Rs. 510Hence, the selling price of the given ball is Rs. 510.(c) Finding the quantity whose percentage is givenLook at the given examples.Example 1 : If 15% of the student is 150, find the total number of students in the school.Solution: Here, we consider 100% as the total number of student of the school.Now, 15% of the student = 1501% of the student = 15015100% of the student = 15015 × 100 = 1000Hence, the total number of student is 1000.Example 2 : In a class of 40 students, 40% are boys.(a) How many boys are there ?(b) How many girls are there ?Solution: Here, Total number of student = 4040% are boysSo, Number of boys = 40% of 40= 40100 × 40= 16(a) There are 16 boys.(b) Now, number of girls = Total students – boys= 40 –16 = 24There are 24 girls.Rs. 600 15% offAcme Mathematics 6 123
Classwork1. Find the value of:(a) 6% of 24 (b) 10% of 90 (c) 8% of 80(d) 3% of 600 (e) 25% of 1000 (f) 35% of 1502. Find the percentage:(a) 12 of 72 (b) 20 of 200 (c) Rs 48 of Rs 72(d) 2.5 m of 25 m (e) 212 ft of 700 ft (f) 9.2 cm of 100 cmExercise 2.221. Find the percentage in the following cases:(a) 15 of 75 (b) 20 of 90 (c) 24 of 96 (d) 2.5 of 10(e) 14 of 25 (f) 100 of 200 (g) 200 of 200 (h) 300 of 200(i) 13 people of 690 people (j) 50 oranges of 200 oranges(k) Rs. 15 of Rs. 7502. Calculate,(a) 5% of 50 (b) 10% of 90 (c) 7% of 70(d) 3% of 600 (e) 20% of 500 (f) 11% of 1210` (g) 30% of 640 (h) 100% of 700 (i) 26% of 2 kg(j) 40% of 4 hours (k) 616% of Rs. 1300 (l) 823% of 300 kg(m) 200% of 6 litre (n) 100% of 900 ml3. Find the total quantity whose,(a) 2% is Rs 5 (b) 12% is 120 kg (c) 7% is 49 meter(d) 25% is 600 gram (e) 1% is 10 students (f) 70% is Rs 7000(g) 1.5% is 60 hours (h) 212% is 10.124 Acme Mathematics 6
4. Calculate the 5% of the following.(a) (b) (c)Oil 5 l 25 cm 30 kg rice(d) (e) (f)500 people Rs. 750 Rs. 8,00,0005. Study the information and calculate the new selling price.(a) (b) (c)Rs. 700, 5% off Rs. 120, 7% off Rs. 1800, 10% off(d) (e) (f)Rs. 50, 2% off Rs. 8000, 15% off Rs. 8000, 9% off6. 34 of an egg's volume is water. What percent is this ?7. The human body consists of 23 water. What percent is this ? 8. I got the following marks.Maths ........ 1920 , English ........ 3750 ,Nepali .......... 60 75Help me to change the result to percentages.Acme Mathematics 6 125
9. Balram mixed water and milk daily. If the mixture is 20 litre and 20% is water in the mixture, find the quantity of pure milk in the mixture.10. In a class of 36 students, 25% are girls, (a) How many girls are there ?(b) How many boys are there ?11. Who is the first in the class?Name Sachin Nitesh Rita Kiran KrishnaFull marks 25 20 75 100 60Marks obtained 20 17 50 78 5412. Mukunda saves 45% of his income. If his income is Rs. 3600, find the saving.13. In a class of 45 children, 15 are girls:(a) How many boys are there in the class?(b) What percentage of the class are girls?(c) What percentage of the class are boys?14. 25% of a pack of oranges were bad. If 500 kg of the oranges were bad, find the number of good oranges.15. Kisu scores 68 marks in English. If full marks is 75, find her percentage.16. The population of a town is 10,000. If 52% of them are men, find the number of women.17. A school worked 220 days in a year. Bishnu was absent for 11 days. Find his attendance percentage of the Bishnu for the year.18. Hom Nath gets a monthly salary of Rs. 12000. His salary is increased by 15%. Find his new salary.19. Calculate the price of each items after discount.Festival Discount 2083 15% DiscountRs. 700 Rs. 400 Rs. 200 Rs. 1000 Rs. 500126 Acme Mathematics 6
20. Divide the amount Rs. 1,00,000 among the following persons.Father 40% Mother 20% Son 30% Daughter 10%Project WorkCollect the information about 7 families in your house nearby and complete the given chart.Head of the family Male Female Children below 10 years123456.7.TotalNow, try to find the answer of the following questions given below.(a) How many people are there all together ?(b) What percentage are male ?(c) What percentage are female ?(d) What percentage are children ?Present it in your class room.Acme Mathematics 6 127
2.6 Profit and Loss A. IntroductionLook at the picture carefully:In the figure a market is shown where things are bought and sold. The process of buying and selling the things is business.Profit and loss are terms used in business. In business, men buy things and sell them. Cost price, selling price, profit and loss are related to business. The concept of cost price, selling price and loss or profit will be clear from the given example.Birat is a book seller.He bought a text book of mathematics for Rs. 200 and sold it to a student for Rs. 220. Here, he charged the student Rs. 20 more than he has paid. In this example Rs 200 is the cost price (C.P.). Rs 220 is the selling price (S.P.) and Rs. 20 is the profit (P). The relation between C.P. , S.P and profit can be expressed as,Profit (P) = S.P – C.P. [SP > C.P.]Birat made a profit of Rs. 20 in buying and selling the text book of mathematics.What will happen if cost price is Rs. 200 and selling price is Rs. 180 ?When selling price is less than its cost price, a loss (L) is made.Loss (L) = C.P – S.P. [CP > S.P.]Solved ExampleExample 1 : Amit bought a watch for Rs. 90 and sold it for Rs. 120, find his profit.Solution: C.P of the watch = Rs. 90S.P. of the watch = Rs. 120Here, S.P. > C.P. So, profit is made.Profit = S.P. – C.P.= Rs. 120 – Rs. 90= Rs. 30His profit is Rs. 30.128 Acme Mathematics 6
Example 2 : Kundan buys a bicycle for Rs 1800 and sells it for Rs 1600 find his loss.Solution: Here, CP of bicycle = Rs. 1800SP. of bicycle = Rs. 1600 Now, Loss = CP – SP= Rs 1800 – Rs 1600= Rs 200His loss is Rs. 200.Example 3 : A man wants to make profit of Rs 15 by buying 1 dozen bananas at Rs 48. Find the selling price.Solution: Here, Profit = Rs 15Cost price = Rs 48Now, Selling price = Cost price + profit= Rs 48 + Rs 15= Rs 63.Selling price is Rs. 63.Exercise 2.231. Fill in the blanks:Selling price Cost price Profit(a) Rs 800 Rs. 500 .....................(b) Rs. 1000 ...................... Rs. 100(c) Rs. 1200 Rs. 800 ....................(d) ............................ Rs. 400 Rs. 50.582. Fill in the blanks:Selling price Cost price Loss(a) Rs. 100 Rs. 120 .......................(b) Rs. 900 Rs. 1000 .......................(c) Rs. 11.50 ...................... Rs. 5.07(d) .................. Rs. 400 Rs. 17.75Profit and Gain are same.Acme Mathematics 6 129
3. A table is made at a cost of Rs. 700, what is the profit, if it is sold for Rs. 1000 ?4. Robin bought 5 apples for Rs. 50 and sold each apple at the rate of Rs. 12, how much did he gain ?5. Sabin bought 1 dozen pen at the rate of Rs. 35 per pen and sold at the rate of Rs. 40 per pen. Find his total profit.6. Six pens are bought for Rs. 180 and sold for Rs. 35 each. Find the total profit.7. Nabin bought 6 quintals of sugar at the rate of Rs. 75 per kg and sold at the rate of Rs. 74 per kg, find his loss.8. The selling price of a TV is Rs. 12500 and loss is Rs. 600 find the cost price of the TV.9. If loss is Rs 200 and cost price Rs. 900, find its selling price.10. Ram bought a radio for Rs. 1550 and sold it at a profit of Rs. 315, find its selling price.11. A greengrocer bought 10 kg orange at the rate of Rs 80 per kg and sold them at a profit of Rs. 243. Find the selling price of 10 kg of orange.12. Shyam bought a cassette player for Rs. 1400 and sold it at a loss of Rs. 374. Find its selling price.Project WorkList 5 things from the nearest market. Ask their buying price and selling price to the shopkeepers and calculate their profit or loss and present it to your class room.Items Cost price (in Rs.) Selling price (In Rs.) Profit or Loss (in Rs.)1. 2.3.4.5.130 Acme Mathematics 6
2.7 Unitary Method IntroductionStudy the given information carefully.Total cost Rs. 75 It's cost Rs.It's cost Rs. 50 Total cost Rs. We can find the cost of one thing when cost of more things is given. We can find the cost of more things when cost of one thing is given.A. Cost of 1 thingGuess the cost of 1 eraser.Total cost Rs. 25 It's cost Rs.Here, Total cost = Rs. 25Number of erasers = 5Cost of 1 eraser is less.One eraser costs = Rs. 25 ÷ 5= Rs. 5Acme Mathematics 6 131
When cost of more things is given, we can find the cost of one thing by dividing the total cost by number of things. This method is called the unitary method.Value of 1 thing = Total costNo. of thingsB. Cost of more thingsGuess the cost of 5 erasers.Cost Rs. 5 Total cost Rs.Here, Cost of one eraser is Rs. 5Number of erasers is 5.Cost of 5 erasers is more. Cost of 5 erasers = 5 × Rs. 5 = Rs. 25.Value of more things = number of things × cost of one thingExample 1 : If the cost of a pen is Rs. 25. Find the cost of 4 such pens.Solution: Here, Cost of 1 pen = Rs. 25Cost of 4 pens = Rs. 25 × 4 = Rs. 100The cost of 4 pens is Rs. 100Example 2 : If the cost of 5 pencils is Rs. 30, find the cost of 1 pencil.Solution: Here, The cost of 5 pencils = Rs. 30The cost of 1 pencil = Rs. 30 ÷ 5 = 305= Rs. 6Thus, the cost of 1 pencil is Rs. 6.Dividing 5) 30 (6 – 30 ×132 Acme Mathematics 6
Classwork1. Fill in the blanks.A book costs Rs. 100Number of books 2 3 4 5 6 7Cost of books (Rs.)2. Match the following.Rs. 5Rs. 50Rs. 30Rs. 10Rs. 10Rs. 20Rs. 60Rs. 103. Solve the following problems.(a) If 1 chocolate costs Rs. 15, find the cost of 5 such chocolates.(b) If 1 hen is 2 kg. Find the weight of 8 such hens.(c) If 1 radio cost Rs. 200, find the cost of 5 such radios.(d) If 5 caps cost Rs. 500, find the cost of 1 such cap.(e) If 6 books cost Rs. 900, find the cost of 1 such book.(f) If 10 cows give 80 litres of milk, find the milk given by a cow.Acme Mathematics 6 133
4. The cost of a book is Rs. 200, find the cost of:(a) 3 books (b) 5 books (c) 10 books5. A tray contains 30 eggs, how many eggs are contained in(a) 7 trays (b) 10 trays (c) 20 traysExercise 2.241. The cost of 30 eggs is Rs. 450, find the cost of,(a) 1 egg (b) 3 eggs (c) 7 eggs2. Solve the following word problems carefully.(a) There are 14 benches in a class room, how many benches are there in 10 such class rooms?(b) Kabir spends Rs. 600 in 2 months for 'Khaja'. How much does he spend in 6 months?(c) There are 500 questions in 5 books. How many questions are there in 2 such books?(d) 30 children sit in 10 benches, how many children sit in 6 such benches?(e) Narayan Kazi paid Rs. 400 for 5 kg mangoes. How much did he pay for 7 kg of the mangoes?134 Acme Mathematics 6
A. Finding the unit cost and total costLook at the given figures carefully.Rs. 400 Rs. 2000(i) The cost of one T-shirt is Rs, 400.(ii) The cost of 5 T-shirt is Rs. 2000.If the cost of 1 T-shirt is Rs 400, what will be the cost of 4 T-shirt ? Here, Cost of 4 T-shirt = 4 × cost of 1 T-shirt= 4 × Rs 400= Rs 1600.Thus, the cost of 4 T-shirt is Rs 1600. The cost of 5 T-shirt is Rs 2000. Find the cost of 2 T-shirt ?Here, Cost of 5 T-shirt = Rs 2000Cost of 1 T-shirt = Rs 20005 = Rs 400Cost of 2 T-shirt = Rs 400 × 2 = Rs. 800Thus, the cost of 2 T-shirt is Rs 800. If the cost of 1 item is known, we can find the cost of total items.Total cost = Number of items × cost of 1 item If the cost of total items is known, we can find the cost of 1 item.Cost of 1 item = Total costNumber of itemsThe method of finding value by finding first, the value of unit quantity by division and then the value of the required quantities by multiplication is called the unitary method.Acme Mathematics 6 135
Solved ExampleExample 1 : If 1 boy can consume 500 gram of rice in a day, how much will 12 such boys consume in a day ?Solution: Here, 1 boy consume = 500 gramNumber of boys = 12Now, 12 boys will consume = 500 gram × 12 = 6000 gram = 6 kg. Hence, 12 boys consume 6 kg of rice in a day.Example 2 : If the cost of 5 balls is Rs 1500, find the cost of 3 such balls.Solution: Here, Total balls = 5Now. Cost of 1 ball = Total cost No. of balls = Rs 15005 = Rs. 300Cost of 3 balls = Rs 300 × 3 = Rs. 900Hence, cost of 3 balls is Rs. 900.ClassworkLook at the following goods and their price list.Rs. 15 Rs. 80 Rs. 10Rs. 20 Rs. 15 Rs. 8 Now, complete the table.Name of goods Unit price Cost of 5 unitsSoapOilChocolateBiscuitMilkEgg136 Acme Mathematics 6
Exercise 2.251. Look at the pictures and complete the table. (Here total cost is given).Rs. 20 Rs. 60 Rs. 300 Rs. 300Name of goods Number of goods Total cost Unit cost2. Complete the table:Unit cost Total cost Number of goodsRs 5 Rs 100Rs 15 Rs 150Rs 20 Rs 100Rs 18 Rs 903. If 1 m of cloth cost Rs 72, how much will 13 m of such cloth cost ?4. A text book has 215 pages. How many pages will 8 such text books have ?5. If the cost of 2 pen is Rs 60, find the cost of 15 such pens.6. A car travels 90 km in 1.5 hour. How far does it travel in 8 hours.7. A worker earns Rs 4000 in 5 days. How much will he earn in 2 days? 8. 10 bags of cement cost Rs 5884. Find the cost of 3 bag of such cement.9. If a dozen of bananas cost Rs 48, find the cost of such 4 banana.10. A packet of chocolate cost Rs 348.25. If a packet contains 25 pieces, find the cost of 10 chocolate.Acme Mathematics 6 137
11. Choose the cheaper shop.SHOP-A5 kg Sugar = Rs. 3106 kg Dal = Rs. 64010 Eggs = Rs. 60SHOP-B7 kg Sugar = Rs. 4554 kg Dal = Rs. 4405 Eggs = Rs. 3512. List 5 things from the nearest market. Ask their selling price and calculate the selling price of the 7 such selected items and discuss with your friends.B. Problems based on unitary methodStudy the given time and distance travelled by the car.Time 4:00 am 5:00 am 6:00 am 7:00 am 8:00 amDistance travelled 0 km 60 km 120 km 180 km 240 kmYou can see that as time increases, the distance travelled also increases.If there is an increase or decrease in one, there is a corresponding increase or decrease in another is called direct variation. It is a kind of unitary method.Solved ExampleExample 1 : The cost of 7 pens is Rs 210. Find the cost of 15 pens.Solution: Here, Cost of 7 pens = Rs 210So, Cost of 1 pen = Rs 2107= Rs 30Now, Cost of 1 pen = Rs 30Cost of 15 pens = Rs 30 × 15 = Rs 450Hence, the cost of 15 pens is Rs 450.First, find the cost of 1 pen then find the cost of 15 pens.138 Acme Mathematics 6
Example 2 : If a water pipe can fill a 1000 litre tank in 4 hours, in how much time will it fill 12 of the tank ? Solution: Here, 12 of the tank = 12 × 1000 litre = 500 litres.Now, 1000 litre = 4 hours.1 litre = 41000 hours.500 litre = 4 × 500 1000 hours = 2 hours.Hence, 12 of the tank will fill in 2 hours.ClassworkComplete the table:Name of goodsCost of 2 unitsCost of 1 unitCost of 4 unitsCost of 10 unitsTT ball Rs. 10 ................... ................... ...................T-shirt ................... Rs. 400 ................... ...................T-table ................... ................... Rs. 4000 ...................T.V ................... ................... ................... Rs. 40,000Exercise 2.261. 25 copies cost Rs 750, find the cost of 20 copies.2. If 10 marbles cost Rs 20, find the price of 24 marbles.3. If 6 cups of tea costs Rs 60, how many cups of tea can be bought for Rs 150 ?4. A car needs 54 liters of petrol to cover a distance of 648 km. How many kilometers will it cover with 10 liters of petrol ?Acme Mathematics 6 139
5. Dilmaya earns Rs 18000 in 15 months. How much does she earn in 10 months ? 6. If there are 10 chairs in a room, how many chairs will be there in 12 such room ?7. A bus travels at a uniform speed and it covers 435 km in 12 hours. Find how many kilometers will it travel in 5 hours ?8. Krishna's income per year is Rs 4,32,000. Find his income in 9 months and 15 months.9. I paid Rs 415 for 5 kg of sugar.(a) How much do I have to pay for 50 kg of sugar ?(b) How much do I have to pay for 12 kg of sugar ?10. If 34 of the bag is 40 kg, find the weight of 13 of the bag.11. 13 part of the land is 5 'Bigaha'. Find the 34 part of the land.Project WorkGo to the market near by and ask the shopkeeper about selling price of 7 different goods and complete the given chart.Goods Selling price (in Rs.) of 1 goodSelling price (in Rs.) of 5 goodsSelling price (in Rs.) of 30 goods1. a pair of shoes 1050 5250 Profit : Rs. 31500234567Present it to your class room.140 Acme Mathematics 6
Mixed Exercise1. Anjali has bought 12 pens for her children from stationery costing Rs. 1200 (a) What was the cost of one pen? (b) If a shopkeeper made a profit of Rs. 96 by selling 12 pens, how much had the shopkeeper paid for buying one pen?(c) If Anjali gave 6 pen out of 12 pens to her daughter, what would be the percentage allocated to her son and daughter?(d) If 50% of the total pen had been given to a daughter, how many more or less pen would she get?2. Sita has bought 12 biscuits for her children costing Rs. 600.(a) What is the cost of one biscuit?(b) If a shopkeeper made a profit of Rs. 50, what is the cost price for shopkeeper?(c) If Sita gave 25% of biscuits to her son then how many biscuits does she give?3. A road is 2 km long. It is under construction.(a) 500 meter was completed yesterday. How long road is not complete?(b) How much percent is left to complete?(c) If 100 workers can complete 1000 m in 100 days, how many worker are needed to complete the remaining road in 10 days?(d) Calculate the total number of workers to complete the construction in 100 days.4. Do the following.(a) Calculate 20% of Rs. 200.(b) If 10 pens cost Rs. 300, calculate the cost of 6 such pens.(c) If shopkeeper sells 10 pens for Rs. 375, find his profit.(d) I bought a pen for Rs 28, find the loss of shopkeeper.5. There are 500 students in a hostel. 60% of them are boys.(a) Write the percent of girls.(b) Find the number of boys.(c) Find the number of girls.(d) If 500 kg food is needed for hostel per day. How much kg of food will each students get?6. Ritesh bought a laptop for Rs. 49,000 and sold it at 10% profit. Acme Mathematics 6 141
(a) Calculate 10% of Rs. 49000. (b) Write the profit amount.(c) Calculate the selling price.(d) Calculate the cost price of 2 such laptop.7. (a) Express: 320 as percentage (b) Calculate 20% of 100 paisa.(c) Divide Rs. 500 among A, B and D as share of A, 20%, share of B, 30% and share of D, 50%.(d) If the cost of 1 pen is Rs. 20, find the cost of 5 such pens.8. Study the given figure alongside.(a) Calculate the percent of apples.(b) What percentage are footballs.(c) A dozen pencils are bought for Rs. 70 and each are sold for Rs. 5.50. Find the loss or profit.(d) Calculate the profit when SP = Rs. 5 and CP = Rs. 39. (a) Calculate the loss when CP = Rs. 19 and SP = Rs. 16(b) If 10 cows give 50 litre of milk per day, find the litre of milk per cow per day.(c) If 6 cups of tea cost Rs. 75, how many cups of tea can be bought for Rs. 312.50 ?10. Study the rate of items in the Shop - A and Shop - B.SHOP - A SHOP - BMENU RATEMo:Mo Rs. 120/plateChaumin Rs. 100/platePencil Rs. 10Copy Rs. 20Exercise book Rs. 100(a) Urmela has 500 rupees. She spent 120 rupees to eat mo:mo and 100 rupees to buy exercise books. How much money is left with her?(b) Sabita brought 5 pencils from shop B and she gave a Rs. 100 note to the shopkeeper for the payment. How much rupees did the shopkeeper return to her?(c) Find the total cost of 3 copies, 2 plates mo:mo and 3 pencils.(d) Find the cost of 5 plates of chaumin.142 Acme Mathematics 6
EvaluationTime: 45 minutes Full Marks: 191. (a) Rita bought 10 pens for Rs. 100 and she sold it for Rs. 150. (i) What was the cost of one pen? [1] (ii) Find the profit percent. [2](b) The cost of 3 copies is Rs. 270. How much will 5 copies cost? [2] 2. Sumina bought 15 copies for her children at Rs. 1500 in total.(a) Find the cost of 1 copy. [1](b) If the shopkeeper makes Rs. 150 profits while selling 15 copies then find his selling price. [1](c) If she gave 6 copies to her son then what percentage of copies did she give to her son and daughter. [2](d) If she gave 60% of copies to her son how many more copies did her son get than before ? 3. A shopkeeper bought a watch for Rs 1500 and sold it for Rs 1250. (a) Write the formula for finding loss amount. [1](b) Find the profit or loss amount. [2](c) 1 dozen of pencils costs Rs 96. (i) Find the cost of 1 pencil. [1](ii) Find the cost of 27 pencils. [1]4. Ram has bought 5 books for Rs 500.(a) What was the cost of one book. [1] (b) If a shopkeeper made a profit Rs 50 by selling 5 books, how much had the shopkeeper paid for buying one book? [1](c) If Ram gave 3 books out of 5 books to his friend Hari, what would be the percentage allocated to his friend? [2](d) If Ram has bought 7 books, how much money is required ? [1]Acme Mathematics 6 143
3UNIT Mensuration1. Fill in the blanks.(a) Perimeter of the given triangle is .................. cm.(b) Perimeter of the given square is .................... cm.(c) Perimeter of the given quadrilateral is ............ cm.(d) Which figure is bigger in area?Figure ..................... is bigger.2. Study the given figures, and fill in the blanks.(a) Area of the figure A is.......... cm2.(b) Area of the figure B is .......... cm2.(c) Area of the figure E is .......... cm2.(d) Area of the figure C is .......... cm2.(e) Area of the figure D is .......... cm2. (f) Which figures are bigger than B ?3. Find the volume of the following solids.V = ................. cm3 V = ............... cm3 V = ............... cm3A BC3 cm4 cm2 cm2 cm 2 cm2 cm2 cm5 cm3 cm4 cm2 cmA B1 cm2EA CB DWarm Up Test144 Acme Mathematics 6
scale in inchscale in centimeter (cm) How long is your scale? It is 15 centimeter (cm) long. It is 6 inches (In.) long. How far is your school from your home ?• Can you guess in cm. ? • Can you guess in inches ? Which unit is used for measuring the long distance ?• The length of the space between two points is called distance.• We use different units to measure the length or distance. 10 mm = 1 cm 12 inches = 1 feet 1 inch = 2.54 cm100 cm = 1 m 3 feet = 1 yard 1 m = 39.37 inches1000 m = 1 km 1760 yard = 1 mile 1 feet = 30.48 cm1 feet = 0.3048 mMeters to Feet Conversion Scale00 1010ftm20 30 5 15 255A. Conversion of Inch and centimeterWe can convert one unit to the other units. To convert: We use given relation and unitary method.3.1 DistanceAcme Mathematics 6 145
Now study the given examples.Solved ExampleExample 1 : Convert 10 inches to the centimeter.Solution: From the above table, we have the following relation.1 inch = 2.54 cmor, 10 inches = 10 × 2.54 cmso, 10 inches = 25.4 cmExample 2 : Convert 30.48 centimeter to the inches.Solution: From the above table, we have the following relation.2.54 cm = 1 inchor, 1 cm = 12.54 inchor, 30.48 cm = 12.54 × 30.48 inchso, 30.48 cm = 12 inchB. Conversion of feet and centimeterNow study the given examples.Example 3 : Convert 2 feet to the centimeter.Solution: From the above table, we have the following relation. 1 feet = 30.48 cmor, 2 feet = 2 × 30.48 cmso, 2 feet = 60.96 cmExample 4 : Convert 90 centimeter to the feet.Solution: From the above table, we have the following relation.30.48 cm = 1 feetor, 1 cm = 130.48 feet or, 90 cm = 130.48 × 90 feetso, 90 cm = 2.95 feet146 Acme Mathematics 6
C. Conversion of inch and meterNow study the given examples.Example 1 : Convert 80 inches to the meter.Solution: From the above table, we have the following relation.39.37 inches = 1 mor, 1 inches = 139.37 mor, 80 inches = 139.37 × 80 mso, 80 inches = 2.032 mExample 2 : Convert 3.48 meter to the inches.Solution: From the above table, we have the following relation.1 m = 39.37 inchesor, 3.48 m = 3.48 × 39.37 inchesso, 3.48 cm = 137 inchesD. Conversion of Feet and MeterNow study the given examples.Example 1 : Convert 4 feet to the meter.Solution: From the above table, we have the following relation.1 feet = 0.3048 mor, 4 feet = 4 × 0.3048 mso, 4 feet = 1.2192 mExample 2 : Convert 9 meter to the feet.Solution: From the above table, we have the following relation.0.3048 m = 1 feetor, 1 m = 10.3048 feetor, 9 m = 10.3048 × 9 feetso, 9 m = 29.53 feet10 m35 ft30 ft8 m6 m4 m2 m25 ft20 ft15 ft10 ft5 ftAcme Mathematics 6 147
E. Conversion of Inch and feetNow study the given examples.Example 1 : Convert 120 inches to the feet.Solution: From the above table, we have the following relation.12 inch = 1 feetor, 1 inch = 112 feet or, 120 inches = 112 × 120 feetso, 120 inches = 10 feetExample 2 : Convert 1.48 feet to the inches.Solution: From the above table, we have the following relation.1 feet = 12 inchor, 1.48 feet = 12 × 1.48 inchso, 1.48 feet = 17.76 inchNote: We write 2 feet and 4 inches as 2’4’’.Classwork1. Fill in the blanks.1 m = ........ cm 2 feet = ........ inches 24 inch = ........ feet1 cm = ........ mm 6 feet = ........ yard 100 mm = ........ cm1 km = ........ m 1 mile = ........ yard 1 feet = ........ cm2. Match the followingInches Feet and inches84 14’7’100 7’7”175 16’98 8’4”148 Acme Mathematics 6
Inches Feet and inches91 12’192 8’2”144 7’3. Fill in the missing number(a) 1 feet = ……inches (b) 200 cm = ……m(c) 6 feet = ……. yard (d) 1 mile = ……..yard(e) 4 yard = …..feetExercise 3.11. The height of 5 students are given below Kushal Kamal Sonika Bindu Manju168 cm 140 cm 150 cm 125 cm 155 cmExpress the height in inches.2. Complete the table.(a)Feet 5 7 12 15 20 25 50 100 200Meter(b)Meter 1 3 5.5 10 11 17 20 30 100Feet3. Convert given feet into the centimeter and vice-versa.(a) 2 ft (b) 15 cm (c) 1.3 ft (d) 30 cm(e) 75 cm (f) 2.5 ft (g) 90 cm (h) 3.3 ft4. Convert given meter into the inch and vice-versa.(a) 1 m (b) 100 inches (c) 1.4 m (d) 2.3 inches(e) 3.5 m (f) 25 inches (g) 9 m (h) 13.3 inches5. Measure the height of your 5 friends in the classroom and complete the given table.Acme Mathematics 6 149
Name Height(cm)Height(m)Height(inch)Height(feet)1.2.3.4.5.6. A rectangular field is 600 ft 10 inch long and 200 ft 6 inch broad.(a) Express the length in meter.(b) Express the breadth in meter.(c) How long is its length than its breadth in meter.7. A wall is 900 m 60 cm long. Another wall is 900 ft 10 inch long.(a) Express both length in meter.(b) Express both length in feet.(c) Calculate the total length of wall in feet.8. A road 6788 m 50 cm long is to be constructed. 1950 ft 11 inch is constructed by local people. (a) How much long road is constructed by local people? Find out in meter.(b) How long road is left to construct? Find out in meter.(c) How long is road in feet?150 Acme Mathematics 6