84651_VI - 70_222310048-VISA-STUDENT-WORKBOOK-MATHEMATICS-G05-PART2_CompressPdf

................................................................................. ................................................................................. 10.2 I Explore (H.O.T.S.) Short Answer Question 21) Multiply: a) 4 , 8 , 9 b) 3 , 7 ,13 , 3 898 4 4 3 13 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) Multiply the following: a) 5 , 9 , 7 b) 6 , 4 , 6 , 7 c) 3 , 7 , 2 , 3 d) 4 , 3 , 5 979 5576 4432 353 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Fractions - II 47

................................................................................. ................................................................................. ................................................................................. ................................................................................. Concept 10.3: Reciprocals of Fractions 10.3 I Recall Multiple Choice Questions 1) If 9 × 4 = 36, then 36 ÷ 9 is __________________. [] [] (A) 1 (B) 36 (C) 9 (D) 4 [] 2) If 63 ÷ 9 = 7, then 9 × 7 is __________________. (A) 13 (B) 63 (C) 9 (D) 7 3) Multiplication and _____________________ are inverse operations. (A) division (B) addition (C) subtraction (D) sum 10.3 I Remember and Understand Multiple Choice Questions 4) The only number that does not have a multiplicative inverse is __________________. [ ] ] (A) 0 (B) 1 (C) 3 (D) 2 ] 5) The reciprocal of 1 is __________________. [ (A) 2 (B) 0 (C) 3 (D) 1 6) The reciprocal of a mixed fraction is ______________ fraction. [ (A) an improper (B) a proper (C) a mixed (D) like Fill in the Blanks 7) The reciprocal of a proper fraction is a(n) ______________________ fraction. 8) Fractions are reduced to their lowest terms before finding their ______________________. 48

9) The reciprocal of 6 is __________. 7 Very Short Answer Questions 10) Find the reciprocal of the fraction 1 . 7 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Find the reciprocal of the fraction 5 . 14 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) Find the multiplicative inverse of 3. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Find the reciprocals of: a) 3 b) 1 1 4 6 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 14) Find the reciprocals of: a) 2 b) 9 2 8 7 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Fractions - II 49

Long Answer Questions b) 3 2 c) 24 1 d) 64 15) Find the multiplicative inverses of: a) 4 1 7 3 5 9 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 16) Write the multiplicative inverses of: a) 4 b) 2 c) 46 5 d) 0 26 36 8 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 10.3 I Apply Short Answer Questions 17) Solve: 1 ÷ 2 79 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 18) Solve: 5 ÷ 7 68 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Fractions - II 51

Long Answer Questions 19) Shyam had 7 litres of water. He poured it equally into 3 glasses. How many litres of water 2 are there in each glass? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) A book shelf is 42 inches long. Each book on the shelf is 7 inches wide. How many books 6 will fit on the shelf? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 10.3 I Explore (H.O.T.S.) Short Answer Question 21) If 6 chocolates are broken into quarters, how many chocolate pieces do we get? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. 52

................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) a) R eena took 5 bread slices from a packet of 30 bread slices. She cut each of them into two equal pieces. What is the fraction of 4 such pieces of the whole packet? b) There is 15 litres of milk in a can. Raj poured it equally into 5 glasses. What is the 25 quantity of milk in each glass? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Fractions - II 53

Practice Questions 1) Add the following mixed fractions. a) 8 1 + 6 5 b) 4 8 + 7 4 c) 3 5 and 8 5 98 15 9 13 13 2) Add the following: a) 5 and 5 3 b) 10 7 and 17 c) 114 and 74 78 9 19 15 75 3) Add the following mixed fractions. a) 13 + 12 and 5 1 b) 5 4 + 5 2 and 4 c) 1 and 3 2 + 1 3 55 3 75 35 6 11 22 4) Subtract the following mixed fractions. a) 7 1 from 10 1 b) 5 1 from 5 7 c) 5 23 from 115 9 18 6 12 30 6 5) Subtract 1 from the following mixed fractions. d) 512 a) 2 1 b) 2 7 c) 1 1 13 19 111 101 d) 5 1 6) Subtract 5 1 from the following mixed fractions. 4 4 a) 6 1 b) 3 2 c) 5 1 9 23 2 7) Multiply the following fractions. a) 5 × 8 b) 9 × 6 c) 20 × 2 d) 3 × 5 7 11 19 7 21 5 7 12 8) Multiply the following fractions. a) 9 × 12 b) 11 × 11 c) 15 × 3 d) 10 × 5 17 13 5 61 9) Multiply the following mixed fractions. a) 2 1 and 11 b) 7 1 and 2 1 c) 12 and 3 5 95 62 36 54

10) Multiply the following fractions. Find the missing numerator/denominator. a) 15 × 4 = [ ] b) [] × 6 = 42 9 72 12 84 [ ] [ ] [ ]× 2 = 34 d) 3 ×[ ] = 24 c) [ ] 5 65 7 [ ] 49 11) Find the reciprocal of the following fractions. a) 10 b) 22 c) 8 d) 7 1 19 3 2 12) Multiply the following fractions. a) 1 and reciprocal of 1 9 18 b) reciprocal of 7 1 and 7 62 c) reciprocal of 5 2 and reciprocal of 9 5 36 13) Add the following fractions. a) 7 and reciprocal of 3 98 b) reciprocal of 3 1 and 7 4 13 c) reciprocal of 2 and reciprocal of 5 3 11 14) Subtract the following fractions from their reciprocals. a) 1 b) 2 c) 7 d) 1 2 7 11 4 15) Find the value of: a) 2 1 of 11 b) 12 of 7 c) 2 of 11 d) 13 of 11 98 11 3 13 143 16) Solve the following fractions. c) 5 ÷ 1 d) 49 ÷ 7 7 17 9 a) 4 1 ÷ 6 1 b) 24 ÷ 6 98 11 Fractions - II 55

17) Solve the following fractions. Find the missing numerator/denominator. a) 5 ÷ 10 = 30 b) [ ] ÷ 6 = 42 c) [ ] ÷ 2 = 15 d) 3 [ ] = 24 9 [] 90 7 30 [ ] 5 24 7 ÷[ ] 49 5 18) Find the multiplicative inverse of the following fractions. a) 19 b) 2019 c) 101 d) 9 2 17 2018 3 19) Solve the following: a) 7 ÷ reciprocal of 3 98 b) reciprocal of 3 1 ÷ 7 4 13 c) reciprocal of 2 ÷ multiplicative inverse of 5 3 11 d) 6 ÷ multiplicative inverse of 6 11 11 20) Raju painted 5 2 of a classroom and Raheem painted 6 1 of the same room. What 32 part of the room did they paint together? 21) 3 1 of a bucket is filled with water. 7 3 of the same bucket is empty. Find the total 44 capacity of the bucket in litres. 22) Maya’s family consumed 12 1 kg rice from a 25 kg bag. How many kilograms of rice 2 remain in the bag? 23) Swetha’s mother wanted to tie a rope between two poles. The distance between the poles is 211 metres. She needs 3 more metres for tying it around the poles. She has 44 a rope that measures 13 1 metres. By how many metres is the rope shorter than the 2 required length? 24) A carpenter needs 13 metres of wood to make a leg for a table. If each table has 4 4 legs, what is the total length of the wood needed to make legs for 5 tables? 56

25) Nupur’s mother needs 7 1 litres of water for every 3 3 kg of flour to prepare cattle feed 24 for their buffaloes. How many litres of water does she need for 15 kg of flour? 26) A farmer bought 15 water pipes. Each pipe is 12 1 ft long. Find the total length if all the 4 pipes are connected together. 27) Maya is preparing a project for the summative assessment. She has a ribbon that is 300 cm long. She needs two short pieces, one which is 15 1 cm and the other is 2 81 cm. If she cuts 12 pieces of each type from the ribbon, what part of the ribbon is 4 left? 28) Four students are playing a game. The first student tells a fraction to the second one. The second student will add 1 to the reciprocal of the fraction and tells the result to the third. The third student repeats the process carried out by the second student and tells the result to the fourth one. What result will the fourth student get, if the first one’s fraction is 3 ? 5 29) A milkman wants to pour 25 1 litres milk into bottles. If the capacity of each bottle is 2 11 litres, how many bottles will he need? 2 30) The cost of 1 kg potatoes is 36 1 rupees. What is the cost of 15 1 kg potatoes? 22 31) There are 225 students in a hostel. They consume 67 1 litres of milk every day. What 2 quantity of the milk does each student consume? Fractions - II 57

Chapter Decimals - I 11 Concept 11.1: Like and Unlike Decimals 11.1 I Recall Multiple Choice Questions 1) A number with one decimal place is written as a fraction having ______ [] as the denominator. [] [] (A) 2 (B) 0 (C) 10 (D) 100 2) A number with two decimal places is written as a fraction having ______ as the denominator. (A) 2 (B) 1 (C) 10 (D) 100 (B) 6.5 3) 56 = ______ (C) 5.06 (D) 0.56 100 (A) 5.6 11.1 I Remember and Understand Multiple Choice Questions 4) The first place to the right of the decimal point is called the ________________. [ ] (A) hundredths (B) tenths (C) thousandths (D) zero 5) In the number 435.12, the digit in the hundredths place is ________________. [] (A) 4 (B) 5 (C) 1 (D) 2 6) The digit in the tenths place of 102.104 is ________________. [] (A) 2 (B) 4 (C) 1 (D) 10 Fill in the Blanks 7) Decimal numbers having an equal number of decimal places are called ______________ decimals. 58

8) The decimal form of 5569 is ______________. 1000 9) Decimal numbers having equal values are called _______________ decimals. Very Short Answer Questions 10) In the number 308.205, which digit is in the thousandths place? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) What is the place value of 8 in 87.54? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) In 0.53, which digit is in the hundredths place? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Write the numbers 255.67 and 31.03 in the decimal place value chart. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 14) Convert the following unlike decimals into like decimals. a) 38.6, 13.72, 29.02, 65.203 b) 49.091, 76.1, 30.28, 18.49 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 15) Write the expanded forms of the given decimals. Express these decimal numbers in words. a) 445.34 b) 23.456 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decimals - I 59

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 16) Write the digits in the tens, ones, tenths and hundredths places of the following numbers. a) 72.5 b) 75.05 c) 12.89 d) 99.271 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 11.1 I Apply Short Answer Questions 17) 55 of the 100 staff members of a school are teachers. Express the fraction of the number of teachers in the decimal form. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

................................................................................. ................................................................................. ................................................................................. ................................................................................. 18) Reva has 1000 dairy milk chocolates out of which she distributed 276 chocolates. Express in decimal form, the fraction of chocolates that Reva distributed. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 19) The weights of apples, chickoos and watermelons that Kamla bought are 2343 g, 4123 g and 8902 g respectively. Express the weight of each type of fruit in kilograms. Also, find their total weight in grams. How many kilograms of fruit did Kamla buy in all? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) Yamini has 280 cm of rope and Amar has 164 cm of rope. How many metres of rope does each of them have? What is the total length of the rope? Give your answer in metres. Decimals - I 61

Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 11.1 I Explore (H.O.T.S.) Short Answer Question 21) Out of 100 people, 28 people travelled by bus and 31 travelled by train. Find the fraction of people who travelled by bus and train. Express the fractions in the decimal form. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) 58 out of 100 students in a class play football and the rest play cricket. Express the number of students playing football and cricket as fractions and also in their decimal equivalents. Write the decimals in the place value chart. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. 62

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Concept 11.2: Compare and Order Decimals 11.2 I Recall Multiple Choice Questions 1) The pair of unlike decimals is ________________. [] [] (A) 12.03, 45.62 (B) 1.24, 9.84 (C) 13.9, 32.82 (D) 132.7, 289.6 [] (D) 63.10 2) The decimal equivalent to 63.1 is ________________. (D) 125.05 (A) 6.31 (B) 0.631 (C) 631 3) The decimal equivalent to 12.5 is ________________. (A) 12.50 (B) 12.05 (C) 1.25 11.2 I Remember and Understand Multiple Choice Questions 4) Compare 3.4 and 4 using >, < or =. [ ] (D) Both (A) and (C) ] (A) < (B) > (C) = ] [ 5) Which of the following statements is true? (D) 9.8 > 8.9 (A) 2.3 > 3.2 (B) 1.4 < 0.1 (C) 1.5 > 5.1 [ (D) Both (B) and (C) 6) Compare 5.60 and 5.64 using >, < or =. (A) > (B) < (C) = Fill in the Blanks Put the correct sign >, < or = in the blanks. 7) 15.94 ____ 15.49 Decimals - I 63

8) 8.01 ____ 8.10 9) 99.9 ____ 99.90 Very Short Answer Questions 10) Arrange the decimal numbers in ascending order: 2.01, 2.001, 1.02 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Compare 54.3 and 5.43. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) Which is greater, 7.03 or 7.30? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Find the greater number in the following pairs of decimals. a) 755.33 and 255.33 b) 26.79 and 26.798 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. 14) Arrange the following decimal numbers in the ascending and descending orders. 30.24, 30.5, 30.63, 30.191 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 15) Compare the following pairs of decimals using >, < or =. a) 405.68 and 405.681 b) 345.66 and 342.66 c) 46.296 and 47.296 d) 119.487 and 118.486 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 16) a) Arrange the decimal numbers in the descending order: 51.147, 51.32, 51.6, 51.940 b) Convert these unlike decimals into like decimals: 72.5, 560.635, 5, 64.7 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Decimals - I 65

11.2 I Apply Short Answer Questions 17) The price of sugar is ` 29.50 per kg and that of 2 kg of rice is ` 58. Which item costs more than the other? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. 18) One student weighs 35.53 kg and another student weighs 35.532 kg. Which one is heavier than the other? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 19) Ali arranged four wooden boards of lengths 4.5 m, 4.52 m, 4 m, and 4.505 m from the longest to the shortest and vice versa. What are Ali’s orders of the boards? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 66

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) Kishan wrote down the lengths of a few sticks as 32.40 cm, 23.124 cm, 23.523 cm and 65.763 cm. He arranged the sticks from the shortest to the longest. He also arranged them in the other way. Find the longest and the shortest lengths of sticks. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 11.2 I Explore (H.O.T.S.) Short Answer Question 21) The heights of six students standing in a line from the shortest to the tallest are 1.22 m, 1.28 m, 1.35 m, 1.40 m, 1.48 m, and 1.50 m. Raju is the seventh and the last student to stand in the line. What should be his height? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decimals - I 67

................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) a) Six students were running a race. The time taken by the first five students to reach the finish line are 1.6 min, 1.62 min, 1.67 min, 1.65 min, and 1.71 min. A rrange their timings in ascending order. What should be the time taken by the last runner to reach the finish line? b) Sulekha purchased a few items that cost ` 21.61, ` 20.70, ` 22.84, ` 22.91 and ` 20.80. What are the costs of the objects with the least and the highest amounts? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Concept 11.3: Add and Subtract Decimals 11.3 I Recall Multiple Choice Questions 1) Which of the following pairs represents like decimals? [ ] (D) 132.7, 289.656 (A) 72.03, 53.70 (B) 1.24, 9.8 (C) 13.9, 32.82 68

2) 75.32 and 96.44 are _____________________ decimals. [] [] (A) equivalent (B) like (C) unlike (D) equal (D) all of these 3) An equivalent decimal of 46.600 is __________________. (A) 46.6 (B) 46.60 (C) 46.6000 11.3 I Remember and Understand Multiple Choice Questions 4) 200.011 + 200.022 = ________ [] [] (A) 200.022 (B) 200.033 (C) 400.033 (D) 200.300 [] (C) 1 (D) 110.000 5) 111.111 – 110.111 = _______  (C) 111.111 (D) 111.000 (A) 1.000 (B) 001.000 6) 999.000 – 888.000 = _______  (A) 0.111 (B) 001.000 Fill in the Blanks 7) Before adding or subtracting decimals, convert the unlike decimals to _________________ decimals. 8) The ________________ points of the decimal numbers to be added or subtracted must be placed exactly one below the other. 9) 101.330 + 101.331 = ___________________ Very Short Answer Questions 10) Add: 112.02 and 110.01 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Subtract: 400.023 from 611.132 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) Add: 333.433 and 444.344 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Solve: a) 119.056 + 142.153 b) 456.172 – 222.210 Decimals - I 69

Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. 14) Solve: a) 567.810 – 218.900 b) 286.114 + 118.296 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 15) Find: a) 557.65 + 23.45 b) 345.9 – 56.89 c) 143.21 + 467.801 d) 516.128 – 231.027 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 16) Solve: a) 100.148 + 800.162 b) 500.551 + 250.337 c) 247.800 – 118.276 d) 749.782 – 258.817 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 11.3 I Apply Short Answer Questions 17) In a week, Kesav spends 11.75 hours reading English, 23.5 hours for Maths and 13.25 hours for Science. How many hours does he spend studying? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 18) Teena bought crayons, water colours and colour pencils. Their prices are ` 127.50, ` 150 and ` 175.00 respectively. Find the total cost of the items that she bought. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. Decimals - I 71

................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 19) Shiva bought dry beans, dry peas, pigeon peas and lentils. The respective weights of these pulses were 212 g, 145 g, 229 g and 300 g. Express these weights in kilograms. What is the total weight (in kilograms) of the pulses that he bought? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................ ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) Rohan bought 100 pencils, 100 pens, 100 sharpeners and a box of 100 erasers. The respective costs of these items were ` 165.50, ` 931.80, ` 318.15 and ` 306.25. What is the total cost of the items he bought? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 72

11.3 I Explore (H.O.T.S.) Short Answer Question 21) Dilip had to give ` 85.90 to Annu and ` 46.56 to Firoz. However, he fell short of ` 75.20. How much money did he have? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) Subtract the sum of 72.612 and 6.489 from the sum of 92.708 and 8.314. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Decimals - I 73

Practice Questions 1) Write the following decimals in the place value chart. a) 5.231 b) 987.236 c) 2564.23 2) Write the expanded forms of the following decimals. a) 565.238 b) 78987.6 c) 15368.22373 3) Convert the given unlike decimals into like decimals. a) 765.728, 565, 3.125, 5.65, 1.2 b) 1.1, 11.11, 111.111, 1.01 c) 9.1, 99.01, 9.001, 99.101 d) 1.2, 1.23, 1.234, 1.345, 1 e) 10, 2, 0.3, 4.002 4) Which is the greater of the given decimals? a) 348.8752 and 348.8751 b) 123.987 and 321.789 c) 78987.78988 and 78987.78909 d) 1.899 and 1.988 5) Which is the smaller of the given decimals? a) 985.365 and 985.366 b) 1.1234 and 1.3214 c) 99.99 and 99.990 d) 98.0000 and 98.0001 6) Arrange the given decimal numbers in ascending order. a) 9.987, 9.989, 8.999, 8.998 b) 789.368, 789.3608, 798.3612, 987.1 c) 111.123, 101.321, 11.987, 1.9989 d) 869.8564, 7896.9875, 59.0112, 1234.001 e) 1234.123, 789.789, 1002.875, 998.3256 7) Arrange the given decimal numbers in descending order. a) 9.7864, 7, 9.072, 7.001 b) 7789.45, 239.38, 7798.45, 7889.121 b) 11.123, 11.321, 11.987, 11.9989 c) 89.898, 9.989, 89.9000, 89.9101 e) 1.231, 1.2311, 1.875, 1.3256 8) Write 5 decimals: a) between 8.598 and 8.569 b) more than 99.9 c) less than 1.01 74

9) Add the following decimal numbers. a) 7789.45 + 239.38 b) 98.4015 + 789.78 c) 111.123 + 11.321 d) 5684.987 + 158.9989 10) Add the following decimal numbers. a) 1.23, 1.265, 3.256 b) 6.21, 365.2569, 5.1 c) 1.254, 11.584, 100.123 d) 1.11, 11.11, 111.111 11) Which is the bigger sum? a) 123.145 + 89.38 or 623.145 + 139.386 b) 2398.4015 + 789.78 or 3.2101 + 3.2156 c) 111.123 + 19.321 or 65.25 + 65.24 d) 84.987 + 18.9989 or 84.9989 + 18. 987 12) Subtract the second decimal number from the first. a) 7789.45, 7458.7842 b) 1.987, 1.2357 c) 11.7864, 2.325 d) 8349.898, 8110.9259 e) 1.01, 1.001 13) Subtract each decimal number from 1. a) 0.897 b) 0.1265 c) 0.1 d) 0.9999 e) 0.0001 14) Subtract: a) 123.145 + 189.38 from 623.145 + 139.386 b) 9398.4015 + 789.78 from 9873.2101 + 1233.2156 c) 125.823 + 109.321 from 65.25 + 565.24 d) 184.987 + 184.9989 from 368.9989 + 10. 987 15) Which is bigger? a) 923.1 – 81.38 or 923.145 – 81.386 b) 8.45 – 7.78 or 10.45 – 9.78 c) 891.823 – 819.321 or 891.25 – 819.24 d) 8.215 – 4.9019 or 8.89 – 4. 872 16) Find the missing number. a) 89.63 + ? = 135.28 b) 17. 96.21 – ? = 72.76 Decimals - I 75

17) Solve: a) Add a decimal number to 6.125 to get 8.589 b) Subtract a decimal number from 9.99 to get 1.123 18) Solve: a) Express 18 as the sum of two decimal numbers. b) Express 1.25 as the difference of the two decimal numbers. 19) 16 bananas weigh 1.256 kg. 12 apples weigh 1.265 kg. Which fruit weighs more? 20) According to the National Institute of Nutrition, the protein content per 100 g in rajma is 22.9 g and 22.5 g in chana. Which grain has more protein content? 21) Compare: a) 46.65 and 49.65 b) 21.21 and 12.12 c) 100.100 and 100.1000 22) Arrange the sizes of the disc in ascending and descending orders according to a) inner extent and b) outer extent Discs Inner Extent Outer Extent Disc 1 1.28 3.17 Disc 2 1.12 2.33 Disc 3 1.29 3.34 Disc 4 1.62 2.54 23) Nutrition information given on a food item is as given below. Nutrition information per 100 g Fat 12.5 g Carbohydrate 78.2 g Sugar 25.6 g Protein 6.5 g Salt 0.73 g How many grams of fat, carbohydrate and salt do you get per 100 g? 24) Aditya’s father filled 3 litres of petrol for his bike and paid ` 270.15. He paid ` 267.66 for 3 litres of petrol a few days back. How much extra did he pay? 76

25) Read the table. PROTEIN CONTENT OF GRAINS (INDIAN NAMES) Soyabean (Soybean) 43.2 Masur (Lentil) Moong Daal 25.1 24.5 Chavli (Cow pea) 24.1 Moong (Green gram) 24 Udad Daal (Black gram dal) 24 Matki (Moth beans) 23.6 Rajma (Fr. Beans) 22.9 Chana (Bengal gram, roasted) 22.5 Kuleeth (House gram) 22 Chana Daal 20.8 Peas (Dry) 19.7 Chana (Bengal grams) 17.1 11.8 Wheat Bajra 11.6 Maka (Maize) 11.1 Maida (Refined flour) FITJOG.COM NUTRITION CHARTS©2010FITJOG.COM Find the total protein content in moong, matki and bajra. Decimals - I 77

26) Read the table and add the densities of the planets Mercury, Earth and the Moon. Body Density Earth 5.514 Mercury 5.427 The Moon 3.344 27) In the above table, whose density is more, Earth or the Mercury? By how much? 28) From the below table, whose distance (in aeronautical units (AU)) from the Sun is more, Saturn or Uranus? By how much? Body Mass (kg) Distance to Sun (AU) Mercury 330.200 0.390 4,868.500 0.720 Venus 5,973.600 1.000 Earth 641.850 1.520 Mars 1,898,600 5.200 Jupiter 568,460 9.540 Saturn 86,832 19.180 Uranus 102,430 30.060 Neptune 13.105 39.440 Pluto 29) In the above table, a) Whose mass is less, Mercury or Mars? By how much? b) Find the difference between the masses of Venus and Earth. 30) T he length of a rectangular field is 456.284 metres and its breadth is 213.54 metres. Find the length of all the four sides combined. 78

Chapter Decimals - II 12 Concept 12.1: Multiply and Divide Decimals 12.1 I Recall Multiple Choice Questions 1) The product of 1500 and 10 is ______. [] [] (A) 15001 (B) 15000 (C) 10510 (D) 11500 [] 2) The quotient when 200 ÷ 5 is ________. (A) 40 (B) 400 (C) 1000 (D) 100 3) The product of 600 and 10 is ________. (A) 3050 (B) 600 (C) 6000 (D) 3500 12.1 I Remember and Understand Multiple Choice Questions 4) The product 200.50 × 10 is ______. [] [] (A) 20.50 (B) 250.5 (C) 2005 (D) 205 [] (C) 423.5 (D) 42.35 5) The product 4.235 × 10 is ________. (C) 0.100 (D) 10.01 (A) 4.235 (B) 0.4235 6) The quotient 100.1 ÷ 10 is ________. (A) 100.1 (B) 10.1 Fill in the Blanks 7) The decimal point is shifted to the right by one digit if the multiplier is ______________. 8) 9.9999 ÷ 10 = __________________ 9) The decimal point is shifted to the right by three digits if the multiplier is ________________. 79

Very Short Answer Questions 10) Solve: 1.0581 × 10 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Find the product of 9.876 and 100. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) Solve: 7.9452 × 1000 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Solve: a) 21.333 ÷ 3 b) 46.345 × 11 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 14) Solve: a) 22.944 ÷ 2 b) 29.168 × 29 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 80

Long Answer Questions 15) Solve: a) 198.50 × 24 b) 364.16 ÷ 16 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 16) Solve: a) 4.36 × 4.4 b) 20284 ÷ 14 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Decimals - II 81

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 12.1 I Apply Short Answer Questions 17) The weight of a rice bag is 15.55 kg. What is the total weight of 15 such bags? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 18) Ram bought 4 shirts for ` 900.75 each. How much did he pay in all? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 82

Long Answer Questions 19) Tony has 154.3 kg of coffee powder. He puts them equally into 8 bags. How much coffee powder will be there in each bag? Will there be any amount of powder left? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) The cost of 10 mangoes is ` 330.60 and 10 oranges is ` 200.50. What is the total cost of 1 mango and 1 orange? Find the total cost of 10 mangoes and 10 oranges. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Decimals - II 83

12.1 I Explore (H.O.T.S.) Short Answer Question 21) Find the missing numbers. a) _______________ × 100 = 235.2 b) 11.012 × _______________ = 1101.2 c) 781.4 × ______________ = 7814 d) 99.012 × _____________ = 990.12 Long Answer Question 22) The cost of 1.2 kg long grain rice is ` 185.64. What is the cost of one kg of long grain rice? If 1 kg of short grain rice costs ` 54, which item costs less and by how much? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 84

Concept 12.2: Percentages 12.2 I Recall Multiple Choice Questions 1) 0.75 expressed as a fraction is ______. [] [] (A) 75 (B) 75 (C) 0.75 (D) 7.5 [] 100 10 10 100 [] 2) The fraction equivalent to 0.55 is _______. [] [] (A) 0.5 (B) 55 (C) 1 (D) 0.55 100 100 5 1000 3) 0.62 = ______ (A) 62 (B) 6.2 (C) 0.62 (D) 62.0 100 100 10 1000 12.2 I Remember and Understand Multiple Choice Questions (D) 3.05% 4) The percentage equivalent of 35 is _______________. 100 (A) 3.5% (B) 35% (C) 0.35% 5) The fraction equivalent to 92% is _______________. (A) 0.92 (B) 9.2 (C) 92 (D) 9 100 100 100 2 6) The fraction equivalent to 20% is _______________. (A) 0.2 (B) 2.0 (C) 0.02 (D) 20 100 100 100 100 Fill in the Blanks 7) The fraction equivalent to 5.4% is _________. Decimals - II 85

8) If 25% is converted into a fraction, the result is ____________. 9) To convert 50.1% into a fraction, we divide 501 by __________. Very Short Answer Questions 10) Convert 22 into percentage. 100 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Express 12% as a fraction. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) What is the percentage of 24 ? 50 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Convert the following percentages into fractions and decimals. a) 90% b) 45% Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 14) Convert the following fractions into percentages and mention how they are read. Express the fractions as decimals. a) 63 b) 57 100 100 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 86

Long Answer Questions 15) Convert the given percentages into fractions and decimals. Percentages Fractions Decimals 20% 55% 25% 15% 16) Convert the following into percentages and read them. a) 54 b) 28 c) 4 d) 2 100 50 10 5 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 12.2 I Apply Short Answer Questions 17) 9 of a glass is filled with water. What percentage of the glass is filled with water? 25 Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. Decimals - II 87

18) Out of 25 students, 20 students were present in the Maths class. What percentage of the students were present in the class? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 19) Out of 50 students, 20 students like playing football, 16 students like kabaddi and the others like cricket. What percentage of students like each game? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 20) Out of 100 marks in each subject, Ankita scored 35 marks in Maths, 91 marks in English, 45 marks in Science and 80 marks in Social Studies. What is the percentage of marks scored in each subject? In which subjects did she score the maximum and the minimum percentages? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 88

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. 12.2 I Explore (H.O.T.S.) Short Answer Question 21) A class has 40 students divided in two teams - red and blue, of which 28 belong to the red team. What percentage of students belong to the blue team? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Question 22) Rahul has ` 1000. He spent 15% on groceries, 17% on petrol, and 26.5% on clothes and 14% on medicines. What amount is left? What are his total expenses? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. Decimals - II 89

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Practice Questions 1) Multiply the following decimal numbers. a) 7789.45 × 10 b) 98.4815 × 100 c) 111.1236 × 1000 d) 5684.9 × 1000 e) 7789.45 × 100 f) 98.4815 × 1000 g) 111.1236 × 10 h) 84.9 × 100 2) Multiply the following decimal numbers. a) 234.12 × 2 b) 4 × 98.48 c) 23.6 × 125 d) 56.89 × 12 e) 9.1 × 111 f) 8.485 × 9 g) 12.12 × 12 h) 56 × 5.2 3) Multiply the following decimal numbers. a) 234.12 × 1.2 b) 2.4 × 42.15 c) 23.6 × 5.6 d) 56.89 × 7.2 e) 9.41 × 11.1 f) 98.48 × 9.24 g) 12.12 × 1.2 h) 100 × 15.22 4) Multiply the following decimal numbers by 1000. a) 123.1 b) 123.123 c) 123.12 d) 1.234 e) 12.345 f) 12.34 g) 123.4567 h) 1.2345 90

5) Multiply 99.999 by the following: a) 10 b) 100 c) 1000 d) 10000 6) Fill in the blanks with missing numbers a) 7.8 × ? = 78 b) 7.89 × ? = 789 c) 67.89 × ? = 678.9 d) 67.89 × ? = 6789 e) 6.789 × ? = 678.9 f) 67.89 × ? = 67890 7) Multiply the following decimal numbers. a) 1.2 × 1.2 × 10 b) 2.4 × 4.2 × 100 c) 2.6 × 7 × 10 d) 2.6 × 70 8) Divide the following: a) 77.41 ÷ 10 b) 98.23 ÷ 100 c) 1112.6 ÷ 100 d) 5714.9 ÷ 1000 e) 5289.454 ÷ 10 f) 18.47 ÷ 1000 g) 1.36 ÷ 1000 h) 5634.9 ÷ 100 9) Divide 1234.99 by the following: a) 10 b) 100 c) 1000 10) Divide the following decimal numbers by 10, 100 and 1000. a) 173.1 b) 423.123 c) 923.12 d) 1.284 e) 78.345 f) 98.34 g) 188.454 h) 4.2795 11) Divide the following decimal numbers. a) 7.7 ÷ 11 b) 98.2 ÷ 2 c) 67.125 ÷ 3 d) 57.141 ÷ 9 e) 529.424 ÷ 4 f) 1.818 ÷ 18 g) 21.35 ÷ 5 h) 93.24 ÷ 6 12) Divide the following decimal numbers. a) 144 ÷ 1.2 b) 625 ÷ 0.5 c) 196 ÷ 1.4 d) 475 ÷ 2.5 e) 1035 ÷ 1.5 f) 1818 ÷ 1.8 g) 2135 ÷ 0.7 h) 468 ÷ 3.6 13) Divide the following decimal numbers. a) 1.69 ÷ 1.3 b) 62.5 ÷ 2.5 c) 1.96 ÷ 1.4 d) 4.75 ÷ 0.5 e) 1.425 ÷ 2.5 f) 18.18 ÷ 1.8 g) 213.5 ÷ 0.7 h) 0.468 ÷ 3.6 Decimals - II 91

14) Convert the following into percentage. a ) 2 b) 12 c) 123 d) 85 e) 56 f) 9 100 100 100 100 100 100 g) 895 h) 256 i) 72 j) 43 k) 785 l) 1 100 100 100 100 100 100 m) 100 n) 50 100 100 15) Convert the following fractions into percentage. a) 7 b) 7 c) 7 d) 7 e) 7 f) 7 10 50 25 20 4 2 g) 85 h) 56 i) 78 j) 4 k) 12 l) 20 20 25 10 10 50 25 m) 9 n) 5 10 20 16) Convert the following percentages into fractions. a) 12% b) 78% c) 99% d) 1% e) 100% f) 225% g) 25% h) 2% 17) Convert the following percentages into decimals. a) 72% b) 8% c) 229% d) 1% e) 10% f) 147% g) 5% h) 69% 18) Convert the following decimals into fractions. a) 12.5 b) 9.7 c) 12.65 d) 5.008 e) 8.28 f) 0.2 g) 0.25 h) 0.623 19) Convert the following fractions into percentages and decimals. a) 4 b) 12 c) 17 d) 15 e) 1 3 10 50 25 20 4 f) 4 g) 5 h) 16 i) 28 j) 14 k) 19 l) 25 10 10 50 25 20 25 m) 3 n) 16 10 20 92

20) Convert the following decimals into percentages. a) 4.5 b) 8.2 c) 12.3 d) 5.0 e) 0.2 f) 0.02 g) 0.25 h) 0.30 21) Convert the following into percentages. a) 4 + 8 b) 12 + 17 c) 17 + 32 10 100 25 100 50 50 f) 0.2 + 2.5 d) 15 + 48 e) 1 + 4 100 100 2 10 g) 8.5 +1.2 h) 0.3 + 0.9 i) 6.5 + 14.5 j) 0.25 + 0.75 22) Cost of 1 kg tomato is ` 19.5. Find the cost of 12.25 kg tomatoes. 23) Cost of 3 litres petrol is ` 274.89. Find the cost of one litre? 24) A ditya and his two friends went to a bakery. They ordered 3 cakes for ` 12.5 each. They also ordered 6 burgers costing ` 35.5 each. Find the total bill and divide the bill amount equally among the three friends. 25) Look at the following table. Prepare the bill with total cost for each item. Item Cost per item (`) Number of items Pen 9.5 120 Eraser 3.25 150 Pencil 4.75 100 26) N isha ordered the following items on Teacher’s day. Prepare the bill with the missing numbers. Item Cost per item (`) Number of items Total cost (`) Chocolate ? 25 62.5 Sweet 7.25 ? 217.5 Juice packet (100 mℓ) 10.5 ? 157.5 Grand total ? 27) The length of a pipe is 25.68 metres. Find the length of 24 such pipes. 28) T he length of a rope is 35.25 metres. The length of a park is equal to 13.5 such ropes. Find the length of the park in metres. 29) The Goods and Service tax on electronics is 18%. Express this percentage in decimals. 30) M aya got 24 marks out of 50 in a Mathematics exam. Find the percentage of the marks. Decimals - II 93

Chapter Measurements 13 Concept 13.1: Perimeter, Area and Volume 13.1 I Recall Multiple Choice Questions PO 1) The corners of the given figure are ______________. [] [] MN [] (A) M, N, P, Q (B) M, Q, N, S (C) N, O, M, P (D) M, R, O, T TS 2) The sides of the given figure are ______________. Q R (A) Q, R, T and S (B) QR, RS, ST and TQ (C) QS, RT, RQ and ST L (D) RQ, RT, and RS 3) The given 2-D shape is a ______________. JK (A) triangle (B) square (C) rectangle (D) circle 13.1 I Remember and Understand Multiple Choice Questions C [] , AB and DC represent ______________. [ ] D [ ] 4) In the given figure AB (A) area (B) length (C) breadth (D) perimeter 5) The product that gives the area of a square is ______________. (A) s × s (B) 4s (C) ℓ × b (D) 2 (ℓ + b) 6) The units of area are ______________. (A) sq. m (B) cm (C) sq. cm (D) m 94

Fill in the Blanks 7) Perimeter of a rectangle is given by _______________________. 8) Perimeter of a square is given by _______________________. 9) A cube of edge 1 cm is called a _______________________ cube. Very Short Answer Questions 10) Write the formula for the area of a triangle. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11) Find the area of a square having sides 4 cm. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12) A rectangle is 4 metres long and 2 metres wide. What is its perimeter? Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Answer Questions 13) Find the perimeter of the following figures. 4 cm a) 2 cm b) 6 cm Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. 14) Find the perimeter and area of a square if the length of its sides is 4.1 cm. Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurements 95

................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. ................................................................................. Long Answer Questions 15) Find the perimeter of the given figures. a) b) 5 cm 5 cm 2 cm 4 cm c) 3 cm d) 12 cm 6 cm 6 cm Solution: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................. ................................................................................. ................................................................................. 96