Division of Numbers PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Five Division of numbers Introduction Division is a mathematical process of distributing things or a group of things...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Five Division of numbers Introduction Division is a mathematical process of distributing things or a group of things LY into a specified number of parts. In Standard Four, you learnt about division of numbers having a maximum of three digits by a divisor having a maximum of two digits. In this chapter, you will learn how to divide a number not exceeding N one million by a divisor having up to three digits, with and without a remainder. A knowledge of division will help you in budgeting, making decisions concerning O living expenses on a monthly or daily basis, distribution of resources and so on. Exercise 1: Revision SE Answer the following questions: U 1. Arrange the following books into six groups with equal number of books in each group. E N LI N O R FO How many books does each group have? 68 MATH std 5.indd 68 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Eighteen sweets were divided equally among 3 children. How many sweets did each child get? 3. If 28 avocados are divided equally to 14 groups, how many avocados will each group get? 4. 125 ÷ 5 = 5. 96 ÷ 3 = LY 6. 7 532 7. 85 850 8. 27 243 N 9. A primary school has 240 pupils and 12 classrooms. If the number of pupils in each class is the same, how many pupils are in each class? O 10. If the cost of 15 sweets is 300 shillings, what is the cost of one such sweet? SE 11. Use the method of repeated subtraction to answer the following U questions: (a) 20 ÷ 4 = (b) 50 ÷ 10 = E N Dividing a number without a remainder LI In division, the number being divided is called the dividend. The number which divides the dividend is called the divisor. The answer is called the quotient. N For example; 2522 ÷ 97 = 26. O In this example, 2 522 is the dividend, 97 is the divisor, and 26 is the quotient. R Long division method FO In long division, the dividend, divisor and the quotient are arranged as follows: Quotient Divisor Dividend 69 MATH std 5.indd 69 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 32 14496 Solution Steps: 1. Divide 14 by 32. This is not LY sufficient. Shift to the next digit, 4 which is 4, to the right to get 144. 32 14496 N Divide 144 by 32. The answer is 4 with a remainder. Write 4 in the O quotient position. 2. Multiply 32 by 4 to get 128. Write 4 128 below 144 and subtract to get 16. SE 32 14496 – 128 16 U 3. Bring down the digit 9 to the right of 16 to get 169. Divide 169 by 32 45 32 14496 to obtain 5 and a remainder. Write E – 128 5 in the quotient position, at the 169 N right of 4. 4. Multiply 32 by 5, to get 160. Write 45 LI 160 below 169 and subtract 160 32 14496 from 169 to get 9. – 128 N 169 – 160 O 9 5. Bring down the digit 6 to the right 453 R of 9 to get 96. 32 14496 – 128 FO Divide 96 by 32 to get 3 without a remainder. Write 3 in the quotient 169 position at the right of 5. – 160 96 70 MATH std 5.indd 70 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 6. Multiply 32 by 3 to get 96. 453 Write 96 below 96 and subtract 32 14496 to get 0. – 128 169 – 160 96 – 96 LY 0 N Therefore, 32 14496 is equal to 453. O Example 2 696 561672 SE Solution U Steps: 1. Divide 561 by 696. This is not sufficient. Shift to the next digit, E which is 6, to get 5616. Divide 8 N 5616 by 696. The answer is 8 696 561672 with a remainder. Write 8 in the LI quotient position. 2. Multiply 696 by 8 to get 5568. 8 N Write 5568 below 5616 and 696 561672 O subtract to get 48. – 5568 48 R 3. Bring down the digit 7 to the right of the remainder 48 to get 487. 80 FO Divide 487 by 696. This is not 696 561672 sufficient. Write 0 in the quotient – 5568 position at the right of 8. 487 71 MATH std 5.indd 71 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. Multiply 696 by 0 to obtain 0. Write 80 0 below 487 and then subtract 696 561672 0 from 487. This leaves 487 – 5568 unchanged. 487 – 000 487 5. Bring down the digit 2 to the right 807 LY of 487 to get 4872. Divide 4872 by 696 561672 696 to get exactly 7. Write 7 in the – 5568 quotient position at the right of 0. 487 N – 000 4872 O 6. Multiply 696 by 7 to get 4872. 807 Write 4872 below 4872 and 696 561672 subtract to get 0. SE – 5568 487 – 000 U 4872 – 4872 0 E N Therefore, 696 561672 is equal to 807. LI Example 3 Solution N 980 978040 998 O 980 978040 – 8820 R 9604 – 8820 FO 7840 – 7840 0 Therefore, 980 978040 = 998. 72 MATH std 5.indd 72 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Answer the following questions: 1. 7 49000 2. 10 29190 3. 25 505000 4. 909 32724 5. 43 26789 6. 364 22932 LY 7. 791 88592 8. 75 28950 9. 200 980000 10. 33 110979 11. 20 81520 12. 36 726984 N 13. 364 942032 14. 800 100000 15. 623 26789 O 16. 781 82005 17. 63 204687 18. 303 188163 19. 99 678249 20. SE 444 447996 U Short division method In the short division method, the arrangement of the dividend, divisor and E quotient is as follows: Divisor Divident N Quotient LI Example 1 N O 2 84620 Steps: R 1. Start by dividing the dividend from left to right. FO 8 ten thousands divided by 2 gives 4 ten 2 84620 thousands. Write 4 under the ten thousands 4 position. 73 MATH std 5.indd 73 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Divide the 4 thousands by 2 to get 2. Write 2 84620 2 under the thousands position. 42 3. Divide the 6 hundreds by 2 to get 3. Write 3 2 84620 under the hundreds position. 423 4. Divide the 2 tens by 2 to get 1. Write 1 under 2 84620 LY the tens position. 4231 5. Divide the 0 ones by 2 to get 0. Write 0 under 2 84620 N the ones position. 42310 O Therefore, 2 84620 = 42310. SE Example 2 U 23 14260 E Steps: N 1. Divide 14 by 23. This is not sufficient. Hence, 23 14260 take 142 and divide it by 23. One gets 6 LI 6 but with some remainder. Write 6 under the Remainder is 4 N hundreds position. Multiply 23 by 6 to get 138. Subtract 138 from 142 to get 4 hundreds. O 2. The 4 hundreds and the 6 tens give 46 tens. 23 14260 Divide 46 by 23 to get 2. Write 2 under the 62 R tens position. 3. Divide 0 ones 23 to get 0. Write 0 under the 23 14260 FO ones position. 620 Therefore, 23 14260 = 620. 74 MATH std 5.indd 74 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 312 500 ÷ 125 = 2500. Exercise 3 Answer the following questions: LY 1. 2 8640 2. 9 36927 3. 7 56574 4. 100 89400 5. 25 10000 6. 60 66000 N 7. 13 15613 8. 605 55055 9. 101 26765 O 10. 10 356250 11. 956 203628 12. 213 202776 13. 16. 543 29865 26 118586 14. 17. 926 77784 SE 150 354000 15. 18. 78 23400 87 82389 U 19. 164 513648 20. 442 195364 Use the short division method to find the quotient in problems 21 to 32. E 21. 22033 ÷ 11 = 22. 48800 ÷ 61 = N 23. 307350 ÷ 45 = 24. 164000 ÷ 820 = LI 25. 89089 ÷ 89 = 26. 730800 ÷ 812 = N 27. 380324 ÷ 476 = 28. 156400 ÷ 230 = O 29. 755480 ÷ 85 = 30. 360000 ÷ 600 = R 31. 331920 ÷ 922 = 32. 32220 ÷ 45 = FO Division of a number and getting a remainder In some cases, the dividend may not be an exact multiple of the divisor. In such cases, division gives a quotient and a remainder. 75 MATH std 5.indd 75 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Long division method Example 1 27 866 Solution Steps: LY 1. Divide 86 by 27 to get 3. Write 3 above the tens position. 3 N 27 866 O 2. Multiply 27 by 3 to get 81. Write 81 under 86 3 and subtract to get 5. SE 27 866 – 81 5 U 3. Drop the 6 ones to the 5 tens to get 56. Divide 32 56 by 27 to get 2. Write 2 above the ones 27 866 E position. – 81 N 56 LI 4. Multiply 27 by 2 to get 54. Write 54 below 56 32 and subtract 56 from 54 to get 2. 27 866 N – 81 O 56 – 54 R 2 FO Therefore, 27 866 = 32 remainder 2. 76 MATH std 5.indd 76 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 7 148 Solution Steps: 1. Divide 14 by 7. The answer is 2. Write 2 LY above the tens position. 2 7 148 N O 2. Multiply 7 by 2 to get 14. Write 14 under 14 and subtract: 14 – 14 = 0. 2 7 148 SE – 14 U 3. Drop the 8 ones to the 0 tens to get 8 ones. 21 Divide 8 by 7 to get 1. Write 1 above the 7 148 ones position. – 14 E 8 N 4. Multiply 7 by 1 to get 7. Write 7 below 8 and 21 LI subtract: 8 – 7 = 1. The number 1 is the 7 148 remainder. – 14 N 8 O – 7 1 R FO Therefore, 7 148 = 21 remainder 1. 77 MATH std 5.indd 77 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 4 Answer the following questions: 1. 6 467 2. 8 891 3. 5 327 4. 25 815 5. 90 405 6. 77 620 7. 88 220 8. 43 267 9. 11 241 LY 10. 58 494 11. 84 847 12. 34 120 N 13. 25 555 14. 60 786 15. 15 148 O 16. 11 139 17. 32 347 18. 14 535 19. 28 234 20. 38 234 SE Short division method U Example 1 E 6 82 N Steps: LI 1. Divide 8 by 6. The answer is 1 with remainder 2. 6 82 N O 2. Write 1 under 8 in the tens position. Combine 6 82 the 2 tens that remained and the 2 ones to 1 make 22. R 3. Divide 22 by 6. The answer is 3 with remainder 6 82 FO 4. Write 3 under the 2 ones. 13 remainder 4 Therefore, 6 82 = 13 remainder 4. 78 MATH std 5.indd 78 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 12 573 Solution Steps: 1. Divide 5 by 12. This is not sufficient. Divide 57 12 573 by 12. The answer is 4 with 9 as remainder. LY 4 Write 4 below 7. 2. Add the 3 ones to the 9 tens remainder to 12 573 N get 93. Divide 93 by 12 to get 7 and 9 as 47 remainder. Write 7 below 3. remainder 9 O Therefore, 12 573 = 47 remainder 9. Example 3 SE Solution U 10 678 10 678 67 remainder 8. E Exercise 5 N Answer the following questions: LI N 1. 3 457 2. 5 99 3. 9 68 4. 22 938 5. 12 405 6. 10 644 O 7. 31 125 8. 70 982 9. 10 831 R 10. 16 401 11. 18 233 12. 30 857 FO 13. 15 286 14. 80 751 15. 9 489 16. 11 383 17. 13 252 18. 24 457 19. 17 500 20. 65 536 79 MATH std 5.indd 79 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Word problems involving division Example 1 Thirteen poultry farmers divided 1 625 chickens equally among themselves. How many chickens did each farmer get? Solution Number of poultry farmers: 13 LY Number of chickens: 1 625 N Divide 1 625 by 13: 125 13 1625 O − 13 32 − 26 65 SE − 65 U 0 Therefore, each poultry farmer got 125 chickens. E N Example 2 LI A class teacher gave her 35 pupils an equal number of oranges. If she had a total of 305 oranges, how many oranges did each pupil get and how N many oranges did the teacher remain with? O Solution Number of oranges = 305 R Number of students = 35 Divide 305 by 35: FO 305 ÷ 35 = 8 remainder 25 Therefore, each pupil got 8 oranges and the teacher remained with 25 oranges. 80 MATH std 5.indd 80 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 6 Answer the following questions: 1. An equal distribution of 133 700 kilograms of rice was done to 50 families that were affected by floods. How many kilograms of rice did each family receive? LY 2. Twenty-four goats were bought for 446 400 shillings. What was the price of one goat if the price was the same for all 24 goats? N 3. A teacher gave an equal number of sheets of paper to 60 students. If the O teacher had 414 sheets of paper, how many sheets of paper did each student get? How many sheets of paper remained with the teacher? SE 4. A standard five class having 50 pupils was awarded a prize of 80 000 shillings for being the best in the school’s competition. If the money was U divided equally among the pupils, how much money did each pupil get? 5. An equal number of bags of maize was distributed to 40 villages. If E there were 955 bags of maize, how many bags of maize did each N village get, and how many bags of maize remained? LI 6. A businessman earned 492 000 shillings by selling 41 pairs of shoes. If the cost of each pair of shoes was the same, what was the selling N price for a pair of shoes? O 7. Juliana earned 720 000 shillings by selling oranges. If the price of one orange was 150 shillings, how many oranges did Juliana sell? R FO 8. An equal distribution of 99 000 books was done among 200 schools. How many books did each school get? 81 MATH std 5.indd 81 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 9. A total of 100 800 pieces of chalk are packaged equally into 700 boxes. How many pieces of chalk does each box contain? 10. Twenty-four members of a cooperative society harvested 986 pineapples. If the pineapples were equally shared among the members, how many pineapples remained? LY 11. Some villagers contributed 325 000 shillings to build a school toilet. If each villager contributed 500 shillings, how many villagers made the N contribution? O 12. An equal distribution of 136 890 pens was done to 30 pupils. How many pens did each pupil get? Exercise 7 SE U Answer the following questions: 1. 32352 ÷ 16 = 2. 170 ÷ 17 = 3. 3069 ÷ 99 = E 4. 363600 ÷ 300 = 5. 31 165 6. 760 174800 N LI 7. 90 405000 8. 998 558880 9. 95 344 N 10. 44 935 11. 55 868230 O 12. Bakari earned 984 000 shillings from selling pineapples. If the price of each pineapple was 820 shillings, how many pineapples did Bakari sell? R 13. Teacher Sara received 508 exercise books for her 95 Standard One FO pupils. If she distributed an equal number of exercise books to her pupils, how many exercise books did each pupil get, and how many exercise books remained? 82 MATH std 5.indd 82 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 14. Using the following table, write all numbers which are divisible by 8. 560 360 124 270 600 94 70 80 208 40 12 63 30 188 120 54 190 49 250 72 LY Summary N 1. The number to be divided is called the dividend. The number used to O divide is called the divisor. The result obtained by dividing a number by another number is called the quotient. SE 2. The quotient may be with a remainder or without a remainder. 3. In dividing a number, divide the digits of the dividend starting from the left most digits of the dividend and move towards the right. U 4. In dividing a number, the divisor may be an exact multiple of the dividend, or there may be a remainder. E N LI N O R FO 83 MATH std 5.indd 83 30/07/2021 14:49