Math Class IV Division PDF

# Chapter Three ## Division of Whole Numbers ### Introduction - In this chapter, you will learn to divide whole numbers. - The competencies developed will enable you to apply the concept of division in arranging and dividing resources fairly in many aspects of daily life. ### Think - Life without...

# Chapter Three ## Division of Whole Numbers ### Introduction - In this chapter, you will learn to divide whole numbers. - The competencies developed will enable you to apply the concept of division in arranging and dividing resources fairly in many aspects of daily life. ### Think - Life without the knowledge of division ### Division of Whole Numbers Without Remainders - When dividing whole numbers, begin with the digit from the left of the number towards the right. - A number that divides another number is known as the dividend and a number used to divide is known as the divisor. - The obtained answer is known as the quotient. ### Division of Whole Numbers by Short Method Without Remainders #### Example 1 68 ÷ 2 = **Steps** 1. Divide 6 tens by 2 to get 3 tens. Write 3 in the tens place. 2. Divide 8 ones by 2 to get 4 ones. Write 4 in the ones place, to the right of 3 tens. Therefore, 68 ÷ 2 = 34. #### Example 2 245 ÷ 5 = **Steps** 1. Divide 2 by 5, it is not sufficient. 2. Take 24 divide by 5 to get 4 with a remainder of 4. Write 4 in the tens place. Regroup 4 into 40 ones. Add ones: 40 + 5 = 45. 3. Divide 45 by 5 to get 9. Write 9 in the ones place, to the right of 4. Therefore, 245 ÷ 5 = 49. #### Example 3 2)284 **Steps** 1. Divide 2 by 2 to get 1. Write 1 in the hundreds place. 2. Divide 8 by 2 to get 4. Write 4 in the tens place, to the right of 1. 3. Divide 4 by 2 to get 2. Write 2 in the ones place, to the right of 4. Therefore, the answer is 142. #### Example 4 12)384 **Solution** 12)384 32 **Steps** 1. Divide 3 by 12, it is not sufficient. Thus, take 38 then divide by 12. You will get 3 with remainder of 2. Write 3 in the tens place. 2. Regroup 2 into 20 ones. Add ones: 20 + 4 = 24. 3. Divide 24 by 12 to get 2. Write 2 in the ones place to the right of 3. Therefore, the answer is 32. ### Exercise 1 1. 70 ÷ 7 = 2. 36 ÷ 6 = 3. 54 ÷ 3 = 4. 86 ÷ 2 = 5. 96 ÷ 6 = 6. 272 ÷ 8 = 7. 981 ÷ 3 = 8. 225 ÷ 5 = 9. 196 ÷ 4 = 10. 175 ÷ 5 = 11. 285 ÷ 19 = 12. 85 ÷ 5 = 13. 378 ÷ 27 = 14. 2) 64 15. 3) 93 16. 8) 168 17. 20) 400 18. 7) 217 19. 12) 264 20. 31 ) 961 21. 75) 825 ### Division of Whole Numbers by Long Method Without the Remainders #### Example 1 69 ÷ 3 = **Solution** **Steps** 1. Divide 6 by 3 to get 2. Write 2 in the tens place. 2. Multiply 2 by 3 to get 6. Write 6 below 6, then subtract: 6 - 6 = 0. 3. Drop 9 ones, then divide by 3 to get 3. Write 3 in the ones place to the right of 2. 4. Multiply 3 by 3 to get 9. Write 9 below 9, then subtract: 9 - 9 = 0. Therefore, 69 ÷ 3 = 23 **Solution** 23 3)69 6↓ 9 -9 0 #### Example 2 80 8080 **Solution** **Steps** 1. Divide 80 by 80 to get 1. Write 1 above the hundreds place. 2. Multiply 80 by 1 to get 80. Write 80 below 80, then subtract: 80 - 80 = 0. 3. Drop 8 tens, then divide 8 by 80 to get 0. Write 0 above the tens place, to the right of 1. 4. Multiply 0 by 80 to get 0. Write 0 below 8 then subtract: 80 = 8. 5. Drop 0 ones on the 8 tens to get 80. Divide 80 by 80 to get 1. Write 1 above the ones place, to the right of 0. 6. Multiply 1 by 80 to get 80. Write 80 below 80, then subtract: 80 - 80 = 0. Therefore, the answer is 101. **Solution** 101 80)8080 -80↓ 8 -0↓ 80 -80 0 #### Example 3 696)561672 **Solution** 807 696)561672 5568 487 000 Therefore, the answer is 807. ### Exercise 2 1. 3)723 2. 605)55055 3. 78)23400 4. 926)77784 5. 25)10000 6. 6)660 7. 10)356250 8. 60)66000 9. 3512)231792 10. 9)126 11. 4255)51060 12. 812)730800 13. 8)824 14. 16)29024 15. 7)847 16. 27)891 17. 124)64852 18. 2512)87920 19. 3)495 20. 32)20192 21. 22)29190 22. 75)28950 23. 34)782 24. 364)22932 25. 84)924 26. 18)684 ### Division of Whole Numbers with the 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. ### Division of Whole Numbers by Short Method With Remainders #### Example 1 6)82 **Solution** **Steps** 1. Divide 8 tens by 6 to get 1 ten and the remainder of 2 tens. 2. Write 1 below 8 and then take the remainder of 2 tens and 2 ones to get 22. 3. Divide 22 by 6 to get 3 remainder 4. 4. Write 3 below 2 and 4 as the remainder to the right of 13. Therefore, the answer is 13 and the remainder is 4. **Solution** 6)82 13 remainder 4 #### Example 2 12) 573 **Solution** **Steps** 1. Divide 5 by 12, it is not sufficient. Take 57 then divide by 12 to get 4 and remainder 9. 2. Write 4 below 7, then combine the remainder 9 and 3 ones to form 93. 3. Divide 93 by 12 to get 7 and remainder 9. Write 7 below 3 and 9 as the remainder to the right of 47. Therefore, the answer is 47 and the remainder is 9. **Solution** 12)573 47 remainder 9 #### Example 3 23)14262 **Solution** 23)14262 620 remainder 2 Therefore, the answer is 620 and the remainder is 2. ### Exercise 3 1. 3)457 2. 5)99 3. 9)68 4. 22)938 5. 12)4005 6. 644 ÷ 10 = 7. 610)313252 8. 43)267 9. 111)2461 10. 58)4940 11. 84)784 = 12. 340)1720 13. 139 ÷ 11 = 14. 32)3407 15. 234 ÷ 38 = 16. 28) 20364 ### Division of Whole Numbers By Long Method With a Remainder #### Example 1 7)148 **Solution** **Steps** 1. Divide 14 by 7 to get 2. Write 2 above the tens place. 2. Multiply 2 by 7 to get 14. Write 14 below 14 then subtract: 14 - 14 = 0. 3. Drop 8 one, then divide by 7 to get 1. Write 1 above the ones place. 4. Multiply 1 by 7 to get 7. Write 7 below 8, then subtract: 8 - 7 = 1. Therefore, the answer is 21 and the remainder is 1. **Solution** 21 7)148 -14↓ 8 -7 1 #### Example 2 27)866 **Solution** **Steps** 1. Divide 86 by 27 to get 3. Write 3 above the tens place. 2. Multiply 3 by 27 to get 81. Write 81 below 86 then subtract: 86 - 81 = 5. 3. Drop the 6 ones to get 56. Divide 56 by 27 to get 2. Write 2 above the ones place, to the right of 3. 4. Multiply 2 by 27 to get 54. Write 54 below 56, then subtract: 56 - 54 = 2. Therefore, the answer is 32 and the remainder is 2. **Solution** 32 27)866 -81 56 -54 2 #### Example 3 8806)880890 **Solution** 100 8806)880890 -8806 2 -0↓ 29 -04 Therefore, the answer is 100 and the remainder is 290. ### Exercise 4 1. 6)467 2. 1279)255812 3. 5)327 4. 25)815 5. 90) 405 6. 25)15397 7. 104)84765 8. 43)267 9. 5850)175594 10. 48)4954 11. 32)14498 12. 12)1235 13. 21)25240 14. 35)159610 15. 164)527756 16. 11)139 17. 1450)72507 18. 14)535 19. 28) 234 20. 200) 502808 ### Word Problems Involving Division of Whole Numbers - Word problems on division show the use of division in daily life activities. #### Example 1 - Thirteen farmers shared 1,625 chickens equally. How many chickens did each farmer get? **Solution** - Number of farmers = 13 - Number of chickens = 1625 - Divide 1625 by 13 to get 125. - Therefore, each farmer got 125 chickens. #### Example 2 - A teacher had 305 oranges. If she distributed them equally among 35 pupils, how many oranges did each pupil receive? How many oranges did the teacher remain with? **Solution** - Number of oranges = 305 - Number of pupils = 35 - Divide 305 by 35 to get 8 and the remainder is 25. - Therefore, each student received 8 oranges and the teacher remained with 25 oranges. ### Exercise 5 1. If 133,700 sacks of maize were distributed equally among 50 villages, how many sacks did each village receive? 2. Twenty-four primary schools planted a total of 446,400 trees. How many trees did each school plant if each school planted an equal number of trees? 3. A teacher distributed 414 papers equally among 60 pupils: - How many papers did each pupil receive? - How many papers did the teacher remain with? 4. On average, 50 factories produce 80,000 tiles per day. How many tiles does each factory produce on average per day? 5. If 955 sacks of maize were distributed equally among 40 households: - how many sacks of maize did each household receive? - how many sacks of maize remained? 6. If 99,000 books were distributed equally among 200 schools, how many books did each school receive? 7. If 100,800 chalks are packed equally in 700 boxes. How many chalks does each box contain? 8. Twenty-four members of the cooperative society shared 986 pineapples. If the pineapples were shared equally, how many pineapples were left over? 9. A businessperson sells 455,000 pens in 14 days. If the sales are the same each day, how many pens does the businessperson sell daily? 10. Classrooms in 30 schools were renovated using 136,890 iron sheets. If each classroom used an equal number of iron sheets, how many iron sheets did each school use? ### Activity - Learning more about the division of whole numbers through online resources and programs ### Description - Explore various examples of dividing whole numbers using online resources and programs such as GeoGebra and Khan Academy. ### Summary 1. A number being divided is known as the dividend, a number that divides another number is known as the divisor, and the number obtained after division is known as the quotient. 2. The quotient may be with or without a remainder. 3. In the division of whole numbers, start dividing the digits of the dividend from the left side towards the right. ### Revision Exercise 1. 32352 ÷ 16 = 2. 500000 ÷ 1125 = 3. 3069 ÷ 99 = 4. 363600 ÷ 300 = 5. 31) 161 6. 760) 174800 7. 90) 405000 8. 998) 558880 9. 95) 344 10. 3500) 46163 11. 55) 868230 12. 1514) 113550 13. 23) 575 14. 2511) 37665 15. 63) 204687 16. A total of 984,000 people cast their votes equally at each polling station. If they voted at 820 stations, how many voters were present at each station? 17. A teacher distributed 508 exercise books among 95 pupils equally. How many exercise books did each pupil receive, and how many did the teacher remain with? 18. From the following table, write all numbers that are divisible by 8 without leaving a remainder. | 560 | 360 | 124 | 270 | 600 | | 94 | 70 | 80 | 208 | 400| | 12 | 63 | 30 | 120 | 180| | 54 | 190 | 49 | 250 | 72 | 19. A total of 814,000 people watched football matches at 37 different venues. If each venue had an equal number of people, how many people were there at each venue? 20. The Government distributed a total of 17,556 bags of fertilizer to 231 farmers. If the bags were allocated equally to each farmer, how many bags of fertilizer did each farmer receive?