Subtraction Of Whole Numbers PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Three Subtraction of whole numbers Introduction Subtraction is a process of taking away some objects from a collection...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Three Subtraction of whole numbers Introduction Subtraction is a process of taking away some objects from a collection of LY objects. It is the opposite of addition. In Standard Four, you learnt how to subtract numbers with not more than five digits. You subtracted numbers by regrouping and without regrouping. You also learnt how to solve word N problems involving subtraction of whole numbers. In this chapter, you will learn subtraction of numbers with not more than six digits by regrouping and O without regrouping. You will also learn how to solve word problems involving subtraction of numbers. You need to understand how to subtract numbers SE in order to perform some activities in real life. Subtraction is used when dealing with money, cooking, travelling, time and other daily life activities. U Exercise 1: Revision Answer the following questions: E 1. 68 549 – 25 127 = 2. 73 458 – 32 135 = N 3. 92 406 – 1 304 = 4. 62 694 – 30 521 = LI N 5. 62 345 – 4 672 = 6. 81 505 – 61 426 = O 7. 92 914 8. 79 461 9. 72 345 – 67 083 – 2 330 – 12 204 R FO 10. 87 910 11. 55 423 12. 63 348 – 45 710 – 5 211 – 1 419 38 MATH std 5.indd 38 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 13. 12 467 14. 54 678 15. 78 934 – 11 448 – 47 629 – 69 983 16. Yohana deposited 98 550 shillings in his bank account. If he withdrew 12 400 shillings from his bank account, what balance remained in his bank account? LY 17. The residents of Songambele village planted 75 620 trees. If 3 210 N trees were burnt, how many trees were not burnt? O 18. If 89 777 pupils sat for the standard four examination and 2 899 pupils failed the examination, find the number of pupils who passed the examination. SE 19. Residents of Maendeleo village owned 25 495 cattle. If they sold U 16 726 cattle, how many cattle remained? 20. Miriamu's mother had 57 000 shillings. She wanted to buy a television E set costing 75 000 shillings. How much money did she lack to buy N the television set? LI Subtraction of numbers without regrouping Subtracting numbers arranged horizontally N Numbers arranged horizontally can be subtracted without regrouping as follows: O Example 1 R 257 645 – 34 413 = FO 39 MATH std 5.indd 39 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Subtract ones: 5 – 3 = 2. 257 645 – 34 413 = _ _ _ _ _ 2 Write 2 in the ones position. 2. Subtract tens: 4 – 1 = 3. 257 645 – 34 413 = _ _ _ _ 32 Write 3 in the tens position. LY 3. Subtract hundreds: 6 – 4 = 2. 257 645 – 34 413 = _ _ _ 232 Write 2 in the hundreds position. N 4. Subtract thousands: 7 – 4 = 3. 257 645 – 34 413 = _ _ 3 232 O Write 3 in the thousands position. 5. SE Subtract ten thousands: 5 – 3 = 2. 257 645 – 34 413 = _ 23 232 Write 2 in the ten thousands position. U 6. Subtract hundred thousands: 257 645 – 34 413 = 223 232 2 – 0 = 2. Write 2 in the hundred E thousands position. N Therefore, 257 645 – 34 413 = 223 232. LI N Example 2 O 478 376 – 255 142 = R Solution FO The question can be answered by using the counting basin. 40 MATH std 5.indd 40 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Steps: 1. Put the counters in the counting basin to match the digits of 478 376 and their place values as shown in the following figure: Hundred Ten thousands thousandsThousands Hundreds Tens Ones LY 4 7 8 3 7 6 N 2. Since the operation is subtraction, cross the counters in each O compartment to match the digits 255 142 and their place values as shown in the following figure: Hundred Ten SE thousands thousandsThousands Hundreds Tens Ones U E N 3. Count and record the uncrossed counters in each compartment of the counting basin according to their place values as shown in the LI following figure: N Hundred Ten thousands thousandsThousands Hundreds Tens Ones O R FO 2 2 3 2 3 4 Therefore, 478 376 – 255 142 = 223 234. 41 MATH std 5.indd 41 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 643 270 – 541 240 = Solution 643 270 – 541 240 = 102 030. LY Exercise 2 N Answer the following questions: O 1. 153 652 – 41 331 = 2. 889 998 – 664 322 = 3. 706 605 – 602 303 = 4. SE 824 335 – 13 112= 5. 623 440 – 2 010 = 6. 753 872 – 641 631 = U 7. 568 237 – 18 113 = 8. 995 698 –12 254 = E 9. 156 789 – 130 000 = 10. 425 310 – 213 110 = N 11. 524 885 – 112 432 = 12. 357 603 – 223 402 = LI 13. 654 235 – 232 113 = 14. 115 752 – 15 231 = N O 15. 788 500 – 501 000 = 16. 534 728 – 134 617 = 17. 399 728 – 188 314 = 18. 496 623 – 285 413 = R FO 19. 247 568 – 113 254 = 20. 524 804 – 103 501 = 42 MATH std 5.indd 42 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Subtraction of numbers arranged vertically Numbers arranged vertically can be subtracted without regrouping as follows: Example 1 457 234 – 134 102 LY Solution N Steps: O 1. Subtract ones: 4 – 2 = 2. Write 2 457 234 in the ones position. – 134 102 SE 2 2. Subtract tens: 3 – 0 = 3. Write 3 457 234 U in the tens position. – 134 102 32 E 3. Subtract hundreds: 2 – 1 = 1. 457 234 N Write 1 in the hundreds position. – 134 102 132 LI 4. Subtract thousands: 7 – 4 = 3. 457 234 N Write 3 in the thousands position. – 134 102 O 3 132 5. Subtract ten thousands: 457 234 R 5 – 3 = 2. Write 2 in the ten – 134 102 FO thousands position. 23 132 43 MATH std 5.indd 43 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 6. Subtract hundred thousands digits: 457 234 4 – 1 = 3. Write 3 in the hundred – 134 102 thousands position. 323 132 Therefore, the answer is 323 132. LY You can also subtract the given numbers by using their expanded forms as shown in the following example. N Example 2 O 463 257 – 221 125 SE Solution U Steps: Thousands Hundreds thousands thousands Hundred Ones Tens E Ten N 4 6 3 2 5 7 – 2 2 1 1 2 5 LI 7 – 5 2 N 50 – 20 3 0 200 – 100 1 0 0 O 3 000 – 1 000 2 0 0 0 60 000 – 20 000 4 0 0 0 0 R 400 000 – 200 000 2 0 0 0 0 0 FO 2 4 2 1 3 2 Therefore, the answer is 242 132. 44 MATH std 5.indd 44 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 can be done directly as follows: 463 257 – 221 125 Solution 463 257 – 221 125 242 132 LY Example 3 N Solution 649 283 O 649 283 – 34 162 – 34 162 615 121 SE U Exercise 3 Answer the following questions: E 1. 652 451 2. 826 666 3. 527 238 N – 331 041 – 714 232 – 20 014 LI 4. 237 972 5. 823 574 6. 912 345 N – 112 451 – 1 230 – 810 212 O R 7. 587 645 8. 353 821 9. 734 726 – 335 243 – 141 711 – 512 413 FO 45 MATH std 5.indd 45 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 10. 789 235 11. 773 002 12. 315 241 – 227 122 – 521 001 – 111 131 13. 632 541 14. 825 789 15. 127 834 – 11 231 – 13 578 – 114 321 LY 16. 953 275 17. 483 255 18. 517 599 – 132 143 – 351 013 – 414 328 N O 19. 889 659 20. 172 637 – 64 236 – 41 332 SE U Subtraction of numbers by regrouping Subtraction of numbers arranged horizontally Numbers arranged horizontally can be subtracted by regrouping as follows: E N Example 1 LI 981 746 – 274 272 = Solution N Steps: 1. Subtract ones: 6 – 2 = 4. Write 4 981 746 – 274 272 = _ _ _ _ _ 4 O in the ones position. R FO 46 MATH std 5.indd 46 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Subtract tens: 4 – 7. This is 981 746 – 274 272=_ _ _ _ 74 not sufficient.Take 1 group of hundreds from the 7 hundreds and change it into tens. This gives 10 tens. Add the tens: 10 + 4 = 14. Now, subtract tens: 14 – 7 = 7. Write 7 in the tens position. 981 746 – 274 272 = _ _ _ 474 LY 3. Remember that, one group of hundreds was taken from the 7 hundreds. Thus only 6 hundreds N remained. Subtract hundreds: 6 – 2 = 4. Write 4 in the hundreds O position. 4. Subtract thousands: 1 – 4. 981 746 – 274 272 = _ _ 7 474 This is not sufficient. Take 1 group of ten thousands from the SE 8 ten thousands and change it U into thousands. This gives 10 thousands. Add thousands: 10 + 1 = 11. Now, subtract E thousands: 11 – 4 = 7. Write 7 in N the thousands position. 5. Remember that, one group of ten 981 746 – 274 272 = _ 07 474 LI thousands was taken from the 8 ten thousands. Thus, only 7 ten N thousands remained. Subtract O thousands: 7 – 7. Write 0 in the ten thousands position. 6. Subtract hundred thousands: 981 746 – 274 272 = 707 474 R 9 – 2 = 7. Write 7 in the hundred FO thousands position. Therefore, 981 746 – 274 272 = 707 474. 47 MATH std 5.indd 47 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 634 207 – 253 478 = Solution Following the steps in example 1, you will get 634 207 – 253 478 = 380 729. LY N Exercise 4 O Answer the following questions: 1. 864 624 – 25 206 = 2. 685 378 – 123 553 = 3. 938 765 – 737 846 = 4. SE 748 760 – 144 690 = U 5. 992 478 – 966 257 = 6. 998 897 – 669 999 = 7. 576 788 – 2 899 = 8. 534 609 – 514 799 = E N 9. 947 842 – 88 847 = 10. 979 988 – 79 999 = LI 11. 479 149 – 288 601 = 12. 398 694 – 296 498 = N 13. 754 382 – 289 = 14. 990 000 – 90 270 = O 15. 319 728 – 187 379 = 16. 489 756 – 298 587 = R 17. 156 742 – 137 833 = 18. 567 810 – 369 523 = FO 19. 246 483 – 137 552 = 20. 615 807 – 326 675 = 48 MATH std 5.indd 48 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Subtraction of numbers arranged vertically Numbers arranged vertically can be subtracted by regrouping as follows: Example 1 Example 2 Example 3 756 456 560 947 537 902 – 484 417 – 67 328 – 449 651 LY N Solution Solution Solution 756 456 560 947 537 902 O – 484 417 – 67 328 – 449 651 272 039 493 619 88 251 SE Exercise 5 U Answer the following questions: 1. 854 623 2. 664 378 3. 928 765 E – 24 205 – 123 453 – 726 847 N LI 4. 148 760 5. 678 246 6. 999 898 N – 145 619 – 76 254 – 769 979 O 7. 996 788 8. 964 234 9. 167 897 R – 239 879 – 78 927 – 56 908 FO 49 MATH std 5.indd 49 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 10. 624 573 11. 367 129 12. 409 530 – 468 786 – 135 237 – 357 142 13. 800 000 14. 650 124 15. 461 385 – 222 075 – 236 745 – 172 843 LY 16. 555 073 17. 562 782 18. 853 076 N – 396 164 – 389 351 – 68 684 O 19. 785 438 20. 295 745 – 90 900 – 276 836 SE U Word problems involving subtraction E Example 1 N A factory manufactures 789 828 bottles of soda daily. Due to electricity LI shortage, the factory manufactured only 537 014 bottles of soda on one of the days. What was the deficit in the production of bottles of soda on N that day? O Solution Daily production of bottles = 789 828. R Production of bottles due to shortage of electricity = 537 014. FO The shortage of production was 789 828 – 537 014 = 252 814. Therefore, the deficit in the production on that day was 252 814 bottles of soda. 50 MATH std 5.indd 50 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 A total of 678 520 people had eye examination at a hospital. If 382 140 people examined were found to have eyes problems, how many people were declared free from eyes problems? Solution Number of people given eye examination = 678 520 LY Number of people found with defective eyes = 382 140 Number of people found to be free from eyes problems was N 678 520 – 382 140 = 296 380. O Therefore, the number of people who were declared free from eye problems was 296 380. Exercise 6 SE U Answer the following questions: 1. A total of 635 740 pupils sat for the standard seven Primary School Leaving Examination. If the number of boys was 312 520, how many E girls sat for the examination? N 2. In a certain region, 796 599 people were vaccinated against a certain LI disease. If the number of women vaccinated was 396 479, how many men were vaccinated? N O 3. A certain food processing factory produced 572 895 litres of sunflower oil. If 351 453 litres were sold, how many litres were not sold? R 4. During the first week of production, a steel company produced 763 264 FO pieces of steel rods. In the second week, the same company produced only 642 143 pieces of steel rods. What was the shortfall of steel rods in the second week? 51 MATH std 5.indd 51 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 5. A total of 705 990 bricks were needed for construction of a village health centre. If the villagers had made only 504 550 bricks, how many more bricks were needed for construction? 6. Muna’s monthly salary is 970 645 shillings. He pays 98 850 shillings as monthly house rent. How much money does Muna remain with after paying house rent each month? LY 7. A total of 545 768 fans watched a football match on television. If N 213 554 among them were women, how many of the fans were men? O 8. A certain region needed 625 800 bags of maize to meet its requirement. The region was supplied with 540 780 bags of maize. How many more SE bags of maize were needed to meet the region’s maize requirement? 9. In June, pupils at Mwachonja primary School used 643 650 litres of U water. In July, they used 599 650 litres. By how many litres did the pupils reduce their water consumption in July compared to June? E 10. In a certain district, 780 558 cattle were marked. If the cattle population N of the district is 978 445, how many cattle were not marked? LI 11. Four tyres of a car cost 745 000 shillings. If Agnes has 680 500 shillings, how much more money does she need for buying the four tyres of her N car? O 12. On Monday, 855 600 shillings tax were collected at a village market. The tax collection on Tuesday was 678 450 shillings. By how much R was the Tuesday tax collection less than the tax collection on Monday? FO 52 MATH std 5.indd 52 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 7 Answer the following questions: 1. 280 000 – 17 000 = 2. 586 424 – 343 315 = 3. 748 869 – 26 879 = 4. 892 135 – 72 013 = LY 5. 966 617 – 134 215 = 6. 873 977 – 762 582 = 7. 538 993 – 429 926 = 8. 969 897 – 2 672 = N 9. 672 354 – 51 132 = 10. 554 732 – 318 472 = O 11. 826 592 – 648 257 = 12. 487 925 – 35 725 = 13. 289 355 – 199 264 = SE 14. 999 999 – 1 285 = 15. 278 914 – 18 288 = 16. 586 424 – 343 315 = U 17. 697 415 – 28 928 = 18. 892 135 – 72 013 = E 19. 842 316 – 145 820 = 20. 423 450 – 230 004 = N 21. 897 050 – 530 478 = LI 22. 167 898 23. 987 025 24. 873 977 N – 12 378 – 35 012 – 762 582 O 25. 504 040 26. 567 893 27. 761 405 R – 139 012 – 125 698 – 234 503 FO 53 MATH std 5.indd 53 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 28. The exercise books requirement for ten schools is 175 038. If the benefactors donated 10 750 exercise books, what is the shortage of exercise books at the schools? 29. A cooperative society made 287 891 cement bricks out of a total of 482 674 bricks that are needed. How many more bricks must be made by the cooperative society? LY 30. Kilimanjaro Region planted 988 000 trees in various parts of the Region. If only 798 000 trees grew, how many trees did not grow? N 31. A constructor was paid 845 750 shillings for paying labours during O the construction of a school toilet. If the labour charge was 974 500 shillings, how many more shillings were needed to complete payment of the labour charge? SE 32. A total of 905 700 litres of water flow into a water tank daily. If the U daily water consumption is 700 478 litres, how many litres of water remain in the tank? E 33. A school has a chicken farming project. The annual profit of the N project is 745 850 shillings. If 420 500 shillings are used annually to buy chicks, how much money remains for the school each year? LI 34. A factory used 797 800 Kilowatts of electricity in a first period of three N months. During a second period of three months, the factory used O 580 730 Kilowatts. What is the difference in electricity consumption between the two periods? R 35. Last year, Kilosa district admitted 345 730 pupils into Standard FO One. If 2 320 pupils dropped out, how many Standard One pupils remained at the school? 54 MATH std 5.indd 54 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. Subtraction of numbers is done by arranging numbers either horizontally or vertically. 2. In subtraction, start by subtracting ones, then tens, hundreds, thousands, ten thousands and hundred thousands. 3. In solving word problems, consider the following: (a) Read the given word problem to identify the arithmetic operation LY to be performed. (b) Perform the operation on the numbers mentioned in the problem. (c) After the calculations, conclude by answering the question asked N in the problem. O 4. In any situation where you are required to subtract a larger digit from a smaller digit, always look at the digit immediately to the left of the SE smaller digit, and take 1 group from it. Change the taken group into 10 ones, or 10 tens, or 10 hundreds, or 10 thousands, or 10 ten thousands, depending on the place value of the digit being subtracted. Add 10 to U the smaller digit which was insufficient to subtract in the first place and then perform the subtraction. 5. When subtracting numbers by vertical arrangement, make sure that E the digits are properly aligned, ones placed under ones, tens placed under tens, and so on. N LI N O R FO 55 MATH std 5.indd 55 30/07/2021 14:49