Addition of Whole Numbers PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Two Addition of whole numbers Introduction Addition is a process of bringing two or more number...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Two Addition of whole numbers Introduction Addition is a process of bringing two or more numbers (or objects) together LY to obtain their total. The numbers to be added are called addends, while the result you get after adding is the sum or the total. In Standard Four, you learnt how to add whole numbers up to 99 999. In this chapter, you will learn N how to add numbers up to 999 999. You will also learn about solving word problems involving addition. The ability to add up numbers is important in all O aspects of life, at home, at school, at work and to the society. This chapter will help you to master the relationships between numbers and understand how quantities relate to one another. SE Exercise 1: Revision U Answer the following questions: 1. 61 345 + 32 134 = 2. 82 071 + 7 928 = E N 3. 463 + 11 125 = 4. 44 455 + 3 342 = LI 5. 35 678 + 4 375 = 6. 3 607 + 56 124 = 7. 25 041 + 7 268 = 8. 65 487 + 25 380 = N O 9. 48 507 10. 6 457 11. 38 735 + 38 690 + 23 564 + 51 306 R FO 12. 62 664 13. 26 663 14. 4 073 + 817 + 32 310 + 21 825 21 MATH std 5.indd 21 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 15. 36 457 16. 75 543 + 53 442 + 432 17. If Elineema has 56 784 oranges and Flora has 33 912 oranges, how many oranges do they have in total? LY 18. Mvomero District had 34 006 primary school pupils and 28 543 secondary school pupils. Find the total number of pupils in the district. N 19. Ujamaa village has 78 000 goats and Muungano village has 16 492 O goats. What is the total number of goats in the two villages? 20. Teachers attended a training seminar in two groups. The first group SE had 44 200 teachers while the second group had 55 407 teachers. How many teachers attended the seminar? U Adding numbers without regrouping E When adding numbers, it is important to consider the place value of the digits in the numbers being added. Start by adding the ones followed by the tens, N hundreds, thousands, ten thousands and hundred thousands digits. LI Addition of numbers arranged horizontally N Numbers arranged horizontally can be added without regrouping as follows: O Example 1 R FO 888 888 + 110 011 = 22 MATH std 5.indd 22 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Add ones: 888 888 + 110 011= _ _ _ _ _ 9 8 + 1 = 9. Write 9 in the ones position. 2. Add tens: 888 888 + 110 011 = _ _ _ _ 99 LY 8 + 1 = 9. Write 9 in the tens position. 888 888 + 110 011= _ _ _ 899 N 3. Add hundreds: 8 + 0 = 8. Write 8 in the hundreds O position. 4. Add thousands : 888 888 + 110 011= _ _ 8 899 5. Add ten thousands: SE 8 + 0 = 8. Write 8 in the thousands position. 888 888 + 110 011= _ 98 899 U 8 + 1 = 9. Write 9 in the ten thousands position. 6. Add hundred thousands: E 8 + 1 = 9. Write 9 in the hundred 888 888 + 110 011 = 998 899 thousands position. N LI Therefore, 888 888 + 110 011 = 998 899. N Example 2 O 34 487 + 42 002 = R Solution FO 34 487 + 42 002 = 76 489 23 MATH std 5.indd 23 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Add the following numbers: 1. 445 702 + 231 264 = 2. 45 536 + 210 431 = 3. 647 775 + 200 003 = 4. 803 414 + 121 405 = LY 5. 715 109 + 263 780 = 6. 610 243 + 379 542 = N 7. 665 544 + 332 255 = 8. 785 432 + 213 467 = O 9. 835 201 + 163 348 = 10. 631 594 + 246 305 = 11. 13 451 + 240 037 = SE 12. 524 321 + 143 442 = 13. 912 340 + 45 426 = 14. 230 000 + 144 348 = U 15. 374 136 + 25 862 = 16. 811 133 + 141 556 = E 17. 666 777 + 333 222 = 18. 344 342 + 454 656 = N LI 19. 334 434 + 544 204 = 20. 567 891 + 431 107 = N Addition of numbers arranged vertically Numbers arranged vertically can be added without regrouping as follows: O Example 1 R 235 641 FO + 621 357 24 MATH std 5.indd 24 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Arrange the numbers vertically as follows to match their place values: Hundred thousands Ten thousands Thousands Hundreds Ones Tens LY 2 3 5 6 4 1 + 6 2 1 3 5 7 N 8 5 6 9 9 8 O Therefore, the answer is 856 998. Example 2 SE 453 472 U + 316 513 E Solution N Steps: 1. Arrange the numbers vertically as follows to match their place values: LI Hundred thousands N Ten thousands O Thousands Hundreds R Ones Tens FO 4 5 3 4 7 2 + 3 1 6 5 1 3 7 6 9 9 8 5 25 MATH std 5.indd 25 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Add ones: 2 + 3 = 5. Write 5 in the ones position. 3. Add tens: 7 + 1 = 8. Write 8 in the tens position. 4. Add hundreds: 4 + 5 = 9. Write 9 in the hundreds position. 5. Add thousands: 3 + 6 = 9. Write 9 in the thousands position. LY 6. Add ten thousands: 5 + 1 = 6.Write 6 in the ten thousands position. 7. Add hundred thousands: 4 + 3 = 7. Write 7 in the hundred thousands N position. O Therefore, the answer is 769 985. Example 3 SE U 238 275 + 500 623 E N LI Solution N 238 275 + 500 623 O 738 898 R FO 26 MATH std 5.indd 26 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 3 Answer the following questions: 1. 731 546 2. 99 999 3. 342 643 + 166 422 + 100 000 + 455 136 LY 4. 232 738 5. 857 432 6. 41 755 + 756 041 + 131 456 + 328 142 N O 7. 800 000 8. 224 466 9. 340 405 + 167 489 200 000 + 314 582 + 550 533 SE 10. 137 452 11. 75 000 12. 934 533 U + 62 540 + 504 643 + 45 302 E 13. 630 402 14. 720 340 15. 244 336 N + 207 294 + 108 637 135 452 + 210 111 LI N 16. 712 734 17. 710 247 18. 569 732 O + 275 005 + 9 340 + 430 021 R 19. 10 113 20. 430 124 FO 129 274 + 546 004 + 60 612 27 MATH std 5.indd 27 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Adding numbers by regrouping Addition of numbers arranged horizontally Numbers arranged horizontally can be added by regrouping as follows: Example 1 846 484 + 152 486 = LY Solution 1. Add ones: 846 484 + 152 486 = _ _ _ _ _ 0 N 4 + 6 = 10. Regroup ten ones as 1 tens and 0 ones. Write 0 in the O ones position. Take 1 group of tens to the tens position. 2. Add tens: 1 + 8 + 8 = 17. Regroup 17 tens SE 846 484 + 152 486 = _ _ _ _ 70 as 1 hundreds and 7 tens. Write 7 U in the tens position. Take 1 group of hundreds to the hundreds position. E 3. Add hundreds: 846 484 + 152 486 = _ _ _ 970 N 1 + 4 + 4 = 9. Write 9 in the hundreds position. LI 4. Add thousands: 6 + 2 = 8. Write 8 in the thousands 846 484 + 152 486 = _ _ 8 970 N position. 5. Add ten thousands: O 4 + 5 = 9. Write 9 in the ten 846 484 + 152 486 = _ 98 870 thousands position. R 6. Add hundred thousands: FO 8 + 1 = 9. Write 9 in the hundred 846 484 + 152 486 = 998 970 thousands position. Therefore, 846 484 + 152 486 = 998 970. 28 MATH std 5.indd 28 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 239 879 + 46 823 = Solution 239 879 + 46 823 = 286 702 LY Exercise 4 N Answer the following questions: O 1. 162 845 + 134 027 = 2. 293 586 + 26 323 = 3. 721 318 + 183 518 = 4. SE 526 517 + 34 048 = U 5. 2 964 + 298 576 = 6. 784 049 + 108 187 = 7. 881 054 + 9 999 = 8. 786 951 + 118 275 = E N 9. 216 783 + 678 357 = 10. 484 888 + 200 286 = LI 11. 69 000 + 209 179 = 12. 567 183 + 384 921 = N 13. 943 573 + 56 327 = 14. 700 852 + 279 168 = O 15. 526 507 + 386 549 = 16. 298 745 + 650 124 = R 17. 465 327 + 388 169 = 18. 7 250 + 428 866 = FO 19. 881 178 + 11 356 = 20. 877 778 + 66 665 = 29 MATH std 5.indd 29 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Addition of numbers arranged vertically Numbers arranged vertically can be added by regrouping as follows: Example 1 228 186 + 374 899 LY Solution N Steps: 1. Arrange the numbers vertically as follows to match their place values O Hundred Ten thousands thousands Thousands Hundreds 2+1 2+1 8+1 1+1 SE Tens 8+1 Ones 6 U +3 7 4 8 9 9 6 1 0 1 3 1 0 1 8 1 5 6 0 3 0 8 5 E N 2. Add ones: 6 + 9 = 15. Regroup 15 as 1 tens and 5 ones. Write 5 in the LI ones position and add 1 to the tens position. 3. Add tens: 1+ 8 + 9 = 18. Regroup 18 as 1 hundreds and 8 tens. Write N 8 in the tens position and add 1 to the hundreds position. O 4. Add hundreds: 1 + 1 + 8 = 10. Regroup 10 as 1 thousands and 0 hundreds. Write 0 in the hundreds position and add 1 to the thousands position. R 5. Add thousands: 1 + 8 + 4 = 13. Regroup 13 as 1 ten thousands and FO 3 thousands. Write 3 in the thousands position and add 1 to the ten thousands position. 30 MATH std 5.indd 30 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 6. Add ten thousands: 1 + 2 + 7 = 10. Regroup 10 as 1 hundred thousands and 0 ten thousands. Write 0 in the ten thousands position and add 1 to the hundred thousands position. 7. Add hundred thousands: 1 + 2 + 3 = 6. Write 6 in the hundred thousands position. Therefore, the answer is 603 085. LY Example 2 N 456 736 + 13 497 O Solution Steps: SE 1. Add ones: 6 + 7 = 13. Regroup U 456 736 13 as 1 tens and 3 ones. + 13 497 Write 3 in the ones position and 3 E add 1 to the tens position. N 2. Add tens: 1 + 3 + 9 = 13. Regroup 456 736 LI 13 as 1 hundreds and 3 tens. + 13 497 Write 3 in the tens position, and 33 N add 1 to the hundreds position. O 3. Add hundreds: 1 + 7 + 4 = 12. Regroup 12 as 1 thousands 456 736 R and 2 hundreds. Write 2 in the + 13 497 hundreds position, and add 1 to 233 FO the thousands position. 31 MATH std 5.indd 31 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. Add thousands: 1 + 6 + 3 = 10. Regroup 10 as 1 ten thousands 456 736 and 0 thousands. Write 0 in the + 13 497 thousands position, and add 1 to 0 233 the ten thousands position. 5. Add ten thousands: 1 + 5 + 1 = 7. 456 736 LY Write 7 in the ten thousands + 13 497 position. 70 233 N 6. Add hundred thousands: 4 + 0 = 4. 456 736 Write 4 in the hundred thousands + 13 497 O position. 470 233 Therefore, the answer is 470 233. Example 3 SE Solution U 192 574 192 574 + 3 648 + 3 648 E 196 222 N LI Exercise 5 N Answer the following questions: O 1. 856 956 2. 88 456 3. 489 765 + 134 689 + 134 689 + 94 538 R FO 4. 324 857 5. 708 924 6. 889 900 + 143 073 + 79 989 + 73 281 32 MATH std 5.indd 32 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 7. 454 899 8. 818 819 9. 834 532 378 716 + 71 719 + 134 068 + 120 102 10. 40 546 11. 679 448 12. 489 660 + 221 768 298 765 + 427 488 LY + 1 000 N 13. 507 609 14. 779 988 15. 24 454 O 382 517 + 78 866 + 138 457 + 13 170 SE 16. 679 884 17. 666 777 18. 488 574 U + 243 029 + 112 990 + 433 126 E 19. 884 007 20. 555 666 N + 107 994 111 000 200 234 LI + 32 152 N O Word problems involving addition of numbers Example 1 R FO A meat processing factory bought 137 527 cows the year before last year. The same factory bought 222 062 cows last year. How many cows were bought by the factory in both years? 33 MATH std 5.indd 33 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Number of cows bought the year before last year 137 527 Number of cows bought last year + 222 062 Total number of cows bought 359 589 Therefore, the factory bought 359 589 cows. Example 2 LY Three lorries transported mangoes as follows: N The first lorry transported 225 768 mangoes, the second lorry transported 19 435 mangoes, and the third lorry transported 22 202 mangoes. How O many mangoes were transported by the three lorries? Solution SE Number of mangoes transported by the first lorry 225 768 Number of mangoes transported by the second lorry 19 435 U Number of mangoes transported by the third lorry + 22 202 Total number of mangoes transported by three lorries 267 405 E Therefore, 267 405 mangoes were transported by the three lorries. N Exercise 6 LI Answer the following questions: N 1. The number of residents in three wards are as follows: O Mgori ward has 216 819 residents, Mhonda ward has 258 776 residents and Balangida ward has 126 000 residents. What is the total number of residents in the three wards? R FO 2. Hango has a saving of 830 900 shillings. If he received a loan of 160 550 shillings from a bank, what is the total amount of money does he have? 34 MATH std 5.indd 34 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Handeni district has 561 217 tree seedlings while Manyoni district has 393 888 tree seedlings. How many tree seedlings do the two districts have? 4. Dodoma Regional Library has 678 213 books and Mbeya Regional Library has 298 994 books. What is the total number of books in both libraries? LY 5. Students enrollment into Form V for three consecutive years was as N follows: 65 123 students were enrolled in 2015, 87 112 students were enrolled in 2016, and 98 430 students were enrolled in 2017. What O was the total number of students enrolled during the three years? SE 6. The harvests of various crops were as follows: 216 997 bags of beans, 230 000 bags of maize and 340 775 bags of sunflower seeds. What were the total number of bags of crops U harvested? 7. Kongwa National Ranch has 483 125 cattle while Sagara National E Ranch has 375 166 cattle. Find the total number of cattle kept by both N Ranches. LI 8. Njombe Region harvested 713 128 pieces of timber while Iringa Region harvested 280 193 pieces of timber. How many pieces of timber were N harvested by both regions? O 9. Jamhuri Primary School has 2 588 desks, Mwanga Primary School has 8 813 desks and Mihayo Primary School has 10 554 desks. Find R the total number of desks in the three schools. FO 10. A certain company bought 491 235 cars by cash and 508 761 cars on loan. How many cars did the company buy? 35 MATH std 5.indd 35 30/07/2021 14:49  FOR ONLINE USE ONLY Exercise 7 DO NOT DUPLICATE Answer the following questions: 1. 431 635 + 200 163 = 2. 888 887 + 66 677 = 3. 548867 + 33 567 = 4. 213 + 56 334 + 700 451 = LY 5. 566 780 + 11 002 + 300 054 = 6. 19 610 + 40 133 + 20 223 = 7. 243 489 + 452 007 = 8. 7 840 + 63 450 + 220 006 = N 9. 244 444 + 677 555 = 10. 777 784 + 112 241 = O 11. 666 666 12. + 332 113 SE 405 306 + 379 908 U 13. 244 726 14. 340 045 + 339 493 + 35 975 E N 15. 453 659 16. 467 438 LI + 546 341 + 6 005 N O 17. 355 325 18. 389 535 + 241 023 + 1 003 R FO 36 MATH std 5.indd 36 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 19. 723 461 20. 989 999 126 873 + 1 492 + 138 912 21. Pohama village has 98 214 chickens and Mazae village has 415 999 chickens. How many chickens are there in both villages? LY 22. My aunt has 168 000 shillings. If she gets a loan of 90 000 shillings, find the total amount of money that my aunt will have. N 23. A farmer got 400 000 shillings after selling chickens. He also got 500 000 shillings by selling goats. How much money did he receive O from both sales? 24. Mwanza Region sold 304 301 tons of cotton and Shinyanga Region SE sold 532 175 tons of cotton. How many tons of cotton were sold by both regions? 25. My father bought a television set for 689 000 shillings, a sewing machine U for 150 000 shillings and a bicycle for 160 000 shillings. How much money did my father spend on all three items? E Summary N 1. When adding numbers, arrange the numbers either horizontally or LI vertically. Start by adding the ones digits, followed by the tens digits, the hundreds digits, the thousands digits, the ten thousands digits and N the hundred thousands digits. O 2. When adding numbers, always start from the rightmost digit and end with the leftmost digit. R 3. In solving word problems, consider the following: (a) Read the word problem to identify the mathematical operation to FO be performed. (b) Perform the operation on the numbers mentioned in the problem. (c) After calculations, conclude by answering the question. 37 MATH std 5.indd 37 30/07/2021 14:49