Multiplication of Numbers PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Four Multiplication of numbers Introduction Multiplication is a mathematical operation performed on a pair of n...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Four Multiplication of numbers Introduction Multiplication is a mathematical operation performed on a pair of numbers in order to obtain a number called a product. In Standard Four, you learnt LY how to multiply numbers with up to three digits. In this chapter, you will learn to multiply numbers that give a product with not more than six digits. You will also solve word problems involving multiplication of numbers. Learning N multiplication will provide you with appropriate knowledge to work on other O mathematical concepts like division, fraction and algebra. Multiplication is used in real life activities like calculating pay rates, profits, variety of sums, expenses and so on. Exercise 1: Revision SE U Answer the following questions: 1. 509 × 1 = 2. 243 × 4 = 3. 999 × 9 = E 4. 541 × 10 = 5. 143 × 50 = 6. 172 × 80 = N LI 7. 104 × 100 = 8. 312 × 13 = 9. 474 × 15 = N 10. 616 × 12 = 11. 467 × 12 = O 12. 213 13. 237 14. 304 × 6 × 9 × 12 R FO 15. 472 16. 132 17. 322 × 16 × 13 × 12 56 MATH std 5.indd 56 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 18. 431 19. 250 20. 342 × 22 × 14 × 24 21. 722 × 14 LY 22. If a class has 53 pupils and the teacher gives 4 pencils to every N student. What is the total number of pencils given to the pupils? O 23. A cow produces 15 litres of milk each day. How many litres of milk will be produced in 100 days? SE 24. Magoma makes 220 cement bricks a day. Find the number of cement bricks that he will make in 11 days. U 25. A loaf of bread is sold at 800 shillings. If Johari buys 46 loaves of bread, how much money will she pay? E 26. Furaha sold 26 bags of oranges. If the price of one bag of oranges N is 950 shillings, how much money did he get? LI 27. If 685 cement bricks are required to build a chicken coop, how many cement bricks are required to build 11 chicken coops? N O 28. Find the product of 117 and 33. 29. If 134 mangoes are harvested every day, how many mangoes R will be harvested in 70 days? FO 30. A tree plantation has 287 rows of trees. If each row has 66 trees, how many trees are there in the farm? 57 MATH std 5.indd 57 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 31. A soap factory manufactures 825 soaps in one hour. If each soap is sold at 50 shillings, how much money will the factory get per hour? Multiplication of a number by a multiplier having up to two digits In multiplying a number by the multiplier, consider the place values of the digits in the multiplier. Start by multiplying the number by the ones, followed by the tens, the hundreds, the thousands, the ten thousands and finally by the hundred thousands. LY Multiplication of a number having up to four digits by a multiplier with up to two digits N Example 1 O 278 × 13 = Solution SE The answer can be obtained by horizontal arrangement of the numbers: U Multiply 278 by 3 ones: 278 × 3 = 834. Multiply 278 by 1 tens: 278 × 10 = 2 780. Add the two results obtained; that is, 834 + 2 780 = 3 614. E N Therefore, 278 × 13 = 3 614. LI The answer for this example can also be obtained by vertical arrangement of the numbers as follows: N Thousands Hundreds Tens Ones O 2 7 8 × 1 3 3 × 8 2 4 R 3 × 70 2 1 0 3 × 200 6 0 0 FO 10 × 8 8 0 10 × 70 7 0 0 10 × 200 + 2 0 0 0 3 6 1 4 58 MATH std 5.indd 58 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE This equals to 278 × 13 834 + 2 780 3 614 LY Therefore, 278 × 13 = 3 614. N Example 2 O 2 165 × 3 = Solution SE U Thousands Hundreds Tens Ones 2 1 6 5 × 3 E 3 × 5 1 5 N 3 × 60 1 8 0 3 × 100 3 0 0 LI 3 × 2 000 + 6 0 0 0 6 4 9 5 N O The answer for this example can also be obtained directly as follows: 2 1 6 5 × 3 R 6 4 9 5 FO Therefore, 2 165 × 3 = 6 495. 59 MATH std 5.indd 59 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Answer the following questions: 1. 497 × 3 = 2. 3 237 × 4 = 3. 1 220 × 8 = 4. 306 × 12 = LY 5. 511 × 15 = 6. 432 × 22 = N 7. 281 × 59 = 8. 374 × 62 = O 9. 721 × 28 = 10. 189 × 84 = 11. 4 156 × 78 = SE 12. 2 213 × 23 = U 13. 1 332 × 21 = 14. 2 113 × 22 = 15. 3 122 × 13 = 16. 2 346 × 14 = E N 17. 3 334 × 25 = 18. 4 167 × 17 = LI 19. 1 324 × 18 = 20. 2 415 × 16 = N 21. 3 217 × 23 = 22. 1 433 × 14 = O 23. 2 246 × 27 = 24. 3 417 × 32 = R 25. 1 619 × 43 = FO 60 MATH std 5.indd 60 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Multiplication of a number having up to five digits by a multiplier with up to two digits Example 1 24 615 × 5 = Solution LY Hundred Ten thousands thousands Thousands Hundreds Tens Ones 2 4 6 1 5 N × 5 O 5 × 5 2 5 5 × 10 5 0 5 × 600 5 × 4 000 2 SE 3 0 0 0 0 0 0 0 U 5 × 20 000 + 1 0 0 0 0 0 1 2 3 0 7 5 E Therefore, 24 615 × 5 = 123 075. N LI The answer can also be obtained directly as follows: 2 4 6 1 5 N × 5 O 1 2 3 0 7 5 R Example 2 FO 10 308 × 28 61 MATH std 5.indd 61 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution 10 308 × 28 82 464 + 206 160 288 624 LY N Exercise 3 O Answer the following questions: 1. 42 983 × 20 = 2. 53 490 × 14 = SE3. 71 762 × 12 = 4. 33 768 × 24 = 5. 432 10 × 2 = 6. 63 281 × 15 = U 7. 53 249 × 13 = 8. 30 167 × 20 = 9. 20 070 × 28 = E 10. 10 101 × 99 = 11. 90 909 × 11 = 12. 261 40 × 3 = N 13. 33 004 × 2 = 14. 30 874 × 3 = LI 15. 21 423 16. 32 247 17. 41 165 N × 23 × 12 × 21 O 18. 36 792 19. 20 081 20. 23 414 R × 11 × 24 × 32 FO 62 MATH std 5.indd 62 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Multiplication of a number by a multiplier having up to three digits Example 1 452 × 56 = Ten Solution thousands Thousands Hundreds Tens Ones 4 5 2 LY × 5 6 6 × 2 1 2 N 6 × 50 3 0 0 6 × 400 2 4 0 0 O 50 × 2 1 0 0 50 × 50 2 5 0 0 50 × 400 + 2 0 0 2 SE 5 3 0 1 0 2 U Altenatively, 4 5 2 × 5 6 E 2 7 1 2 N + 2 2 6 0 0 2 5 3 1 2 LI N Therefore, 452 × 56 = 25 312. O Example 2 R 276 FO × 123 63 MATH std 5.indd 63 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution 276 × 123 828 5 520 + 27 600 33 948 LY Therefore, the answer is 33 948. N Exercise 4 O Answer the following questions: 1. 109 × 125 = 2. 159 × 145 = SE 3. 255 × 204 = 4. 202 × 200 = 5. 227 × 200 = 6. 384 × 400 = U 7. 608 × 32 = 8. 509 × 64 = 9. 919 × 251 = E 10. 231 × 213 = 11. 411 × 124 = 12. 322 × 213 = N 13. 109 14. 413 15. 521 LI × 241 × 142 × 132 N 16. 236 17. 346 18. 422 O × 242 × 244 × 142 R FO 19. 714 20. 812 × 102 × 242 64 MATH std 5.indd 64 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Word problems involving multiplication Example One crate contains 24 bottles of soft drinks. How many bottles of soft drinks will be in 5 624 crates? Solution LY The number of crates = 5 624 Number of bottles in one crate = 24 N 5 624 O × 24 22 496 + 112 480 134 976 SE U Therefore, there will be 134 976 bottles in 5 624 crates. Exercise 5 E N Answer the following questions: 1. A garment manufacturing company produces 654 metres of cloth per LI day. How many metres of cloth will be produced in 23 days? N 2. A pair of kitenge costs 30 500 shillings. What is the cost of 8 pairs of O kitenge? R 3. A lorry can transport 629 sacks of cement in one trip. If the lorry makes 65 trips, how many bags of cement will be transported? FO 4. A certain book has 6 285 lines of text. If each line has 14 words, how many words does the book contain? 65 MATH std 5.indd 65 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 5. Which product is larger than the other between 531 × 6 and 351 × 7? 6. A teacher instructed each of his 258 pupils to collect 122 counters. How many counters were collected by pupils? 7. Maria sold 66 chickens at 15 000 shillings each. How much money did she get for selling all the chickens? LY 8. Each of 136 bricklayers made 40 concrete bricks. Find the number of N concrete bricks made by all the bricklayers? O 9. Baraka sells 2 560 kilograms of meat a day. How many kilograms of meat will he sell in 31 days? SE 10. A water tank has a capacity of 2 500 liters of water. What is the capacity of 83 water tanks of the same capacity? U 11. One compartment of a passenger train can carry 98 passengers. What will be the number of passengers in 35 compartments of the same E capacity? N 12. Juhudi Primary school has 1 260 pupils. If each pupil was given 35 LI tree seedlings to plant, how many tree seedlings were planted by all the pupils? N O Exercise 6 R FO Answer all the following questions: 1. 234 × 5 = 2. 528 × 7 = 3. 28 987 × 6 = 66 MATH std 5.indd 66 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. 133 × 10 = 5. 265 × 60 = 6. 741 × 100 = 7. 327 381 × 3 = 8. 33 333 × 3 = 9. 9 605 × 9 = 10. 624 × 531 = 11. 750 × 750 = 12. 308 13. 407 14. 615 × 11 × 206 × 33 LY 15. 3 434 16. 2 131 17. 114 N × 25 × 22 × 142 O 18. 2 005 19. 1 623 20. 723 × 23 × SE 22 × 6 U 21. 33 407 22. 52 743 23. 34 752 × 28 × 13 × 11 E 24. Which product is greater than the other between 587 × 23 and 416 × 29? N LI 25. One match box has 50 sticks. How many sticks are there in 167 match boxes of the same capacity? N Summary O 1. In multiplication, consider the place value of the digit of the multiplier. R Always start to multiply the ones, followed by the tens, hundreds, thousands, ten thousands, and finally the hundred thousands. FO 2. In solving word problems involving multiplication, you have to identify the numbers to be multiplied from the word problem. 3. The product of any number and zero is zero. 67 MATH std 5.indd 67 30/07/2021 14:49