Math Class IV Multiplication PDF

## Chapter Two ### Multiplication of Whole Numbers #### Introduction In this chapter, you will learn about multiplication of whole numbers. The concept of multiplication is applied in everyday activities such as business, construction, statistics, sports, and financial transactions. The competenc...

## Chapter Two ### Multiplication of Whole Numbers #### Introduction In this chapter, you will learn about multiplication of whole numbers. The concept of multiplication is applied in everyday activities such as business, construction, statistics, sports, and financial transactions. The competencies developed will enable you to use multiplication in various contexts. #### Think Mathematics without the knowledge of multiplication is unimaginable. #### Activity 1 ##### Developing the Concept of Multiplication 1. In your environment, prepare groups of similar objects according to the quantity you need. 2. Count the number of groups you have in Step 1. 3. Identify the number of groups and the total number of objects in each group to find the overall total. 4. Is there any relationship between the number of objects, the number of groups, and the overall total? ### Multiplication of Two-Digit Numbers by a One-Digit Multiplier #### Example 1 62 x 4 = **Steps:** 1. Multiply 2 ones by 4: 2 x 4 = 8. Write 8 in the ones place. 2. Multiply 6 tens by 4: 6 x 4 = 24. Write 4 in the tens place. Regroup 20 tens into 2 hundreds. Therefore, 62 x 4 = 248. #### Example 2 25 x 6 = **Steps:** 1. Multiply 5 ones by 6: 5 x 6 = 30. Write 0 in the ones place. Shift 3 tens to the tens place. 2. Multiply 2 tens by 6: 2 x 6 = 12. Add tens: 2 + 3 = 5. Write 5 in the tens place. Regroup 10 tens into 1 hundreds. Write 1 in the hundreds place. Therefore, 25 x 6 = 150. #### Exercise 1 1. 41 x 9 = 2. 64 x 2 = 3. 38 x 7 = 4. 56 x 7 = 5. 49 x 4 = 6. 72 x 8 = ### Multiplication of Two-Digit Numbers by a Two-Digit Multiplier #### Example 1 23 x 21 = **Solution** Write multiplication problem vertically aligning the digits by place values. **Steps:** 1. 1 x 3 = 3. Write 3 in the ones place. 2. 1 x 20 = 20. Write 2 in the tens place. 3. 20 x 3 = 60. Write 6 in the tens place and 0 in the ones place. 4. 20 x 20 = 400. Write 4 in the hundreds place. 5. Add the results from Steps 1 to 4: 23 + 460 = 483. Therefore, 23 x 21 = 483. #### Example 2 27 x 12 = **Solution** **Steps:** 1. 2 x 7 = 14. Write 4 in the ones place. Regroup 10 ones into 1 tens. Shift 1 tens to the tens place. 2. 2 x 20 = 40. Write 4 tens. Add tens: 4 + 1 = 5. Write 5 in the tens place. 3. 10 x 7 = 70. Write 7 in the tens place and 0 in the ones place. 4. 10 x 20 = 200. Write 2 in the hundreds place. 5. Add the results from Steps 1 to 4: 54 + 270 = 324. Therefore, 27 x 12 = 324. #### Example 3 78 x 69 = **Solution** **Steps:** 1. 9 x 8 = 72. Write 2 in the ones place. Regroup 70 ones into 7 tens. Shift 7 tens to the tens place. 2. 9 x 70 = 630. Write 63 tens. Add tens: 63 + 7 = 70. Write 0 in the tens place and 7 in the hundreds place. 3. 60 x 8 = 480. Write 0 in the ones place and 8 in the tens place. Regroup 40 tens into 4 hundreds. Shift 4 hundreds to the hundreds place. 4. 60 x 70 = 4200. Write 42 hundreds. Add 4 hundreds: 42 + 4 = 46. Write 6 in the hundreds place. Regroup 40 hundreds into 4 thousands. Write 4 in the thousands place. 5. Add the results from Steps 1 to 4: 702 + 4680 = 5382. Therefore, 78 x 69 = 5,382. #### Exercise 2 1. 22 x 14 = 2. 28 x 18 = 3. 11 x 13 = 4. 24 x 5 = 5. 23 x 13 = 6. 33 x 33 = 7. 19 x 40 = 8. 42 x 12 = 9. 32 x 11 = 10. 11 x 22 = 11. 97 x 88 = 12. 85 x 60 = 13. 47 x 18 = 14. 53 x 34 = 15. 65 x 24 = 16. 25 x 17 = 17. 37 x 31 = 18. 62 x 13 = 19. 56 x 29 = 20. 74 x 53 = ### Multiplication of Three-Digit Numbers by a Multiplier with Up to Two Digits #### Example 1 217 x 4 = **Solution** **Steps:** 1. 4 x 7 = 28. Write 8 in the ones place. Regroup 20 ones into 2 tens. Shift 2 tens to the tens place. 2. 4 x 10 = 40. Write 4 tens. Add tens: 4 + 2 = 6. Write 6 in the tens place. 3. 200 x 4 = 800. Write 8 in the hundreds place. 4. Add the results from Step 1 to 3: 68 + 800 = 868 Therefore, 217 x 4 = 868. ### Multiplication of Numbers with Up to Six Digits by a Multiplier with Up to Three Digits #### Example 1 3125 * 12 = **Solution** 3125 x 12 6250 + 31250 37500 Therefore, the answer is 37,500. ### Alternative Method You can use the method of boxes by following the steps: 1. Draw boxes according to the digits given both horizontally and vertically. 2. Write the multiplier across the top horizontally and the multiplicand on the right and vertically. 3. Divide each box diagonally to create two triangles. 4. Multiply each digit of the multiplier by each digit of the multiplicand. 5. In each box write the tens in the top triangle and the ones in the bottom triangle. 6. Add the numbers diagonally. #### Example 2 276 x 123 = **Solution** 276 x 123 828 5520 + 27600 33948 Therefore, the answer is 33,948. #### Example 3 42538 x 39 = **Solution** The answer can be obtained through a horizontal arrangement method as follows: 1. Multiply 42538 by 9 ones: 42538 x 9 = 382842. 2. Multiply 42538 by 3 tens: 42538 x 30 = 1276140. 3. Add the results from Steps 1 and 2: 382842 + 1276140 = 1658982. Therefore, 42538 x 39 = 1,658,982 #### Example 4 771481 x 8 6171848 Therefore, the answer is 6,171,848. #### Exercise 4 1. 109 x 125 = 2. 1592 x 145 = 3. 25578 x 24 = 4. 8202 x 200 = 5. 97227 x 20 = 6. 384567 x 19 = 7. 6088 x 40 = 8. 50009 x 120 = 9. 90000 x 90 = 10. 231 x 213 = 11. 4181 x 54 = 12. 3722 x 946 = 13. 239586 x 24 = 14. 95,413 x 42 = 15. 521 x 132 = 16. 3416 x 244 = 17. 42,762 x 52 = 18. 105,000 x 102 = 19. 81,271 x 708 = ### Word Problems Involving Multiplication of Whole Numbers #### Example 1 A businessman bought 170 boxes of bar soap. Each box contains 20 bars of soap. How many bars of soap were bought in total? **Solution** 1 box contains 20 bars of soap. 170 boxes contain 170 x 20 = 3400 bars. Therefore, the businessman bought a total of 3,400 bars of soap. #### Example 2 The school bought 5624 crates of soda. If each crate had 24 bottles of soda, how many bottles of soda were bought in total? **Solution** crates 5,624 Each crate contained 24 bottles of soda. 5624 x 24 22496 + 112480 134976 Therefore, the school bought a total of 134,976 bottles of soda. ### Exercise 5 1. A school bus carries 60 sacks of beans per trip. How many sacks of beans will the bus carry in 19 trips? 2. An average of 128 children are born each month in a certain hospital. How many children are expected to be born in 12 months? 3. Pupils from 309 schools sat for an examination. If each school had 208 pupils, how many pupils in total did the examination? 4. An airport serves 462015 passengers per month. How many passengers will the airport serve in five months if the number remains constant each month? 5. Villagers planted 3841 trees in each nursery. If they planted trees in 389 nurseries, how many trees did the villagers plant in total? 6. A warehouse can store 8985 sacks. How many sacks can 728 such warehouses store in total? 7. A factory prints 685390 books per day. How many books will the factory print in 317 days? 8. A farmer keeps 5998 laying hens. If each hen lays two eggs per day, how many eggs will be layed in nine weeks? ### Activity 2 #### Learning Multiplication Through Online Lessons **Description** Use reliable online lessons to learn more about the concept of multiplication of whole numbers. ### Summary 1. When multiplying numbers, arrange them in either vertical or horizontal order. 2. Multiply the digits starting from the ones, tens, hundreds, and so on. 3. The multiplier is the number used to multiply another number. ### Revision Exercise 1. 86 x 11 = 2. 710 x 12 = 3. 8714 x 126 = 4. 206 x 73 = 5. 650 x 130 = 6. 8475 x 410 = 7. 1500 x 14 = 8. 61721 x 102 = 9. 172 * 13 = 10. 1025 x 105 = 11. 30016 x 12 = 12. 22381 x 111 = 13. 510 x 108 = 14. 80516 x 12 = 15. 315233 * 24 = 16. 93115 x 104 = 17. 7492 x 11 = 18. 165 x 21 = 19. 414 x 232 = 20. 79276 x 15 = 21. If there are 6 boxes of pencils, and each box contains 12 pencils, how many pencils are there in total? 22. A businessman sells 88,960 handbags each day. How many handbags will be sold in total in a 31-days month? 23. A Cooperative society had 172 who collected 85 bags of cashews each. How many bags of cashews did the members collect in total? 24. A textile factory produces 96,540 dresses each day. How many dresses will the factory produce in 365 days? 25. A train transports 61,229 bags of cement in each day. How many bags of cement will the train transport in 65 days?