Year 6: Long multiplication
Part of the Year 6 long multiplication, long division and bodmas chapter. Chapter overview · whole chapter on one page
Long multiplication
A two-digit number is multiplied in two rows. First multiply the top number by the ones digit. Then multiply by the tens digit, but write a 0 place holder first. This is because the tens digit is worth ten times more. Finally, add the two rows together. This is the long multiplication method.
An area model shows why the method works. The number 23 is split into 20 and 3, and 16 is split into 10 and 6. Each box is a partial product. The four partial products add up to the whole answer.
Estimate before you calculate. Round each number to one significant figure and multiply. For 2,345 × 16, the estimate is 2,000 × 20 = 40,000. The exact answer should be close to the estimate. If your answer is far away, check your working.
Key ideas
- Multiply by the ones digit first, then by the tens digit. Each row is a partial product.
- Write a 0 place holder at the start of the tens row: 2,345 × 10 = 23,450, not 2,345.
- Carry tens into the next column in each row, and add them after you multiply the column.
- Add the two rows at the end. Estimate first, so you can see if the answer is sensible.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 16 is 1 ten and 6 ones. We multiply by the ones first, then by the tens.16 = 10 + 6
- Multiply by the ones, which is 6. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 5 × 6 = 30. Write 0 and carry 3.
Tens: 4 × 6 = 24, and 24 + 3 = 27. Write 7 and carry 2.
Hundreds: 3 × 6 = 18, and 18 + 2 = 20. Write 0 and carry 2.
Thousands: 2 × 6 = 12, and 12 + 2 = 14. Write 4 and carry 1.
Ten thousands: nothing left to multiply. Write the carried 1.
2,345 × 6 = 14,070 - Write a 0 place holder, then multiply by the tens, which is 1. The 1 stands for 10. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 5 × 1 = 5. Write 5.
Tens: 4 × 1 = 4. Write 4.
Hundreds: 3 × 1 = 3. Write 3.
Thousands: 2 × 1 = 2. Write 2.
2,345 × 1 = 2,345. With the 0 place holder this row is 23,450 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
2345 × 16 ------- 14070 + 23450 ------- 37520
14,070 + 23,450 = 37,520
Check. Estimate: 2,000 × 20 = 40,000, and 37,520 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 27 is 2 tens and 7 ones. We multiply by the ones first, then by the tens.27 = 20 + 7
- Multiply by the ones, which is 7. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 8 × 7 = 56. Write 6 and carry 5.
Tens: 1 × 7 = 7, and 7 + 5 = 12. Write 2 and carry 1.
Hundreds: 6 × 7 = 42, and 42 + 1 = 43. Write 3 and carry 4.
Thousands: nothing left to multiply. Write the carried 4.
618 × 7 = 4,326 - Write a 0 place holder, then multiply by the tens, which is 2. The 2 stands for 20. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 8 × 2 = 16. Write 6 and carry 1.
Tens: 1 × 2 = 2, and 2 + 1 = 3. Write 3.
Hundreds: 6 × 2 = 12. Write 2 and carry 1.
Thousands: nothing left to multiply. Write the carried 1.
618 × 2 = 1,236. With the 0 place holder this row is 12,360 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
618 × 27 ------- 4326 + 12360 ------- 16686
4,326 + 12,360 = 16,686
Check. Estimate: 600 × 30 = 18,000, and 16,686 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 34 is 3 tens and 4 ones. We multiply by the ones first, then by the tens.34 = 30 + 4
- Multiply by the ones, which is 4. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 2 × 4 = 8. Write 8.
Tens: 7 × 4 = 28. Write 8 and carry 2.
Hundreds: 0 × 4 = 0, and 0 + 2 = 2. Write 2.
Thousands: 4 × 4 = 16. Write 6 and carry 1.
Ten thousands: nothing left to multiply. Write the carried 1.
4,072 × 4 = 16,288 - Write a 0 place holder, then multiply by the tens, which is 3. The 3 stands for 30. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 2 × 3 = 6. Write 6.
Tens: 7 × 3 = 21. Write 1 and carry 2.
Hundreds: 0 × 3 = 0, and 0 + 2 = 2. Write 2.
Thousands: 4 × 3 = 12. Write 2 and carry 1.
Ten thousands: nothing left to multiply. Write the carried 1.
4,072 × 3 = 12,216. With the 0 place holder this row is 122,160 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
4072 × 34 -------- 16288 + 122160 -------- 138448
16,288 + 122,160 = 138,448
Check. Estimate: 4,000 × 30 = 120,000, and 138,448 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Watch out
Do not forget the 0 place holder in the tens row. Without it, the answer is ten times too small. Also, do not add the rows before you have multiplied every column.Exercise 2A Long multiplication with two-digit numbers
Non-calculatorKey words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 23 is 2 tens and 3 ones. We multiply by the ones first, then by the tens.23 = 20 + 3
- Multiply by the ones, which is 3. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 7 × 3 = 21. Write 1 and carry 2.
Tens: 2 × 3 = 6, and 6 + 2 = 8. Write 8.
Hundreds: 1 × 3 = 3. Write 3.
127 × 3 = 381 - Write a 0 place holder, then multiply by the tens, which is 2. The 2 stands for 20. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 7 × 2 = 14. Write 4 and carry 1.
Tens: 2 × 2 = 4, and 4 + 1 = 5. Write 5.
Hundreds: 1 × 2 = 2. Write 2.
127 × 2 = 254. With the 0 place holder this row is 2,540 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
127 × 23 ------ 381 + 2540 ------ 2921
381 + 2,540 = 2,921
Check. Estimate: 100 × 20 = 2,000, and 2,921 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 12 is 1 ten and 2 ones. We multiply by the ones first, then by the tens.12 = 10 + 2
- Multiply by the ones, which is 2. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 6 × 2 = 12. Write 2 and carry 1.
Tens: 4 × 2 = 8, and 8 + 1 = 9. Write 9.
Hundreds: 0 × 2 = 0. Write 0.
Thousands: 1 × 2 = 2. Write 2.
1,046 × 2 = 2,092 - Write a 0 place holder, then multiply by the tens, which is 1. The 1 stands for 10. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 6 × 1 = 6. Write 6.
Tens: 4 × 1 = 4. Write 4.
Hundreds: 0 × 1 = 0. Write 0.
Thousands: 1 × 1 = 1. Write 1.
1,046 × 1 = 1,046. With the 0 place holder this row is 10,460 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
1046 × 12 ------- 2092 + 10460 ------- 12552
2,092 + 10,460 = 12,552
Check. Estimate: 1,000 × 10 = 10,000, and 12,552 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 14 is 1 ten and 4 ones. We multiply by the ones first, then by the tens.14 = 10 + 4
- Multiply by the ones, which is 4. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 5 × 4 = 20. Write 0 and carry 2.
Tens: 0 × 4 = 0, and 0 + 2 = 2. Write 2.
Hundreds: 3 × 4 = 12. Write 2 and carry 1.
Thousands: 2 × 4 = 8, and 8 + 1 = 9. Write 9.
2,305 × 4 = 9,220 - Write a 0 place holder, then multiply by the tens, which is 1. The 1 stands for 10. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 5 × 1 = 5. Write 5.
Tens: 0 × 1 = 0. Write 0.
Hundreds: 3 × 1 = 3. Write 3.
Thousands: 2 × 1 = 2. Write 2.
2,305 × 1 = 2,305. With the 0 place holder this row is 23,050 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
2305 × 14 ------- 9220 + 23050 ------- 32270
9,220 + 23,050 = 32,270
Check. Estimate: 2,000 × 10 = 20,000, and 32,270 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 21 is 2 tens and 1 one. We multiply by the ones first, then by the tens.21 = 20 + 1
- Multiply by the ones, which is 1. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 8 × 1 = 8. Write 8.
Tens: 9 × 1 = 9. Write 9.
Hundreds: 0 × 1 = 0. Write 0.
Thousands: 3 × 1 = 3. Write 3.
3,098 × 1 = 3,098 - Write a 0 place holder, then multiply by the tens, which is 2. The 2 stands for 20. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 8 × 2 = 16. Write 6 and carry 1.
Tens: 9 × 2 = 18, and 18 + 1 = 19. Write 9 and carry 1.
Hundreds: 0 × 2 = 0, and 0 + 1 = 1. Write 1.
Thousands: 3 × 2 = 6. Write 6.
3,098 × 2 = 6,196. With the 0 place holder this row is 61,960 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
3098 × 21 ------- 3098 + 61960 ------- 65058
3,098 + 61,960 = 65,058
Check. Estimate: 3,000 × 20 = 60,000, and 65,058 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 36 is 3 tens and 6 ones. We multiply by the ones first, then by the tens.36 = 30 + 6
- Multiply by the ones, which is 6. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 8 × 6 = 48. Write 8 and carry 4.
Tens: 0 × 6 = 0, and 0 + 4 = 4. Write 4.
Hundreds: 4 × 6 = 24. Write 4 and carry 2.
Thousands: nothing left to multiply. Write the carried 2.
408 × 6 = 2,448 - Write a 0 place holder, then multiply by the tens, which is 3. The 3 stands for 30. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 8 × 3 = 24. Write 4 and carry 2.
Tens: 0 × 3 = 0, and 0 + 2 = 2. Write 2.
Hundreds: 4 × 3 = 12. Write 2 and carry 1.
Thousands: nothing left to multiply. Write the carried 1.
408 × 3 = 1,224. With the 0 place holder this row is 12,240 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
408 × 36 ------- 2448 + 12240 ------- 14688
2,448 + 12,240 = 14,688
Check. Estimate: 400 × 40 = 16,000, and 14,688 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 47 is 4 tens and 7 ones. We multiply by the ones first, then by the tens.47 = 40 + 7
- Multiply by the ones, which is 7. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 5 × 7 = 35. Write 5 and carry 3.
Tens: 7 × 7 = 49, and 49 + 3 = 52. Write 2 and carry 5.
Hundreds: 6 × 7 = 42, and 42 + 5 = 47. Write 7 and carry 4.
Thousands: 2 × 7 = 14, and 14 + 4 = 18. Write 8 and carry 1.
Ten thousands: nothing left to multiply. Write the carried 1.
2,675 × 7 = 18,725 - Write a 0 place holder, then multiply by the tens, which is 4. The 4 stands for 40. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 5 × 4 = 20. Write 0 and carry 2.
Tens: 7 × 4 = 28, and 28 + 2 = 30. Write 0 and carry 3.
Hundreds: 6 × 4 = 24, and 24 + 3 = 27. Write 7 and carry 2.
Thousands: 2 × 4 = 8, and 8 + 2 = 10. Write 0 and carry 1.
Ten thousands: nothing left to multiply. Write the carried 1.
2,675 × 4 = 10,700. With the 0 place holder this row is 107,000 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
2675 × 47 -------- 18725 + 107000 -------- 125725
18,725 + 107,000 = 125,725
Check. Estimate: 3,000 × 50 = 150,000, and 125,725 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 38 is 3 tens and 8 ones. We multiply by the ones first, then by the tens.38 = 30 + 8
- Multiply by the ones, which is 8. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 6 × 8 = 48. Write 8 and carry 4.
Tens: 5 × 8 = 40, and 40 + 4 = 44. Write 4 and carry 4.
Hundreds: nothing left to multiply. Write the carried 4.
56 × 8 = 448 - Write a 0 place holder, then multiply by the tens, which is 3. The 3 stands for 30. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 6 × 3 = 18. Write 8 and carry 1.
Tens: 5 × 3 = 15, and 15 + 1 = 16. Write 6 and carry 1.
Hundreds: nothing left to multiply. Write the carried 1.
56 × 3 = 168. With the 0 place holder this row is 1,680 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
56 × 38 ------ 448 + 1680 ------ 2128
448 + 1,680 = 2,128
Check. Estimate: 60 × 40 = 2,400, and 2,128 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 65 is 6 tens and 5 ones. We multiply by the ones first, then by the tens.65 = 60 + 5
- Multiply by the ones, which is 5. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 4 × 5 = 20. Write 0 and carry 2.
Tens: 0 × 5 = 0, and 0 + 2 = 2. Write 2.
Hundreds: 9 × 5 = 45. Write 5 and carry 4.
Thousands: nothing left to multiply. Write the carried 4.
904 × 5 = 4,520 - Write a 0 place holder, then multiply by the tens, which is 6. The 6 stands for 60. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 4 × 6 = 24. Write 4 and carry 2.
Tens: 0 × 6 = 0, and 0 + 2 = 2. Write 2.
Hundreds: 9 × 6 = 54. Write 4 and carry 5.
Thousands: nothing left to multiply. Write the carried 5.
904 × 6 = 5,424. With the 0 place holder this row is 54,240 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
904 × 65 ------- 4520 + 54240 ------- 58760
4,520 + 54,240 = 58,760
Check. Estimate: 900 × 70 = 63,000, and 58,760 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 26 is 2 tens and 6 ones. We multiply by the ones first, then by the tens.26 = 20 + 6
- Multiply by the ones, which is 6. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 2 × 6 = 12. Write 2 and carry 1.
Tens: 3 × 6 = 18, and 18 + 1 = 19. Write 9 and carry 1.
Hundreds: nothing left to multiply. Write the carried 1.
32 × 6 = 192 - Write a 0 place holder, then multiply by the tens, which is 2. The 2 stands for 20. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 2 × 2 = 4. Write 4.
Tens: 3 × 2 = 6. Write 6.
32 × 2 = 64. With the 0 place holder this row is 640 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
32 × 26 ----- 192 + 640 ----- 832
192 + 640 = 832
Check. Estimate: 30 × 30 = 900, and 832 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 36 is 3 tens and 6 ones. We multiply by the ones first, then by the tens.36 = 30 + 6
- Multiply by the ones, which is 6. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 5 × 6 = 30. Write 0 and carry 3.
Tens: 2 × 6 = 12, and 12 + 3 = 15. Write 5 and carry 1.
Hundreds: 1 × 6 = 6, and 6 + 1 = 7. Write 7.
125 × 6 = 750 - Write a 0 place holder, then multiply by the tens, which is 3. The 3 stands for 30. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 5 × 3 = 15. Write 5 and carry 1.
Tens: 2 × 3 = 6, and 6 + 1 = 7. Write 7.
Hundreds: 1 × 3 = 3. Write 3.
125 × 3 = 375. With the 0 place holder this row is 3,750 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
125 × 36 ------ 750 + 3750 ------ 4500
750 + 3,750 = 4,500
Check. Estimate: 100 × 40 = 4,000, and 4,500 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 46 is 4 tens and 6 ones. We multiply by the ones first, then by the tens.46 = 40 + 6
- Multiply by the ones, which is 6. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 8 × 6 = 48. Write 8 and carry 4.
Tens: 1 × 6 = 6, and 6 + 4 = 10. Write 0 and carry 1.
Hundreds: nothing left to multiply. Write the carried 1.
18 × 6 = 108 - Write a 0 place holder, then multiply by the tens, which is 4. The 4 stands for 40. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 8 × 4 = 32. Write 2 and carry 3.
Tens: 1 × 4 = 4, and 4 + 3 = 7. Write 7.
18 × 4 = 72. With the 0 place holder this row is 720 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
18 × 46 ----- 108 + 720 ----- 828
108 + 720 = 828
Check. Estimate: 20 × 50 = 1,000, and 828 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 13 is 1 ten and 3 ones. We multiply by the ones first, then by the tens.13 = 10 + 3
- Multiply by the ones, which is 3. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 4 × 3 = 12. Write 2 and carry 1.
Tens: 1 × 3 = 3, and 3 + 1 = 4. Write 4.
Hundreds: 2 × 3 = 6. Write 6.
214 × 3 = 642 - Write a 0 place holder, then multiply by the tens, which is 1. The 1 stands for 10. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 4 × 1 = 4. Write 4.
Tens: 1 × 1 = 1. Write 1.
Hundreds: 2 × 1 = 2. Write 2.
214 × 1 = 214. With the 0 place holder this row is 2,140 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
214 × 13 ------ 642 + 2140 ------ 2782
642 + 2,140 = 2,782
Check. Estimate: 200 × 10 = 2,000, and 2,782 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Method. Check Sam's second row. The tens digit of 12 is worth ten times more, so the row must be 35 × 10 = 350.
- Look at Sam's working. Sam wrote 35 for the tens row, but the tens digit 1 means 10, not 1.Sam's second row: 35, but it should be 35 × 10 = 350
- Work out the correct second row. Write a 0 place holder, then multiply 35 by the tens digit 1.35 × 10 = 350
- Add the rows again. Add the correct rows.70 + 350 = 420
Check. 35 × 12 = 420 is the answer. Check: 35 × 10 + 35 × 2 = 350 + 70 = 420. ✓
Watch out. When the tens row is missing its 0 place holder, the answer is far too small.
Method. Write 20 as 2 tens, and check each part of Mia's method.
- Multiply by the 2 tens. The 2 is worth 20, so the answer is ten times 1,234 × 2.1,234 × 2 = 2,468
- Add the zero place holder. Multiplying by 20 means the answer is ten times bigger, so the zero goes on the end.2,468 with a 0 = 24,680
- Compare with the long method. The long method gives the same answer.1,234 × 20 = 24,680
Check. Mia is right: 1,234 × 20 = 24,680. ✓
Watch out. Mia's method works for multiplying by 10, 20 or 30, because the zero shows the tens.
Key words. Long multiplication is a written method for multiplying by a number with two digits. We multiply by the ones digit on one row, then by the tens digit on the next row. The zero place holder keeps the tens digit in the tens column.
Method. Use long multiplication. Multiply by the ones digit, then by the tens digit with a 0 place holder, then add the two rows.
- Split the second number into tens and ones. 52 is 5 tens and 2 ones. We multiply by the ones first, then by the tens.52 = 50 + 2
- Multiply by the ones, which is 2. Start on the right and multiply each digit. Carry any tens to the next column, as in short multiplication.Ones: 9 × 2 = 18. Write 8 and carry 1.
Tens: 0 × 2 = 0, and 0 + 1 = 1. Write 1.
Hundreds: 8 × 2 = 16. Write 6 and carry 1.
Thousands: nothing left to multiply. Write the carried 1.
809 × 2 = 1,618 - Write a 0 place holder, then multiply by the tens, which is 5. The 5 stands for 50. The 0 in the ones column holds the place, so the answer is ten times bigger.Ones: 9 × 5 = 45. Write 5 and carry 4.
Tens: 0 × 5 = 0, and 0 + 4 = 4. Write 4.
Hundreds: 8 × 5 = 40. Write 0 and carry 4.
Thousands: nothing left to multiply. Write the carried 4.
809 × 5 = 4,045. With the 0 place holder this row is 40,450 - Add the two rows. Add the two rows, one column at a time, and carry where you need to.
809 × 52 ------- 1618 + 40450 ------- 42068
1,618 + 40,450 = 42,068
Check. Estimate: 800 × 50 = 40,000, and 42,068 is close to it. ✓
Watch out. Do not forget the 0 place holder on the second row. Without it, the answer is ten times too small.
Method. Divide 1,406 by 37 to find the missing number. Then check by multiplying.
- Set out the division. The missing number is the answer to 1,406 ÷ 37.1,406 ÷ 37
- Work out the division. Find how many 37s fit into 1,406, one digit at a time.
38 37 ) 1406 111 --- 29 296 --- 0 - Check by multiplying. Multiply the answer by 37. It must make 1,406.38 × 37 = 1,406
Check. 38 × 37 = 1,406. ✓
Watch out. Check the answer by multiplying, not by guessing.