Year 6 Arithmetic (SATs) Multiplication and division: check-up and practice test questions

Method. Multiply column by column from the right.

1. Multiply the ones digit 4 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   4 × 7 + 0 = 28, write 8, carry 2
2. Multiply the tens digit 8 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   8 × 7 + 2 = 58, write 8, carry 5
3. Multiply the hundreds digit 3 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   3 × 7 + 5 = 26, write 6, carry 2
4. Multiply the thousands digit 6 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   6 × 7 + 2 = 44, write 4, carry 4
5. Multiply the ten thousands digit 0 by 7. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   0 × 7 + 4 = 4, write 4
6. Write the answer.
   44,688

Check. 44,688 ÷ 7 = 6,384. ✓

Method. Use two partial products.

1. Multiply by the ones digit of 37, which is 7 (7). Write the partial product, and put a zero in each empty column below it.
   508 × 7 = 3,556
2. Multiply by the tens digit of 37, which is 3 (30). Write the partial product, and put a zero in each empty column below it.
   508 × 30 = 15,240
3. Add the partial products. Line up the place values and add.
   3,556 + 15,240 = 18,796
4. Write the answer.
   18,796

Check. About 500 × 40 = 20,000, close to 18,796. ✓

Method. Divide one digit at a time.

1. Divide the thousands part: 6 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.
   6 ÷ 5 = 1 remainder 1
2. Divide the hundreds part: 19 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.
   19 ÷ 5 = 3 remainder 4
3. Divide the tens part: 42 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.
   42 ÷ 5 = 8 remainder 2
4. Divide the ones part: 23 ÷ 5. Write how many times the divisor goes in, and carry the remainder to the next column.
   23 ÷ 5 = 4 remainder 3
5. Write the answer.
   1,384 remainder 3

Check. 1,384 × 5 + 3 = 6,923. ✓

Method. Divide one digit at a time.

1. Bring down the thousands digit to make 3. 3 is less than 28, so this digit of the answer is 0.
   3 < 28, so 0 with remainder 3
2. Bring down the hundreds digit to make 30. 28 goes into 30 1 times, and the remainder is what is left.
   28 × 1 = 28, 30 - 28 = 2
3. Bring down the tens digit to make 26. 26 is less than 28, so this digit of the answer is 0.
   26 < 28, so 0 with remainder 26
4. Bring down the ones digit to make 264. 28 goes into 264 9 times, and the remainder is what is left.
   28 × 9 = 252, 264 - 252 = 12
5. Write the answer.
   109 remainder 12

Check. 28 × 109 + 12 = 3,064. ✓

Method. Multiply as whole numbers, then put the point back.

1. Ignore the decimal point for now. Multiply the digits 418 by 9, as whole numbers.
   418 × 9 = 3762
2. Put the decimal point back. 4.18 has 2 decimal places, so the answer has 2 decimal places.
   3762 → 37.62
3. Write the answer.
   37.62

Check. 4.2 × 9 = 37.8, close to 37.62. ✓

Method. Divide, then continue with decimal places.

1. Divide the whole number first. 5 goes into 9 1 times, with a remainder of 4.
   9 ÷ 5 = 1 remainder 4
2. Write a decimal point, add a 0 and keep dividing. The remainder 4 becomes 40, and 5 goes into 40 8 times.
   40 ÷ 5 = 8 remainder 0
3. Write the answer.
   1.8

Check. 5 × 1.8 = 9. ✓

Method. Multiply by 1000 moves each digit three places left.

1. Move each digit three places left. The 7 moves to the hundreds column.
   0.7 → 700
2. Write the answer.
   700

Check. 700 ÷ 1000 = 0.7. ✓

Method. Multiply the cakes in a box by the number of boxes.

1. Multiply by the ones digit of 27, which is 7 (7). Write the partial product, and put a zero in each empty column below it.
   36 × 7 = 252
2. Multiply by the tens digit of 27, which is 2 (20). Write the partial product, and put a zero in each empty column below it.
   36 × 20 = 720
3. Add the partial products. Line up the place values and add.
   252 + 720 = 972
4. Write the answer.
   972

Check. Estimate: 40 × 30 = 1,200, close to 972. ✓

Method. Work out the right-hand side first.

1. Right-hand side. 180 ÷ 6 = 30.
   180 ÷ 6 = 30
2. Missing number. 5 × 6 = 30.
   5 × 6 = 30
3. Write the answer.
   6

Check. 5 × 6 = 30 = 180 ÷ 6. ✓

Method. Check the multiplication.

1. Multiply. 25 × 160 = 4,000.
   25 × 160 = 4,000
2. Read the remainder. The product equals 4,000, so nothing is left over.
   remainder 0
3. Write the answer.
   Because 25 × 160 = 4,000 exactly, so the remainder is 0.

Check. 25 × 160 = 4,000. ✓

Method. Multiply column by column.

1. Multiply the ones digit 6 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   6 × 5 + 0 = 30, write 0, carry 3
2. Multiply the tens digit 4 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   4 × 5 + 3 = 23, write 3, carry 2
3. Multiply the hundreds digit 0 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   0 × 5 + 2 = 2, write 2
4. Multiply the thousands digit 2 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   2 × 5 + 0 = 10, write 0, carry 1
5. Multiply the ten thousands digit 0 by 5. Write the ones digit of the answer in this column and carry the tens digit to the next column.
   0 × 5 + 1 = 1, write 1
6. Write the answer.
   10,230

Check. 10,230 ÷ 5 = 2,046. ✓

Method. Use two partial products.

1. Multiply by the ones digit of 16, which is 6 (6). Write the partial product, and put a zero in each empty column below it.
   73 × 6 = 438
2. Multiply by the tens digit of 16, which is 1 (10). Write the partial product, and put a zero in each empty column below it.
   73 × 10 = 730
3. Add the partial products. Line up the place values and add.
   438 + 730 = 1,168
4. Write the answer.
   1,168

Check. About 70 × 16 = 1,120, close to 1,168. ✓

Method. Divide one digit at a time.

1. Divide the thousands part: 8 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.
   8 ÷ 3 = 2 remainder 2
2. Divide the hundreds part: 24 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.
   24 ÷ 3 = 8 remainder 0
3. Divide the tens part: 5 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.
   5 ÷ 3 = 1 remainder 2
4. Divide the ones part: 27 ÷ 3. Write how many times the divisor goes in, and carry the remainder to the next column.
   27 ÷ 3 = 9 remainder 0
5. Write the answer.
   2,819 remainder 0

Check. 2,819 × 3 + 0 = 8,457. ✓

Method. Divide one digit at a time with long division.

1. Bring down the thousands digit to make 1. 1 is less than 18, so this digit of the answer is 0.
   1 < 18, so 0 with remainder 1
2. Bring down the hundreds digit to make 17. 17 is less than 18, so this digit of the answer is 0.
   17 < 18, so 0 with remainder 17
3. Bring down the tens digit to make 173. 18 goes into 173 9 times, and the remainder is what is left.
   18 × 9 = 162, 173 - 162 = 11
4. Bring down the ones digit to make 114. 18 goes into 114 6 times, and the remainder is what is left.
   18 × 6 = 108, 114 - 108 = 6
5. Write the answer.
   96 remainder 6

Check. 18 × 96 + 6 = 1,734. ✓

Method. Divide, then decide what the remainder means.

1. Bring down the thousands digit to make 1. 1 is less than 25, so this digit of the answer is 0.
   1 < 25, so 0 with remainder 1
2. Bring down the hundreds digit to make 10. 10 is less than 25, so this digit of the answer is 0.
   10 < 25, so 0 with remainder 10
3. Bring down the tens digit to make 104. 25 goes into 104 4 times, and the remainder is what is left.
   25 × 4 = 100, 104 - 100 = 4
4. Bring down the ones digit to make 46. 25 goes into 46 1 times, and the remainder is what is left.
   25 × 1 = 25, 46 - 25 = 21
5. Write the answer.
   42 classes

Check. 41 classes hold 1,025 pupils, and 21 pupils need a 42nd class. ✓

Watch out. Round up when the remainder pupils still need a place.

Method. Multiply as whole numbers, then put the point back.

1. Ignore the decimal point for now. Multiply the digits 56 by 8, as whole numbers.
   56 × 8 = 448
2. Put the decimal point back. 5.6 has 1 decimal places, so the answer has 1 decimal places.
   448 → 44.8
3. Write the answer.
   44.8

Check. 5.6 is about 6, and 6 × 8 = 48, close to 44.8. ✓

Method. Divide the whole number, then continue with decimal places.

1. Divide the whole number first. 4 goes into 41 10 times, with a remainder of 1.
   41 ÷ 4 = 10 remainder 1
2. Write a decimal point, add a 0 and keep dividing. The remainder 1 becomes 10, and 4 goes into 10 2 times.
   10 ÷ 4 = 2 remainder 2
3. Write a decimal point, add a 0 and keep dividing. The remainder 2 becomes 20, and 4 goes into 20 5 times.
   20 ÷ 4 = 5 remainder 0
4. Write the answer.
   10.25

Check. 4 × 10.25 = 41. ✓

Method. Multiply by 100 moves each digit two places left.

1. Move each digit two places left. The 3 moves to the hundreds and the 9 to the tens.
   3.9 → 390
2. Write the answer.
   390

Check. 390 ÷ 100 = 3.9. ✓

Method. Work out the right-hand side first.

1. Right-hand side. 504 ÷ 4 = 126.
   504 ÷ 4 = 126
2. Missing number. 7 × 18 = 126.
   7 × 18 = 126
3. Write the answer.
   18

Check. 7 × 18 = 126 = 504 ÷ 4. ✓

Method. Multiply as whole numbers, then put the decimal point back.

1. Multiply the digits. 245 × 4 = 980.
   245 × 4 = 980
2. Put the point back. The answer has two decimal places, so 9.80 kg.
   9.80 kg
3. Write the answer.
   Multiply 2.45 by 4 to get 9.80 kg, since 245 × 4 = 980.

Check. 2.45 is about 2.5, and 2.5 × 4 = 10, close to 9.80. ✓