GCSE Maths: Dividing (Higher)

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 56 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.
   7 ) 56
2. Start with the first 2 digits, 56. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.
   56 ÷ 7 = 8 (since 7 × 8 = 56)
3. Write the answer. Read the digits along the top.
   8 5 7) 56
   56 ÷ 7 = 8

Check. Multiply back: 8 × 7 = 56. ✓

Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 81 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.
   9 ) 81
2. Start with the first 2 digits, 81. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.
   81 ÷ 9 = 9 (since 9 × 9 = 81)
3. Write the answer. Read the digits along the top.
   9 8 9) 81
   81 ÷ 9 = 9

Check. Multiply back: 9 × 9 = 81. ✓

Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 132 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.
   12 ) 132
2. Start with the first 2 digits, 13. 12 does not go into the first digit, so we take digits from the left until we have a number that 12 can go into.
   13 ÷ 12 = 1 remainder 1 (since 12 × 1 = 12)
3. Bring down the next digit, 2, to make 12. The remainder 1 goes in front of the 2. This is the same as carrying the remainder to the next column.
   12 ÷ 12 = 1 (since 12 × 1 = 12)
4. Write the answer. Read the digits along the top.
   11 11 12) 132
   132 ÷ 12 = 11

Check. Multiply back: 11 × 12 = 132. ✓

Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 96 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.
   8 ) 96
2. Start with the first digit, 9. Work from the left. We ask how many times 8 goes into 9.
   9 ÷ 8 = 1 remainder 1 (since 8 × 1 = 8)
3. Bring down the next digit, 6, to make 16. The remainder 1 goes in front of the 6. This is the same as carrying the remainder to the next column.
   16 ÷ 8 = 2 (since 8 × 2 = 16)
4. Write the answer. Read the digits along the top.
   12 1 8) 96
   96 ÷ 8 = 12

Check. Multiply back: 12 × 8 = 96. ✓

Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 936 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.
   4 ) 936
2. Start with the first digit, 9. Work from the left. We ask how many times 4 goes into 9.
   9 ÷ 4 = 2 remainder 1 (since 4 × 2 = 8)
3. Bring down the next digit, 3, to make 13. The remainder 1 goes in front of the 3. This is the same as carrying the remainder to the next column.
   13 ÷ 4 = 3 remainder 1 (since 4 × 3 = 12)
4. Bring down the next digit, 6, to make 16. The remainder 1 goes in front of the 6. This is the same as carrying the remainder to the next column.
   16 ÷ 4 = 4 (since 4 × 4 = 16)
5. Write the answer. Read the digits along the top.
   234 11 4) 936
   936 ÷ 4 = 234

Check. Multiply back: 234 × 4 = 936. ✓

Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 6 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 1548 under the "bus stop" and 6 outside it. The answer will be written on top, one digit above each digit we divide.
   6 ) 1548
2. Start with the first 2 digits, 15. 6 does not go into the first digit, so we take digits from the left until we have a number that 6 can go into.
   15 ÷ 6 = 2 remainder 3 (since 6 × 2 = 12)
3. Bring down the next digit, 4, to make 34. The remainder 3 goes in front of the 4. This is the same as carrying the remainder to the next column.
   34 ÷ 6 = 5 remainder 4 (since 6 × 5 = 30)
4. Bring down the next digit, 8, to make 48. The remainder 4 goes in front of the 8. This is the same as carrying the remainder to the next column.
   48 ÷ 6 = 8 (since 6 × 8 = 48)
5. Write the answer. Read the digits along the top.
   258 134 6) 1548
   1548 ÷ 6 = 258

Check. Multiply back: 258 × 6 = 1548. ✓

Watch out. If 6 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 4032 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.
   8 ) 4032
2. Start with the first 2 digits, 40. 8 does not go into the first digit, so we take digits from the left until we have a number that 8 can go into.
   40 ÷ 8 = 5 (since 8 × 5 = 40)
3. Bring down the next digit, 3. The remainder was 0, so the new number to divide is just that digit.
   8 does not go into 3, so write 0 and carry on.
4. Bring down the next digit, 2, to make 32. The remainder 3 goes in front of the 2. This is the same as carrying the remainder to the next column.
   32 ÷ 8 = 4 (since 8 × 4 = 32)
5. Write the answer. Read the digits along the top.
   504 4 3 8) 4032
   4032 ÷ 8 = 504

Check. Multiply back: 504 × 8 = 4032. ✓

Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 5 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 6175 under the "bus stop" and 5 outside it. The answer will be written on top, one digit above each digit we divide.
   5 ) 6175
2. Start with the first digit, 6. Work from the left. We ask how many times 5 goes into 6.
   6 ÷ 5 = 1 remainder 1 (since 5 × 1 = 5)
3. Bring down the next digit, 1, to make 11. The remainder 1 goes in front of the 1. This is the same as carrying the remainder to the next column.
   11 ÷ 5 = 2 remainder 1 (since 5 × 2 = 10)
4. Bring down the next digit, 7, to make 17. The remainder 1 goes in front of the 7. This is the same as carrying the remainder to the next column.
   17 ÷ 5 = 3 remainder 2 (since 5 × 3 = 15)
5. Bring down the next digit, 5, to make 25. The remainder 2 goes in front of the 5. This is the same as carrying the remainder to the next column.
   25 ÷ 5 = 5 (since 5 × 5 = 25)
6. Write the answer. Read the digits along the top.
   1235 112 5) 6175
   6175 ÷ 5 = 1235

Check. Multiply back: 1235 × 5 = 6175. ✓

Watch out. If 5 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 6 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 487 under the "bus stop" and 6 outside it. The answer will be written on top, one digit above each digit we divide.
   6 ) 487
2. Start with the first 2 digits, 48. 6 does not go into the first digit, so we take digits from the left until we have a number that 6 can go into.
   48 ÷ 6 = 8 (since 6 × 8 = 48)
3. Bring down the next digit, 7. The remainder was 0, so the new number to divide is just that digit.
   7 ÷ 6 = 1 remainder 1 (since 6 × 1 = 6)
4. Write the answer. Read the digits along the top.
   81 4 6) 487
   487 ÷ 6 = 81 remainder 1

Check. Multiply back: 81 × 6 = 486, then add the remainder 1: 486 + 1 = 487. ✓

Watch out. If 6 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 1000 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.
   7 ) 1000
2. Start with the first 2 digits, 10. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.
   10 ÷ 7 = 1 remainder 3 (since 7 × 1 = 7)
3. Bring down the next digit, 0, to make 30. The remainder 3 goes in front of the 0. This is the same as carrying the remainder to the next column.
   30 ÷ 7 = 4 remainder 2 (since 7 × 4 = 28)
4. Bring down the next digit, 0, to make 20. The remainder 2 goes in front of the 0. This is the same as carrying the remainder to the next column.
   20 ÷ 7 = 2 remainder 6 (since 7 × 2 = 14)
5. Write the answer. Read the digits along the top.
   142 132 7) 1000
   1000 ÷ 7 = 142 remainder 6

Check. Multiply back: 142 × 7 = 994, then add the remainder 6: 994 + 6 = 1000. ✓

Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 2345 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.
   9 ) 2345
2. Start with the first 2 digits, 23. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.
   23 ÷ 9 = 2 remainder 5 (since 9 × 2 = 18)
3. Bring down the next digit, 4, to make 54. The remainder 5 goes in front of the 4. This is the same as carrying the remainder to the next column.
   54 ÷ 9 = 6 (since 9 × 6 = 54)
4. Bring down the next digit, 5. The remainder was 0, so the new number to divide is just that digit.
   9 does not go into 5, so write 0 and carry on.
5. Write the answer. Read the digits along the top.
   260 25 9) 2345
   2345 ÷ 9 = 260 remainder 5

Check. Multiply back: 260 × 9 = 2340, then add the remainder 5: 2340 + 5 = 2345. ✓

Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 24 into each number in turn, carrying the remainder to the next digit.

1. Write out the 24 times table up to 24 × 9. Having the multiples ready makes it quick to see how many times 24 goes into each number.
   24 × 1 = 24
   24 × 2 = 48
   24 × 3 = 72
   24 × 4 = 96
   24 × 5 = 120
   24 × 6 = 144
   24 × 7 = 168
   24 × 8 = 192
   24 × 9 = 216
2. Set out the division. Write 936 under the "bus stop" and 24 outside it. The answer will be written on top, one digit above each digit we divide.
   24 ) 936
3. Start with the first 2 digits, 93. 24 does not go into the first digit, so we take digits from the left until we have a number that 24 can go into.
   24 goes into 93 3 times: 24 × 3 = 72
   Subtract: 93 − 72 = 21
4. Bring down the next digit, 6, to make 216. The remainder 21 goes in front of the 6. This is the same as carrying the remainder to the next column.
   24 goes into 216 9 times: 24 × 9 = 216
   Subtract: 216 − 216 = 0
5. Write the answer. Read the digits along the top.
   39 24) 936 72 -- 216 216 --- 0
   936 ÷ 24 = 39

Check. Multiply back: 39 × 24 = 936. ✓

Watch out. If 24 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 34 into each number in turn, carrying the remainder to the next digit.

1. Write out the 34 times table up to 34 × 9. Having the multiples ready makes it quick to see how many times 34 goes into each number.
   34 × 1 = 34
   34 × 2 = 68
   34 × 3 = 102
   34 × 4 = 136
   34 × 5 = 170
   34 × 6 = 204
   34 × 7 = 238
   34 × 8 = 272
   34 × 9 = 306
2. Set out the division. Write 7523 under the "bus stop" and 34 outside it. The answer will be written on top, one digit above each digit we divide.
   34 ) 7523
3. Start with the first 2 digits, 75. 34 does not go into the first digit, so we take digits from the left until we have a number that 34 can go into.
   34 goes into 75 2 times: 34 × 2 = 68
   Subtract: 75 − 68 = 7
4. Bring down the next digit, 2, to make 72. The remainder 7 goes in front of the 2. This is the same as carrying the remainder to the next column.
   34 goes into 72 2 times: 34 × 2 = 68
   Subtract: 72 − 68 = 4
5. Bring down the next digit, 3, to make 43. The remainder 4 goes in front of the 3. This is the same as carrying the remainder to the next column.
   34 goes into 43 1 time: 34 × 1 = 34
   Subtract: 43 − 34 = 9
6. Write the answer. Read the digits along the top.
   221 34) 7523 68 -- 72 68 -- 43 34 -- 9
   7523 ÷ 34 = 221 remainder 9

Check. Multiply back: 221 × 34 = 7514, then add the remainder 9: 7514 + 9 = 7523. ✓

Watch out. If 34 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 28 into each number in turn, carrying the remainder to the next digit.

1. Write out the 28 times table up to 28 × 9. Having the multiples ready makes it quick to see how many times 28 goes into each number.
   28 × 1 = 28
   28 × 2 = 56
   28 × 3 = 84
   28 × 4 = 112
   28 × 5 = 140
   28 × 6 = 168
   28 × 7 = 196
   28 × 8 = 224
   28 × 9 = 252
2. Set out the division. Write 4704 under the "bus stop" and 28 outside it. The answer will be written on top, one digit above each digit we divide.
   28 ) 4704
3. Start with the first 2 digits, 47. 28 does not go into the first digit, so we take digits from the left until we have a number that 28 can go into.
   28 goes into 47 1 time: 28 × 1 = 28
   Subtract: 47 − 28 = 19
4. Bring down the next digit, 0, to make 190. The remainder 19 goes in front of the 0. This is the same as carrying the remainder to the next column.
   28 goes into 190 6 times: 28 × 6 = 168
   Subtract: 190 − 168 = 22
5. Bring down the next digit, 4, to make 224. The remainder 22 goes in front of the 4. This is the same as carrying the remainder to the next column.
   28 goes into 224 8 times: 28 × 8 = 224
   Subtract: 224 − 224 = 0
6. Write the answer. Read the digits along the top.
   168 28) 4704 28 -- 190 168 --- 224 224 --- 0
   4704 ÷ 28 = 168

Check. Multiply back: 168 × 28 = 4704. ✓

Watch out. If 28 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 16 into each number in turn, carrying the remainder to the next digit.

1. Write out the 16 times table up to 16 × 9. Having the multiples ready makes it quick to see how many times 16 goes into each number.
   16 × 1 = 16
   16 × 2 = 32
   16 × 3 = 48
   16 × 4 = 64
   16 × 5 = 80
   16 × 6 = 96
   16 × 7 = 112
   16 × 8 = 128
   16 × 9 = 144
2. Set out the division. Write 10000 under the "bus stop" and 16 outside it. The answer will be written on top, one digit above each digit we divide.
   16 ) 10000
3. Start with the first 3 digits, 100. 16 does not go into the first digit, so we take digits from the left until we have a number that 16 can go into.
   16 goes into 100 6 times: 16 × 6 = 96
   Subtract: 100 − 96 = 4
4. Bring down the next digit, 0, to make 40. The remainder 4 goes in front of the 0. This is the same as carrying the remainder to the next column.
   16 goes into 40 2 times: 16 × 2 = 32
   Subtract: 40 − 32 = 8
5. Bring down the next digit, 0, to make 80. The remainder 8 goes in front of the 0. This is the same as carrying the remainder to the next column.
   16 goes into 80 5 times: 16 × 5 = 80
   Subtract: 80 − 80 = 0
6. Write the answer. Read the digits along the top.
   625 16) 10000 96 -- 40 32 -- 80 80 -- 0
   10 000 ÷ 16 = 625

Check. Multiply back: 625 × 16 = 10 000. ✓

Watch out. If 16 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 9 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.
   4 ) 9
2. Start with the first digit, 9. Work from the left. We ask how many times 4 goes into 9.
   9 ÷ 4 = 2 remainder 1 (since 4 × 2 = 8)
3. There is a remainder of 1, so add a 0 on the end and bring it down to make 10. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   10 ÷ 4 = 2 remainder 2 (since 4 × 2 = 8)
4. There is a remainder of 2, so add a 0 on the end and bring it down to make 20. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   20 ÷ 4 = 5 (since 4 × 5 = 20)
5. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   2.25 12 4) 9.00
   9 ÷ 4 = 2.25

Check. Multiply back: 2.25 × 4 = 9. ✓

Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 8 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 3 under the "bus stop" and 8 outside it. The answer will be written on top, one digit above each digit we divide.
   8 ) 3
2. Start with the first digit, 3. Work from the left. We ask how many times 8 goes into 3.
   8 does not go into 3, so write 0 and carry on.
3. There is a remainder of 3, so add a 0 on the end and bring it down to make 30. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   30 ÷ 8 = 3 remainder 6 (since 8 × 3 = 24)
4. There is a remainder of 6, so add a 0 on the end and bring it down to make 60. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   60 ÷ 8 = 7 remainder 4 (since 8 × 7 = 56)
5. There is a remainder of 4, so add a 0 on the end and bring it down to make 40. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   40 ÷ 8 = 5 (since 8 × 5 = 40)
6. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   0.375 364 8) 3.000
   3 ÷ 8 = 0.375

Check. Multiply back: 0.375 × 8 = 3. ✓

Watch out. If 8 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 20 into each number in turn, carrying the remainder to the next digit.

1. Write out the 20 times table up to 20 × 9. Having the multiples ready makes it quick to see how many times 20 goes into each number.
   20 × 1 = 20
   20 × 2 = 40
   20 × 3 = 60
   20 × 4 = 80
   20 × 5 = 100
   20 × 6 = 120
   20 × 7 = 140
   20 × 8 = 160
   20 × 9 = 180
2. Set out the division. Write 17 under the "bus stop" and 20 outside it. The answer will be written on top, one digit above each digit we divide.
   20 ) 17
3. Start with the first 2 digits, 17. 20 does not go into the first digit, so we take digits from the left until we have a number that 20 can go into.
   20 does not go into 17, so write 0 in the answer.
4. There is a remainder of 17, so add a 0 on the end and bring it down to make 170. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   20 goes into 170 8 times: 20 × 8 = 160
   Subtract: 170 − 160 = 10
5. There is a remainder of 10, so add a 0 on the end and bring it down to make 100. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   20 goes into 100 5 times: 20 × 5 = 100
   Subtract: 100 − 100 = 0
6. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   0.85 20) 17.00 160 --- 100 100 --- 0
   17 ÷ 20 = 0.85

Check. Multiply back: 0.85 × 20 = 17. ✓

Watch out. If 20 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Long division: work from the left, dividing 16 into each number in turn, carrying the remainder to the next digit.

1. Write out the 16 times table up to 16 × 9. Having the multiples ready makes it quick to see how many times 16 goes into each number.
   16 × 1 = 16
   16 × 2 = 32
   16 × 3 = 48
   16 × 4 = 64
   16 × 5 = 80
   16 × 6 = 96
   16 × 7 = 112
   16 × 8 = 128
   16 × 9 = 144
2. Set out the division. Write 45 under the "bus stop" and 16 outside it. The answer will be written on top, one digit above each digit we divide.
   16 ) 45
3. Start with the first 2 digits, 45. 16 does not go into the first digit, so we take digits from the left until we have a number that 16 can go into.
   16 goes into 45 2 times: 16 × 2 = 32
   Subtract: 45 − 32 = 13
4. There is a remainder of 13, so add a 0 on the end and bring it down to make 130. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   16 goes into 130 8 times: 16 × 8 = 128
   Subtract: 130 − 128 = 2
5. There is a remainder of 2, so add a 0 on the end and bring it down to make 20. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   16 goes into 20 1 time: 16 × 1 = 16
   Subtract: 20 − 16 = 4
6. There is a remainder of 4, so add a 0 on the end and bring it down to make 40. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   16 goes into 40 2 times: 16 × 2 = 32
   Subtract: 40 − 32 = 8
7. There is a remainder of 8, so add a 0 on the end and bring it down to make 80. Adding a zero after the last decimal place does not change the value of the number, but it lets us keep dividing to get an exact answer.
   16 goes into 80 5 times: 16 × 5 = 80
   Subtract: 80 − 80 = 0
8. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   2.8125 16) 45.0000 32 -- 13 0 128 --- 20 16 -- 40 32 -- 80 80 -- 0
   45 ÷ 16 = 2.8125

Check. Multiply back: 2.8125 × 16 = 45. ✓

Watch out. If 16 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 5 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 7.5 under the "bus stop" and 5 outside it. The answer will be written on top, one digit above each digit we divide.
   5 ) 7.5
2. Start with the first digit, 7. Work from the left. We ask how many times 5 goes into 7.
   7 ÷ 5 = 1 remainder 2 (since 5 × 1 = 5)
3. The next digit is after the decimal point. Put a decimal point in the answer, then bring down 5 to make 25. The decimal point in the answer goes directly above the decimal point in the question.
   25 ÷ 5 = 5 (since 5 × 5 = 25)
4. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   1.5 2 5) 7.5
   7.5 ÷ 5 = 1.5

Check. Multiply back: 1.5 × 5 = 7.5. ✓

Watch out. If 5 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 0.84 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.
   7 ) 0.84
2. The number is less than 1, so the answer starts "0." Put the decimal point in the answer, then look at the first digit after the point, 8. We still ask how many times 7 goes into 8.
   8 ÷ 7 = 1 remainder 1 (since 7 × 1 = 7)
3. Bring down the next digit, 4, to make 14. The remainder 1 goes in front of the 4. This is the same as carrying the remainder to the next column.
   14 ÷ 7 = 2 (since 7 × 2 = 14)
4. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   0.12 1 7) 0.84
   0.84 ÷ 7 = 0.12

Check. Multiply back: 0.12 × 7 = 0.84. ✓

Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 9 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 12.6 under the "bus stop" and 9 outside it. The answer will be written on top, one digit above each digit we divide.
   9 ) 12.6
2. Start with the first 2 digits, 12. 9 does not go into the first digit, so we take digits from the left until we have a number that 9 can go into.
   12 ÷ 9 = 1 remainder 3 (since 9 × 1 = 9)
3. The next digit is after the decimal point. Put a decimal point in the answer, then bring down 6 to make 36. The decimal point in the answer goes directly above the decimal point in the question.
   36 ÷ 9 = 4 (since 9 × 4 = 36)
4. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   1.4 1 3 9) 12.6
   12.6 ÷ 9 = 1.4

Check. Multiply back: 1.4 × 9 = 12.6. ✓

Watch out. If 9 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 20.4 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.
   12 ) 20.4
2. Start with the first 2 digits, 20. 12 does not go into the first digit, so we take digits from the left until we have a number that 12 can go into.
   20 ÷ 12 = 1 remainder 8 (since 12 × 1 = 12)
3. The next digit is after the decimal point. Put a decimal point in the answer, then bring down 4 to make 84. The decimal point in the answer goes directly above the decimal point in the question.
   84 ÷ 12 = 7 (since 12 × 7 = 84)
4. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   1.7 2 8 12) 20.4
   20.4 ÷ 12 = 1.7

Check. Multiply back: 1.7 × 12 = 20.4. ✓

Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 4 into each number in turn, carrying the remainder to the next digit.

1. Make the number you are dividing by a whole number. Multiplying both numbers by 10 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.
   7.2 ÷ 0.4 = 72 ÷ 4
   (7.2 × 10 = 72 and 0.4 × 10 = 4)
2. Set out the division. Write 72 under the "bus stop" and 4 outside it. The answer will be written on top, one digit above each digit we divide.
   4 ) 72
3. Start with the first digit, 7. Work from the left. We ask how many times 4 goes into 7.
   7 ÷ 4 = 1 remainder 3 (since 4 × 1 = 4)
4. Bring down the next digit, 2, to make 32. The remainder 3 goes in front of the 2. This is the same as carrying the remainder to the next column.
   32 ÷ 4 = 8 (since 4 × 8 = 32)
5. Write the answer. Read the digits along the top.
   18 3 4) 72
   72 ÷ 4 = 18

Check. Multiply back: 18 × 4 = 72. ✓

Watch out. If 4 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 7 into each number in turn, carrying the remainder to the next digit.

1. Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.
   5.6 ÷ 0.07 = 560 ÷ 7
   (5.6 × 100 = 560 and 0.07 × 100 = 7)
2. Set out the division. Write 560 under the "bus stop" and 7 outside it. The answer will be written on top, one digit above each digit we divide.
   7 ) 560
3. Start with the first 2 digits, 56. 7 does not go into the first digit, so we take digits from the left until we have a number that 7 can go into.
   56 ÷ 7 = 8 (since 7 × 8 = 56)
4. Bring down the next digit, 0. The remainder was 0, so the new number to divide is just that digit.
   7 does not go into 0, so write 0 and carry on.
5. Write the answer. Read the digits along the top.
   80 5 7) 560
   560 ÷ 7 = 80

Check. Multiply back: 80 × 7 = 560. ✓

Watch out. If 7 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Short division: work from the left, dividing 3 into each number in turn, carrying the remainder to the next digit.

1. Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.
   0.9 ÷ 0.03 = 90 ÷ 3
   (0.9 × 100 = 90 and 0.03 × 100 = 3)
2. Set out the division. Write 90 under the "bus stop" and 3 outside it. The answer will be written on top, one digit above each digit we divide.
   3 ) 90
3. Start with the first digit, 9. Work from the left. We ask how many times 3 goes into 9.
   9 ÷ 3 = 3 (since 3 × 3 = 9)
4. Bring down the next digit, 0. The remainder was 0, so the new number to divide is just that digit.
   3 does not go into 0, so write 0 and carry on.
5. Write the answer. Read the digits along the top.
   30 3) 90
   90 ÷ 3 = 30

Check. Multiply back: 30 × 3 = 90. ✓

Watch out. If 3 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Long division: work from the left, dividing 15 into each number in turn, carrying the remainder to the next digit.

1. Make the number you are dividing by a whole number. Multiplying both numbers by 10 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.
   4.5 ÷ 1.5 = 45 ÷ 15
   (4.5 × 10 = 45 and 1.5 × 10 = 15)
2. Write out the 15 times table up to 15 × 9. Having the multiples ready makes it quick to see how many times 15 goes into each number.
   15 × 1 = 15
   15 × 2 = 30
   15 × 3 = 45
   15 × 4 = 60
   15 × 5 = 75
   15 × 6 = 90
   15 × 7 = 105
   15 × 8 = 120
   15 × 9 = 135
3. Set out the division. Write 45 under the "bus stop" and 15 outside it. The answer will be written on top, one digit above each digit we divide.
   15 ) 45
4. Start with the first 2 digits, 45. 15 does not go into the first digit, so we take digits from the left until we have a number that 15 can go into.
   15 goes into 45 3 times: 15 × 3 = 45
   Subtract: 45 − 45 = 0
5. Write the answer. Read the digits along the top.
   3 15) 45 45 -- 0
   45 ÷ 15 = 3

Check. Multiply back: 3 × 15 = 45. ✓

Watch out. If 15 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Dividing by a decimal: multiply both numbers by 10, 100... until the divisor is a whole number. Then divide. Long division: work from the left, dividing 25 into each number in turn, carrying the remainder to the next digit.

1. Make the number you are dividing by a whole number. Multiplying both numbers by 100 does not change the answer (it is like multiplying the top and bottom of a fraction by the same number). It makes the divisor a whole number, which is much easier.
   18 ÷ 0.25 = 1800 ÷ 25
   (18 × 100 = 1800 and 0.25 × 100 = 25)
2. Write out the 25 times table up to 25 × 9. Having the multiples ready makes it quick to see how many times 25 goes into each number.
   25 × 1 = 25
   25 × 2 = 50
   25 × 3 = 75
   25 × 4 = 100
   25 × 5 = 125
   25 × 6 = 150
   25 × 7 = 175
   25 × 8 = 200
   25 × 9 = 225
3. Set out the division. Write 1800 under the "bus stop" and 25 outside it. The answer will be written on top, one digit above each digit we divide.
   25 ) 1800
4. Start with the first 3 digits, 180. 25 does not go into the first digit, so we take digits from the left until we have a number that 25 can go into.
   25 goes into 180 7 times: 25 × 7 = 175
   Subtract: 180 − 175 = 5
5. Bring down the next digit, 0, to make 50. The remainder 5 goes in front of the 0. This is the same as carrying the remainder to the next column.
   25 goes into 50 2 times: 25 × 2 = 50
   Subtract: 50 − 50 = 0
6. Write the answer. Read the digits along the top.
   72 25) 1800 175 --- 50 50 -- 0
   1800 ÷ 25 = 72

Check. Multiply back: 72 × 25 = 1800. ✓

Watch out. If 25 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. The quotient is the answer to a division. The remainder is what is left over. The divisor is the number you divide by.

Method. Short division: work from the left, dividing 12 into each number in turn, carrying the remainder to the next digit.

1. Set out the division. Write 9.84 under the "bus stop" and 12 outside it. The answer will be written on top, one digit above each digit we divide.
   12 ) 9.84
2. Start with the first digit, 9. Work from the left. We ask how many times 12 goes into 9.
   12 does not go into 9, so write 0 and carry on.
3. The next digit is after the decimal point. Put a decimal point in the answer, then bring down 8 to make 98. The decimal point in the answer goes directly above the decimal point in the question.
   98 ÷ 12 = 8 remainder 2 (since 12 × 8 = 96)
4. Bring down the next digit, 4, to make 24. The remainder 2 goes in front of the 4. This is the same as carrying the remainder to the next column.
   24 ÷ 12 = 2 (since 12 × 2 = 24)
5. Write the answer. Read the digits along the top. The decimal point stays in line with the point in the question.
   0.82 92 12) 9.84
   9.84 ÷ 12 = 0.82

Check. Multiply back: 0.82 × 12 = 9.84. ✓

Watch out. If 12 does not go into a digit, write 0 on top and carry on. Do not skip the 0, or the answer will be too small.

Key words. A decimal place is a digit after the decimal point. 3.45 has 2 decimal places.

Method. Multiply decimals as whole numbers first, then put the decimal point back using the total number of decimal places in the question.

1. Ignore the decimal points and multiply as whole numbers. 0.82 is 82 divided by 100, and 15 is 15 divided by 1. So we can multiply 82 by 15, then fix the size at the end.
   0.82 × 15 → 82 × 15
2. Multiply 82 by the units digit, 5. Work from the right. Multiply each digit of the top number by 5. If the answer is 10 or more, write the units digit and carry the rest into the next column.
   2 × 5 = 10: write 0, carry 1
   8 × 5 + 1 (carried) = 41: write 1, carry 4
   Write the last carry: 4
   So 82 × 5 = 410.
3. Multiply 82 by the tens digit, 1 (which means 10). The 1 is in the tens column, so it is really 10. First write 1 zero on the right as place holder, then multiply by 1.
   2 × 1 = 2: write 2
   8 × 1 = 8: write 8
   82 × 1 = 82, then add 1 zero: 82 × 10 = 820.
4. Add the rows. Long multiplication splits the multiplier into parts (units, tens, ...). Adding the partial answers gives the whole answer.
   410 + 820 = 1230
   82 × 15 ---- 410 820 ----- 1230
5. Put the decimal point back. Count the decimal places in the question: 0.82 has 2 and 15 has 0, so the answer has 2 + 0 = 2 decimal places. Count that many digits in from the right.
   1230 with 2 decimal places: 12.3

Check. Estimate: 0.8 × 20 = 16. 12.3 is close to 16. ✓

Watch out. Count decimal places in both numbers and add them. The answer has as many as the two numbers together.