Step-by-step Maths Level 5 Short division with remainders: check-up and practice test questions

Method. Share the whole number first; the remainder is what is left over.

1. Share the pencils into equal groups. Each child gets the same number.
   20 ÷ 6 = 3 remainder 2
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   3 each and 2 left over
3. Write the answer. Give both parts, as the question asks.
   3 each, 2 left over

Check. Check: 3 × 6 + 2 = 20.

Watch out. The remainder is not shared. Say how many are left.

Method. Use the short method. Share the tens first, then the ones with what is left.

1. The tens are fewer than the number of groups. 6 tens cannot make a group of 8 on their own, so use all of 64.
   64 is the number to share
2. Share 64 into groups of 8. How many groups of 8 are in 64?
   64 ÷ 8 = 8 r 0
3. Write the answer. The remainder is what is left over; write it after the answer.
   8

Check. Check: 8 × 8 + 0 = 64.

Watch out. The remainder must be smaller than the number you divide by.

Method. Use the short method. Share the tens first, then the ones with what is left.

1. Share the tens. Share the 8 tens into groups of 3.
   8 ÷ 3 = 2 r 2
2. Bring down the ones. The tens left over become ten ones each.
   2 tens and 1 ones = 21
3. Share 21 into groups of 3. How many groups of 3 are in 21?
   21 ÷ 3 = 7 r 0
4. Write the answer. The remainder is what is left over; write it after the answer.
   27

Check. Check: 27 × 3 + 0 = 81.

Watch out. The remainder must be smaller than the number you divide by.

Method. Share the whole number first; the remainder is what is left over.

1. Share the pencils into equal groups. Each child gets the same number.
   93 ÷ 5 = 18 remainder 3
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   18 each and 3 left over
3. Write the answer. Give both parts, as the question asks.
   18 each, 3 left over

Check. Check: 18 × 5 + 3 = 93.

Watch out. The remainder is not shared. Say how many are left.

Method. Use the short method. Share the tens first, then the ones with what is left.

1. The tens are fewer than the number of groups. 5 tens cannot make a group of 9 on their own, so use all of 54.
   54 is the number to share
2. Share 54 into groups of 9. How many groups of 9 are in 54?
   54 ÷ 9 = 6 r 0
3. Write the answer. The remainder is what is left over; write it after the answer.
   6

Check. Check: 6 × 9 + 0 = 54.

Watch out. The remainder must be smaller than the number you divide by.

Method. Use the short method. Share the tens first, then the ones with what is left.

1. Share the tens. Share the 4 tens into groups of 2.
   4 ÷ 2 = 2 r 0
2. Bring down the ones. The tens left over become ten ones each.
   0 tens and 2 ones = 2
3. Share 2 into groups of 2. How many groups of 2 are in 2?
   2 ÷ 2 = 1 r 0
4. Write the answer. The remainder is what is left over; write it after the answer.
   21

Check. Check: 21 × 2 + 0 = 42.

Watch out. The remainder must be smaller than the number you divide by.

Method. Divide, then check: answer × divisor + remainder = the number we started with.

1. Find how many groups of 3 are in 74. Use the times table of the divisor.
   24 groups of 3 = 72
2. Find what is left over. The remainder is the number left after the groups.
   74 - 72 = 2
3. Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.
   24 × 3 + 2 = 72 + 2 = 74
4. Write the answer. This is the answer with its remainder.
   24 remainder 2

Check. Check: 24 × 3 + 2 = 74.

Watch out. If the check does not give the number you started with, divide again.

Method. Round up when the remainder still needs one more group.

1. Divide to find the full buses and what is left. 94 children in buses of 9.
   94 ÷ 9 = 10 remainder 4
2. Decide what the remainder means. The children left over still need a bus, so round up.
   4 children left over need 1 more bus
3. Write the answer. Round up when the leftover people still need a place.
   11 buses

Check. Check: 11 buses hold 99 children, which is at least 94.

Watch out. Round up when the leftover still needs a place. Do not give the answer with a remainder.

Method. Share the whole pounds first; the remainder is what is left over.

1. Share the money into equal amounts. Each person gets the same whole pounds.
   £51 ÷ 5 = 10 remainder 1
2. Read the remainder. The remainder is the money left over.
   £1 left over
3. Write the answer. Give the amount each and the amount left.
   £10 each, £1 left over

Check. Check: 10 × 5 + 1 = 51.

Watch out. Keep the pound sign with each amount.

Method. Find the multiple of the divisor that is just below the number. It tells you the whole number of groups.

1. Count in 9s. Keep counting until you go past 72.
   9, 18, ... up to 72
2. Find the largest multiple. It is the last multiple that is not more than the number.
   72 is not more than 72
3. Write the multiple. This is the number that helps you find the division.
   72

Check. Check: 8 × 9 = 72, and 72 is not more than 72.

Watch out. Do not pick the multiple just above the number; it is more than the number.

Method. Divide, then check: answer × divisor + remainder = the number we started with.

1. Find how many groups of 8 are in 60. Use the times table of the divisor.
   7 groups of 8 = 56
2. Find what is left over. The remainder is the number left after the groups.
   60 - 56 = 4
3. Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.
   7 × 8 + 4 = 56 + 4 = 60
4. Write the answer. This is the answer with its remainder.
   7 remainder 4

Check. Check: 7 × 8 + 4 = 60.

Watch out. If the check does not give the number you started with, divide again.

Method. Share the whole number first; the remainder is what is left over.

1. Share the pencils into equal groups. Each child gets the same number.
   77 ÷ 6 = 12 remainder 5
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   12 each and 5 left over
3. Write the answer. Give both parts, as the question asks.
   12 each, 5 left over

Check. Check: 12 × 6 + 5 = 77.

Watch out. The remainder is not shared. Say how many are left.

Method. Share the whole pounds first; the remainder is what is left over.

1. Share the money into equal amounts. Each person gets the same whole pounds.
   £47 ÷ 5 = 9 remainder 2
2. Read the remainder. The remainder is the money left over.
   £2 left over
3. Write the answer. Give the amount each and the amount left.
   £9 each, £2 left over

Check. Check: 9 × 5 + 2 = 47.

Watch out. Keep the pound sign with each amount.

Method. Share the whole number first; the remainder is what is left over.

1. Share the pencils into equal groups. Each child gets the same number.
   87 ÷ 5 = 17 remainder 2
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   17 each and 2 left over
3. Write the answer. Give both parts, as the question asks.
   17 each, 2 left over

Check. Check: 17 × 5 + 2 = 87.

Watch out. The remainder is not shared. Say how many are left.

Method. Round up when the remainder still needs one more group.

1. Divide to find the full buses and what is left. 48 children in buses of 3.
   48 ÷ 3 = 16
2. Decide what the remainder means. The children left over still need a bus, so round up.
   No children are left over
3. Write the answer. Round up when the leftover people still need a place.
   16 buses

Check. Check: 16 buses hold 48 children, which is at least 48.

Watch out. Round up when the leftover still needs a place. Do not give the answer with a remainder.

Method. Share the whole number first; the remainder is what is left over.

1. Share the pencils into equal groups. Each child gets the same number.
   81 ÷ 3 = 27
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   27 each and 0 left over
3. Write the answer. Give both parts, as the question asks.
   27 each, none left over

Check. Check: 27 × 3 + 0 = 81.

Watch out. The remainder is not shared. Say how many are left.

Method. Use the short method. Share the tens first, then the ones with what is left.

1. The tens are fewer than the number of groups. 7 tens cannot make a group of 8 on their own, so use all of 70.
   70 is the number to share
2. Share 70 into groups of 8. How many groups of 8 are in 70?
   70 ÷ 8 = 8 r 6
3. Write the answer. The remainder is what is left over; write it after the answer.
   8 remainder 6

Check. Check: 8 × 8 + 6 = 70.

Watch out. The remainder must be smaller than the number you divide by.

Method. Divide, then check: answer × divisor + remainder = the number we started with.

1. Find how many groups of 3 are in 65. Use the times table of the divisor.
   21 groups of 3 = 63
2. Find what is left over. The remainder is the number left after the groups.
   65 - 63 = 2
3. Check with multiplication and addition. Multiply the answer by the divisor, then add the remainder.
   21 × 3 + 2 = 63 + 2 = 65
4. Write the answer. This is the answer with its remainder.
   21 remainder 2

Check. Check: 21 × 3 + 2 = 65.

Watch out. If the check does not give the number you started with, divide again.

Method. Round down when the remainder cannot make another full group.

1. Divide to find the full bags. Each full bag takes the number of sweets in it.
   43 ÷ 4 = 10 remainder 3
2. Decide what the remainder means. The sweets left over do not make a full bag, so round down.
   3 sweets are left over
3. Write the answer. Only full bags count.
   10 full bags

Check. Check: 10 full bags hold 40 sweets, and 43 - 40 = 3.

Watch out. Round down when only full groups are wanted.

Method. Round down when the remainder cannot make another full group.

1. Divide to find the full bags. Each full bag takes the number of sweets in it.
   39 ÷ 5 = 7 remainder 4
2. Decide what the remainder means. The sweets left over do not make a full bag, so round down.
   4 sweets are left over
3. Write the answer. Only full bags count.
   7 full bags

Check. Check: 7 full bags hold 35 sweets, and 39 - 35 = 4.

Watch out. Round down when only full groups are wanted.