Step-by-step Maths Level 5: What the remainder means in a problem

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

1. Divide to find the full buses and what is left. 47 children in buses of 8.
   47 ÷ 8 = 5 remainder 7
2. Decide what the remainder means. The children left over still need a bus, so round up.
   7 children left over need 1 more bus
3. Write the answer. Round up when the leftover people still need a place.
   6 buses

Check. Check: 6 buses hold 48 children, which is at least 47.

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

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

1. Divide to find the full buses and what is left. 76 children in buses of 7.
   76 ÷ 7 = 10 remainder 6
2. Decide what the remainder means. The children left over still need a bus, so round up.
   6 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 77 children, which is at least 76.

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.
   33 ÷ 4 = 8 remainder 1
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   8 each and 1 left over
3. Write the answer. Give both parts, as the question asks.
   8 each, 1 left over

Check. Check: 8 × 4 + 1 = 33.

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

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.
   66 ÷ 8 = 8 remainder 2
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   8 each and 2 left over
3. Write the answer. Give both parts, as the question asks.
   8 each, 2 left over

Check. Check: 8 × 8 + 2 = 66.

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

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.
   97 ÷ 7 = 13 remainder 6
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   13 each and 6 left over
3. Write the answer. Give both parts, as the question asks.
   13 each, 6 left over

Check. Check: 13 × 7 + 6 = 97.

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

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.
   61 ÷ 3 = 20 remainder 1
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   20 each and 1 left over
3. Write the answer. Give both parts, as the question asks.
   20 each, 1 left over

Check. Check: 20 × 3 + 1 = 61.

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. 31 children in buses of 9.
   31 ÷ 9 = 3 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.
   4 buses

Check. Check: 4 buses hold 36 children, which is at least 31.

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

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.
   87 ÷ 3 = 29
2. Decide what the remainder means. The sweets left over do not make a full bag, so round down.
   No sweets are left over
3. Write the answer. Only full bags count.
   29 full bags

Check. Check: 29 full bags hold 87 sweets, and 87 - 87 = 0.

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

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.
   35 ÷ 4 = 8 remainder 3
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   8 each and 3 left over
3. Write the answer. Give both parts, as the question asks.
   8 each, 3 left over

Check. Check: 8 × 4 + 3 = 35.

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

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.
   88 ÷ 9 = 9 remainder 7
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   9 each and 7 left over
3. Write the answer. Give both parts, as the question asks.
   9 each, 7 left over

Check. Check: 9 × 9 + 7 = 88.

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

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.
   81 ÷ 3 = 27
2. Decide what the remainder means. The sweets left over do not make a full bag, so round down.
   No sweets are left over
3. Write the answer. Only full bags count.
   27 full bags

Check. Check: 27 full bags hold 81 sweets, and 81 - 81 = 0.

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

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

1. Divide to find the full buses and what is left. 23 children in buses of 8.
   23 ÷ 8 = 2 remainder 7
2. Decide what the remainder means. The children left over still need a bus, so round up.
   7 children left over need 1 more bus
3. Write the answer. Round up when the leftover people still need a place.
   3 buses

Check. Check: 3 buses hold 24 children, which is at least 23.

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

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.
   65 ÷ 6 = 10 remainder 5
2. Decide what the remainder means. The sweets left over do not make a full bag, so round down.
   5 sweets are left over
3. Write the answer. Only full bags count.
   10 full bags

Check. Check: 10 full bags hold 60 sweets, and 65 - 60 = 5.

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

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

1. Divide to find the full buses and what is left. 69 children in buses of 3.
   69 ÷ 3 = 23
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.
   23 buses

Check. Check: 23 buses hold 69 children, which is at least 69.

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.
   77 ÷ 9 = 8 remainder 5
2. Read the answer and the remainder. The whole number is each share; the remainder is left over.
   8 each and 5 left over
3. Write the answer. Give both parts, as the question asks.
   8 each, 5 left over

Check. Check: 8 × 9 + 5 = 77.

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. 91 children in buses of 6.
   91 ÷ 6 = 15 remainder 1
2. Decide what the remainder means. The children left over still need a bus, so round up.
   1 children left over need 1 more bus
3. Write the answer. Round up when the leftover people still need a place.
   16 buses

Check. Check: 16 buses hold 96 children, which is at least 91.

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