Division and Remainders
Year 5 · Maths · Free — no account needed
Division and Remainders
When you divide two whole numbers, the answer is called the quotient. If the numbers don't divide evenly, there's an amount left over called the remainder. For example, 17 ÷ 5 = 3 remainder 2, because 5 fits into 17 three whole times, with 2 left over.
Choosing an efficient strategy
For small numbers, use known multiplication facts to find the quotient quickly. For bigger numbers, try partitioning by place value — split the number into friendly chunks that are easy to divide, then add the results. For very large or messy numbers, a calculator is a sensible digital tool to use.
Interpreting the remainder
What you do with a remainder depends on the situation:
- Round up: when everything must be fitted in, even if the last group isn't full (like buses needed for a whole class).
- Round down: when only complete groups count and leftovers can't be used (like full teams).
- Write it as a fraction: when the leftover amount can be shared out equally — the remainder becomes the numerator, and the divisor becomes the denominator.
- Write it as a decimal: when a precise, exact amount is needed — keep dividing the remainder by the divisor.
Checking your answer
You can check any division with a remainder by multiplying the quotient by the divisor, then adding the remainder. The result should match the original number.
Worked Example
A bakery has 138 muffins to pack into trays that each hold 8 muffins. How many full trays can they fill, and how many muffins are left over? Step 1: Find how many times 8 fits into 138 using a known fact. 8 × 17 = 136. Step 2: Subtract to find what's left over. 138 − 136 = 2. Step 3: Write the division with its remainder. 138 ÷ 8 = 17 remainder 2. Step 4: Interpret the remainder in context. The bakery can fill 17 full trays, and 2 muffins are left over — not enough to fill another tray.
Practice
Work out 29 ÷ 4.
Flashcards
What are the two results you get when a division doesn't come out evenly?
A quotient (how many whole groups) and a remainder (what's left over).
How can you check that a division with a remainder is correct?
Multiply the quotient by the divisor, then add the remainder — the result should equal the original number.
When should you round a remainder up to the next whole number?
When everything must fit somewhere, even if the last group isn't full — e.g. working out how many buses are needed.
When should you round a remainder down (drop it)?
When only complete groups count and leftovers can't be used — e.g. working out how many full teams can be made.
How do you turn a remainder into a fraction?
Write it as remainder ÷ divisor — the remainder becomes the numerator, and the divisor becomes the denominator.
How do you turn a remainder into a decimal?
Keep dividing the remainder by the divisor, adding a decimal point and extra zeros as needed.
Name one efficient strategy for dividing large numbers by hand.
Partition the number into friendly parts using place value, divide each part separately, then add the results.
All 15 practice questions
Work out 29 ÷ 4.
- 8 remainder 1
- 7 remainder 2
- 6 remainder 5
- 7 remainder 1
Show the answer to question 1
Answer: 7 remainder 1
4 × 7 = 28, and 29 − 28 = 1, so 29 ÷ 4 = 7 remainder 1.
Work out 53 ÷ 6.
- 9 remainder 1
- 7 remainder 11
- 8 remainder 4
- 8 remainder 5
Show the answer to question 2
Answer: 8 remainder 5
6 × 8 = 48, and 53 − 48 = 5, so 53 ÷ 6 = 8 remainder 5.
Work out 97 ÷ 9.
- 11 remainder 8
- 10 remainder 7
- 9 remainder 16
- 10 remainder 6
Show the answer to question 3
Answer: 10 remainder 7
9 × 10 = 90, and 97 − 90 = 7, so 97 ÷ 9 = 10 remainder 7.
A school is transporting 100 students to a museum in buses that each hold 9 students. How many buses are needed so every student has a seat?
- 11 buses
- 9 buses
- 100 buses
- 12 buses
Show the answer to question 4
Answer: 12 buses
100 ÷ 9 = 11 remainder 1, but the extra student still needs a seat, so the answer is 12 buses.
A coach wants to make complete teams of 7 players from 45 players at training. How many complete teams can he make?
- 45 teams
- 7 teams
- 3 teams
- 6 teams
Show the answer to question 5
Answer: 6 teams
45 ÷ 7 = 6 remainder 3, and the leftover 3 players can't form another full team, so the answer is 6 teams.
27 chocolate bars are shared equally among 4 friends. How many bars does each friend get, expressed as a mixed number?
- 6 and 1/4
- 6 and 4/3
- 6 and 3/4
- 7 and 3/4
Show the answer to question 6
Answer: 6 and 3/4
27 ÷ 4 = 6 remainder 3, and sharing the leftover 3 bars equally among 4 friends gives 3/4 each, so the answer is 6 and 3/4.
Write 45 ÷ 8 as a decimal.
- 5.16
- 5.8
- 5.625
- 5.5
Show the answer to question 7
Answer: 5.625
45 ÷ 8 = 5 remainder 5, and 5 ÷ 8 = 0.625, so the answer is 5.625.
Work out 61 ÷ 7.
- 7 remainder 12
- 9 remainder 2
- 8 remainder 6
- 8 remainder 5
Show the answer to question 8
Answer: 8 remainder 5
7 × 8 = 56, and 61 − 56 = 5, so 61 ÷ 7 = 8 remainder 5.
Work out 84 ÷ 5.
- 16 remainder 5
- 15 remainder 9
- 16 remainder 4
- 17 remainder 4
Show the answer to question 9
Answer: 16 remainder 4
5 × 16 = 80, and 84 − 80 = 4, so 84 ÷ 5 = 16 remainder 4.
A gardener needs to pack 130 seedlings into trays that hold 12 seedlings each, with no seedling left unpacked. How many trays does she need to buy?
- 10 trays
- 12 trays
- 11 trays
- 13 trays
Show the answer to question 10
Answer: 11 trays
130 ÷ 12 = 10 remainder 10, and the leftover 10 seedlings still need a tray, so the answer is 11 trays.
A shop wants to make gift bags, each containing 6 chocolates, from a box of 50 chocolates, using only complete bags. How many complete gift bags can be made?
- 2 bags
- 9 bags
- 6 bags
- 8 bags
Show the answer to question 11
Answer: 8 bags
50 ÷ 6 = 8 remainder 2, and the leftover 2 chocolates aren't enough for another bag, so the answer is 8 bags.
Three campers share 20 metres of rope equally. How many metres does each camper get, expressed as a mixed number?
- 6 and 1/3
- 6 and 2/3
- 6 and 3/2
- 7 and 2/3
Show the answer to question 12
Answer: 6 and 2/3
20 ÷ 3 = 6 remainder 2, and sharing the leftover 2 metres among 3 campers gives 2/3 each, so the answer is 6 and 2/3.
Write 39 ÷ 4 as a decimal.
- 9.75
- 9.34
- 9.5
- 9.25
Show the answer to question 13
Answer: 9.75
39 ÷ 4 = 9 remainder 3, and 3 ÷ 4 = 0.75, so the answer is 9.75.
A student calculates 76 ÷ 9 and gets 8 remainder 4. Which equation checks that this is correct?
- 8 × 4 + 9 = 76
- 9 × 8 + 4 = 80
- 9 × 9 + 4 = 76
- 9 × 8 + 4 = 76
Show the answer to question 14
Answer: 9 × 8 + 4 = 76
9 × 8 = 72 and 72 + 4 = 76, so the correct check is 9 × 8 + 4 = 76.
Which is the most efficient way to solve 648 ÷ 8 without a calculator?
- Add 8 to itself 648 times
- Guess a number and check by multiplying
- Count up by 8s from 0 until you reach 648
- Partition 648 into 640 + 8, divide each by 8, then add the results (80 + 1 = 81)
Show the answer to question 15
Answer: Partition 648 into 640 + 8, divide each by 8, then add the results (80 + 1 = 81)
Splitting 648 into 640 + 8 uses friendly facts (640 ÷ 8 = 80 and 8 ÷ 8 = 1), so the most efficient strategy is to partition 648 into 640 + 8, divide each by 8, then add the results (80 + 1 = 81).
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