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.
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