Concept 3 of 9
What to Do With the Remainder
Today's big idea
One division, three honest answers; what you are sharing decides which to write.
74 divided by 8 is 9 r 2, or 9 and a quarter, or 9.25.
How it works
👀 What's going on?
Share 74 sweets between 8 children and you get 9 each with 2 left over. Share 74 metres of rope between 8 and nobody wants 2 metres left in a heap. The division is identical. What you do with the leftover depends entirely on what is being shared.
💡 Here's the trick
Look at the three answers above. All of them come from 74 divided by 8, and all three are correct for a different question. Left as it is, the answer is 9 remainder 2, which suits sweets because you cannot cut one. As a fraction the leftover 2 is written over the divisor, giving 9 and 2 eighths, which simplifies to 9 and 1 quarter. As a decimal you carry on dividing past the point and get 9.25, which suits rope and money. The remainder never changes. Only the way you report it does, and the question tells you which to use.
🪄 How to do it
- 1.Divide as normal and find the leftover, the way the answers above all start from 74 divided by 8.
- 2.Ask whether the thing being shared can be split into parts.
- 3.Report it as a remainder if it cannot, and as a fraction or decimal if it can.
✍️ Try it
45 litres of paint is shared between 4 tins. Then, 45 children are put into teams of 4. What is different about the two answers?
Both divisions give 11 with 1 left over. Paint pours, so the answer is 11 and 1 quarter litres, or 11.25. Children do not split, so the answer is 11 full teams with 1 child left over. Same numbers, two honest answers.
⚠️ Watch out
You might be thinking a remainder of 2 means point two. It does not. For 74 divided by 8 the remainder 2 becomes 2 over 8, which is 0.25, so the answer is 9.25 and not 9.2. The remainder has to be divided by the divisor before it becomes a decimal.
🌟 Why this matters
Splitting a bill, sharing fuel or cutting cloth all give leftovers that matter, and each one wants a different kind of answer. Reading the situation before writing the answer is most of the skill.
Exam tip: If the answer options mix a decimal with a remainder, the question is testing this choice and nothing else.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“74 ÷ 8. Give the answer three ways.”
- 1
Divide once
8 goes into 74 nine times, and 2 is left over.
- 2
As a remainder
For things you cannot cut, like sweets: 9 r 2.
- 3
As a fraction
Put the leftover over the divisor: 9 and 2/8 = 9 and 1/4
- 4
As a decimal ✓
2 ÷ 8 = 0.25, so the answer is 9.25, not 9.2
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
THE DIVISION
74 ÷ 8
Do the division once. Every question after this uses the same answer, reported differently.
Quick check
✅ VERIFICATION
74 ÷ 8 as a decimal is:
⚡ Finish the activity above first to answer.
Keep going!
Up next: Multi-Step Problems with Large Numbers
Order the boxes first, then let each answer feed the next.