Multiplication and division
Division
Division undoes multiplication. Estimating between two easy answers tells you roughly where your answer must land.
Estimate between two numbers
Find two easy divisions either side of your calculation. For 736 ÷ 8: 800 ÷ 8 = 100 and 720 ÷ 8 = 90. So the answer must be between 90 and 100. That is a much sharper check than a single rough guess.
Short division step by step
Work from the left, one digit at a time, carrying any remainder to the next digit. 736 ÷ 8: 7 ÷ 8 = 0 remainder 7 — carry the 7. 73 ÷ 8 = 9 remainder 1 — write 9, carry the 1. 16 ÷ 8 = 2 — write 2. Answer: 92. And 92 sits between 90 and 100, as predicted.
Division is the inverse of multiplication
Multiplying and dividing undo each other, so you can always check your answer. 736 ÷ 8 = 92, so 92 × 8 should give 736. 92 × 8 = 736 ✓ This is the fastest way to know you have it right.
Remainders
Not every division comes out exactly. What is left over is the REMAINDER. 25 ÷ 4 = 6 remainder 1, because 6 × 4 = 24 and 1 is left. What you do with a remainder depends on the question. If 25 children need seats in cars holding 4, you need 7 cars — you cannot leave one child behind.
Worked examples
736 ÷ 8
- Estimate: 720 ÷ 8 = 90 and 800 ÷ 8 = 100, so between 90 and 100.
- 7 ÷ 8 = 0 r 7; 73 ÷ 8 = 9 r 1; 16 ÷ 8 = 2.
- The answer 92 fits the estimate.
Answer: 736 ÷ 8 = 92
Checking with the inverse
- The answer to 736 ÷ 8 was 92.
- Multiplying should undo the division: 92 × 8.
- 92 × 8 = 736 ✓
Answer: The answer is confirmed
A division with a remainder
- 25 ÷ 4: how many 4s fit into 25?
- 6 × 4 = 24, and 25 − 24 = 1.
Answer: 25 ÷ 4 = 6 remainder 1
Sharing money in a band
- A band of 5 shares $400 equally.
- 400 ÷ 5 = 80.
Answer: Each member gets $80
What an extra member does
- The same money is shared between more people.
- Each share must therefore be smaller.
Answer: Each member gets less
Where you see this in real life
- Sharing a band's fee equally between its members.
- Working out how many boxes of 8 you need for 736 items.
- Splitting a bill between friends and deciding what to do with the pennies left over.
Key words
- Divisor
- The number you are dividing by.
- Inverse operations
- Operations that undo each other, like × and ÷.
- Remainder
- What is left over after dividing.
- Short division
- Dividing in a single row, carrying remainders.
- Estimate
- A rough answer used to check your working.
- Quotient
- The answer to a division.