Comparing, rounding & dividing
Division of 2-digit numbers
Division is splitting a number into equal groups. You can estimate first, divide a number up to 100 by a 1-digit number, and decide what to do with any remainder.
Estimate first
Before you divide, make an estimate so you can check your answer is sensible. To estimate 92 ÷ 4, use easy numbers close to 92: 80 ÷ 4 = 20 and 100 ÷ 4 = 25. So the answer to 92 ÷ 4 must be between 20 and 25.
Dividing with jumps of the times table
You can divide by subtracting groups. To work out 75 ÷ 4, take away lots of 4: • 10 lots of 4 is 40, and 75 − 40 = 35. • 8 lots of 4 is 32, and 35 − 32 = 3. Altogether that is 10 + 8 = 18 lots of 4, with 3 left over.
Remainders
The number left over at the end is called the remainder. It is always smaller than the number you are dividing by. Example: 75 ÷ 4 = 18 remainder 3, written 18 r3, because 4 × 18 = 72 and 75 − 72 = 3.
Round up or round down?
When a problem has a remainder, think about what the answer means. • If everyone or everything must fit, round UP. 60 people in boats of 9 is 6 r6, but the extra 6 people still need a boat, so you need 7 boats. • If you can only count complete groups, round DOWN. 27 apricots in bags of 6 is 4 r3, so there are only 4 full bags.
Worked examples
Estimate 92 ÷ 4
- Find easy numbers near 92 that divide by 4.
- 80 ÷ 4 = 20 and 100 ÷ 4 = 25.
- 92 is between 80 and 100, so the answer is between 20 and 25.
Answer: 92 ÷ 4 is about 23 (between 20 and 25).
Work out 75 ÷ 4
- Take away 10 lots of 4: 75 − 40 = 35.
- Take away 8 lots of 4: 35 − 32 = 3.
- That is 10 + 8 = 18 lots of 4, with 3 left over.
Answer: 75 ÷ 4 = 18 r3.
Find the remainder of 27 ÷ 6
- 6 × 4 = 24, which is as close to 27 as you can get without going over.
- 27 − 24 = 3.
- So 6 goes into 27 four times with 3 left over.
Answer: 27 ÷ 6 = 4 r3.
Boats for 60 people (round up)
- Each boat holds 9, so work out 60 ÷ 9 = 6 r6.
- The 6 people left over still need a boat.
- So round up to the next whole boat.
Answer: 7 boats are needed.
Where you see this in real life
- Sharing 30 cards equally into packs of 6.
- Working out how many weeks 35 days makes.
- Deciding how many buses are needed to take a class on a trip.
- Counting how many full bags of apricots you can make.
Key words
- Division
- Splitting a number into equal groups or parts.
- Divisor
- The number you are dividing by.
- Remainder
- The amount left over when a number does not divide exactly.
- Estimate
- A sensible guess of the answer using easy numbers.
- Round up / round down
- Choosing the next whole number up or down to make sense of a remainder.