Topic 4 of 9
Step 6: Long division and equivalent fractions
Long division with remainders
Step 6 · Long division and equivalent fractions topics
Divide numbers of up to four digits by a one-digit number, place by place, and decide what a remainder means in a story.
Dividing place by place
Long division shares out the biggest places first. Share the hundreds, then trade what is left for tens and share those, then do the same with the ones.
Example: Sharing place by place
What is 852 ÷ 3?
- Hundreds: 8 ÷ 3 = 2 each, with 2 hundreds left over.
- Trade 2 hundreds for 20 tens: 20 + 5 = 25 tens. 25 ÷ 3 = 8 each, with 1 ten left.
- Trade 1 ten for 10 ones: 10 + 2 = 12 ones. 12 ÷ 3 = 4 each.
Answer284
Each step is the same: divide, multiply, subtract, then bring down the next digit.
Remainders
Sometimes things do not share out exactly. What is left over is the remainder, and it is always smaller than the number you divide by.
- left over
Example: A remainder
What is 47 ÷ 5?
- 5 × 9 = 45 is the biggest multiple of 5 that fits.
- 47 − 45 = 2 left over.
Answer9 remainder 2
Check by multiplying back: 9 × 5 + 2 = 47.
What to do with the remainder
In a story, the remainder needs a decision. Read what the question asks.
| Story | 50 ÷ 6 = 8 remainder 2 | Answer |
|---|---|---|
| 50 children ride in vans that seat 6. How many vans? | 2 children still need a seat | 9 vans: round up |
| 50 eggs go in boxes of 6. How many full boxes? | 2 eggs do not fill a box | 8 boxes: leave out the remainder |
| 50 stickers are shared by 6 friends. How many are left? | The remainder is what is asked | 2 stickers |
Try it yourself
Work each one on paper first, then open the answer to check.
What is 96 ÷ 4?
Show answer
24.
What is 735 ÷ 5?
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147.
What is 58 ÷ 7?
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8 remainder 2. 7 × 8 = 56.
What is 1,234 ÷ 6?
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205 remainder 4. 6 × 205 = 1,230.
29 people go on a trip in cars that seat 4. How many cars are needed?
Show answer
8 cars. 29 ÷ 4 = 7 remainder 1, and the last person still needs a car.