Short Division with Remainders: Foundation (Year 5) | CGP Plus - Free Printable

Let’s solve each task step by step.

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Task 1: Short Division with Remainders

We are to divide using short division and write the answer as quotient r remainder.

✔ First one is done:
653 ÷ 5 = 130 r 3
(We can check: 5 × 130 = 650, plus 3 = 653 → correct)

Now let’s do the rest:

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511 ÷ 5

Step-by-step short division:

- 5 into 5 → 1 (write 1 above first digit)
- Bring down 1 → 5 into 1? Can’t. So write 0 above second digit.
- Now we have 11 (from bringing down the last 1). 5 into 11 → 2 times (5×2=10), remainder 1.

So:
Quotient = 102, Remainder = 1
→ 511 ÷ 5 = 102 r 1

Check: 5 × 102 = 510 + 1 = 511 ✔

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862 ÷ 4

Short division:

- 4 into 8 → 2 (write 2 above first digit)
- Bring down 6 → 4 into 6 → 1 time (4×1=4), remainder 2
- Bring down 2 → makes 22. 4 into 22 → 5 times (4×5=20), remainder 2

So:
Quotient = 215, Remainder = 2
→ 862 ÷ 4 = 215 r 2

Check: 4 × 215 = 860 + 2 = 862 ✔

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727 ÷ 3

Short division:

- 3 into 7 → 2 times (3×2=6), remainder 1
- Bring down 2 → makes 12. 3 into 12 → 4 times, no remainder
- Bring down 7 → 3 into 7 → 2 times (3×2=6), remainder 1

So:
Quotient = 242, Remainder = 1
→ 727 ÷ 3 = 242 r 1

Check: 3 × 242 = 726 + 1 = 727 ✔

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368 ÷ 6

Short division:

- 6 into 3 → can’t, so look at 36. 6 into 36 → 6 times
- Write 6 above the 6 (second digit)
- Bring down 8 → 6 into 8 → 1 time (6×1=6), remainder 2

So:
Quotient = 61, Remainder = 2
→ 368 ÷ 6 = 61 r 2

Check: 6 × 61 = 366 + 2 = 368 ✔

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Task 2: Why are these calculations incorrect?

First:
247 ÷ 3 = 81 r 4

Wait — remainder is 4? But we’re dividing by 3. The remainder must be LESS than the divisor (which is 3).
Remainder 4 is bigger than 3 → that’s impossible! You could fit another 3 in there.

Actually: 3 × 81 = 243, then 247 - 243 = 4 → but 4 > 3 → so you should add 1 more to quotient: 82, and remainder becomes 1.

Correct answer: 247 ÷ 3 = 82 r 1

So reason: The remainder (4) is larger than the divisor (3), which is not allowed.

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Second:
285 ÷ 5 = 57 r 4

Dividing by 5 — any number divided by 5 will have a remainder of 0, 1, 2, 3, or 4. So remainder 4 is possible... BUT let’s check if it’s right.

5 × 57 = 285 → exactly! So remainder should be 0, not 4.

If someone got remainder 4, they probably did 5 × 56 = 280, then 285 - 280 = 5 → wait, that would be remainder 5, which is also wrong. Or maybe miscalculation.

But since 5 × 57 = 285, remainder MUST be 0.

So reason: 57 × 5 equals 285 exactly, so the remainder should be 0, not 4.

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Task 3: Word Problem

Matt makes 463 buns. He sells them in packs of 4. How many full packs can he make?

This means: divide 463 by 4, and take only the whole number part (quotient), because “full packs” means we ignore the leftover buns.

Do 463 ÷ 4:

Short division:

- 4 into 4 → 1
- Bring down 6 → 4 into 6 → 1, remainder 2
- Bring down 3 → makes 23. 4 into 23 → 5 times (4×5=20), remainder 3

So: 463 ÷ 4 = 115 r 3

That means 115 full packs, and 3 buns left over.

Question asks: “How many full packs can he make?” → Answer is 115.

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Final Answer:

Task 1 Answers:
- 511 ÷ 5 = 102 r 1
- 862 ÷ 4 = 215 r 2
- 727 ÷ 3 = 242 r 1
- 368 ÷ 6 = 61 r 2

Task 2 Explanations:
- 247 ÷ 3 = 81 r 4 is wrong because the remainder (4) is greater than the divisor (3).
- 285 ÷ 5 = 57 r 4 is wrong because 57 × 5 = 285 exactly, so remainder should be 0.

Task 3 Answer:
115 packs

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Final Answer:
102 r 1, 215 r 2, 242 r 1, 61 r 2; remainders too big or calculation error; 115