Math worksheet teaching how to express remainders as fractions in division problems.

Let’s solve each problem step by step.

We are dividing numbers and writing the remainder as a fraction.
The rule is:
Remainder goes on top (numerator), divisor (the number you’re dividing by) goes on bottom (denominator).

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1. 22 ÷ 5 = 4 remainder ?

5 × 4 = 20
22 - 20 = 2 → remainder is 2
So, 22 ÷ 5 = 4 remainder 2 or 4 2/5

✔ Check: 4 + 2/5 = 22/5? → 4×5=20, 20+2=22 → yes!

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2. 32 ÷ 10 = 3 remainder ?

10 × 3 = 30
32 - 30 = 2 → remainder is 2
So, 32 ÷ 10 = 3 remainder 2 or 3 2/10

But we can simplify 2/10 to 1/5 — but since the worksheet doesn’t ask to simplify, we’ll leave it as 2/10 unless told otherwise. However, looking at the example in the image (21÷5=4 r1 or 1/5), they didn’t simplify either — so we keep it as is.

Wait — actually, let’s check the pattern from the example:
In the example: 21 ÷ 5 = 4 remainder 1 → written as 1/5 → numerator = remainder, denominator = divisor.

Same here: remainder 2, divisor 10 → 2/10.

But maybe they expect simplified? Let’s see other problems.

Actually, looking again — in problem 3: 27 ÷ 5 = 5 remainder 2 → would be 2/5 — which is already simplified.

Problem 4: 28 ÷ 3 = 9 remainder 1 → 1/3

Problem 5: 26 ÷ 4 = 6 remainder 2 → 2/4 → which simplifies to 1/2, but again, the example didn’t simplify.

Wait — in the instruction box: “the remainder goes on the top line... and the bottom number is the number you have divided by.” So no mention of simplifying.

So we will write the fraction with remainder over divisor, even if it can be simplified.

BUT — let’s look at the example given: 21 ÷ 5 = 4 remainder 1 or 1/5 → that’s already simplified.

Another example shown: 37 ÷ 5 = 7 remainder 2 or 2/5 → also simplified.

Hmm… 2/5 is simplified, 1/5 is simplified.

What about 32 ÷ 10? Remainder 2, divisor 10 → 2/10. Should we reduce?

Since the worksheet says “relate fractions to division” and shows examples that are already reduced, perhaps we should reduce when possible.

But wait — 2/10 reduces to 1/5. Is that what they want?

Let me think differently — maybe the worksheet expects unsimplified because it’s teaching the concept first.

Looking at problem 5: 26 ÷ 4 = 6 remainder 2 → 2/4 → which is 1/2. If they wanted simplified, they’d write 1/2. But if not, 2/4.

I think for consistency with the examples given (which are all simplified), and since this is about understanding remainders as fractions, we should present the fraction in simplest form.

But let’s double-check with the instructions: “the remainder goes on the top line... and the bottom number is the number you have divided by.” It doesn’t say to simplify.

However, in math education, when converting remainders to fractions, it’s standard to simplify unless specified otherwise.

To be safe, I’ll do both and see which fits better.

Wait — let’s calculate all and then decide.

Actually, let’s just follow the exact method from the example:

Example: 21 ÷ 5 = 4 remainder 1 → fraction is 1/5 → remainder over divisor.

Another example: 37 ÷ 5 = 7 remainder 2 → 2/5.

So for 32 ÷ 10 = 3 remainder 2 → fraction is 2/10.

But 2/10 is equal to 1/5, but the divisor is 10, so technically it should be 2/10.

However, in many curricula, they teach to simplify.

I recall that in some worksheets, they leave it unsimplified to emphasize the relationship.

Given that the header says “Understand remainders. Relate fractions to division”, I think they want the direct relation: remainder / divisor, without simplifying.

Moreover, in problem 5: 26 ÷ 4 = 6 remainder 2 → if we write 2/4, that clearly shows remainder 2, divisor 4.

If we write 1/2, it hides that information.

So I think for this worksheet, we should NOT simplify — keep remainder over divisor.

Yes, that makes sense for learning the concept.

So:

2. 32 ÷ 10 = 3 remainder 2 or 3 2/10

Similarly,

5. 26 ÷ 4 = 6 remainder 2 or 6 2/4

Okay, confirmed.

Now continue.

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3. 27 ÷ 5 = 5 remainder ?

5 × 5 = 25
27 - 25 = 2 → remainder 2
So, 27 ÷ 5 = 5 remainder 2 or 5 2/5

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4. 28 ÷ 3 = 9 remainder ?

3 × 9 = 27
28 - 27 = 1 → remainder 1
So, 28 ÷ 3 = 9 remainder 1 or 9 1/3

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5. 26 ÷ 4 = 6 remainder ?

4 × 6 = 24
26 - 24 = 2 → remainder 2
So, 26 ÷ 4 = 6 remainder 2 or 6 2/4

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6. 84 ÷ 9 = 9 remainder ?

9 × 9 = 81
84 - 81 = 3 → remainder 3
So, 84 ÷ 9 = 9 remainder 3 or 9 3/9

Again, 3/9 can be simplified to 1/3, but per our reasoning, we keep it as 3/9 to show the direct relationship.

But let’s verify: 9 + 3/9 = 84/9? 9×9=81, 81+3=84 → yes.

And 3/9 is correct as remainder/divisor.

So final answers:

1. remainder 2, fraction 2/5
2. remainder 2, fraction 2/10
3. remainder 2, fraction 2/5
4. remainder 1, fraction 1/3
5. remainder 2, fraction 2/4
6. remainder 3, fraction 3/9

Now, to write them in the boxes.

For each, there are two blanks: one for the remainder number, and two for the fraction (numerator and denominator).

So:

1. 22 ÷ 5 = 4 remainder [2] or 4 [2]/[5]
2. 32 ÷ 10 = 3 remainder [2] or 3 [2]/[10]
3. 27 ÷ 5 = 5 remainder [2] or 5 [2]/[5]
4. 28 ÷ 3 = 9 remainder [1] or 9 [1]/[3]
5. 26 ÷ 4 = 6 remainder [2] or 6 [2]/[4]
6. 84 ÷ 9 = 9 remainder [3] or 9 [3]/[9]

All checked.

Final Answer:
1. 2, 2/5
2. 2, 2/10
3. 2, 2/5
4. 1, 1/3
5. 2, 2/4
6. 3, 3/9