Mixed Fractions worksheet with step-by-step instructions and practice problems for converting mixed numbers to improper fractions.

Let’s solve each mixed fraction conversion step by step.

We follow these 3 steps for every problem:
1. Multiply the whole number part by the denominator.
2. Add the numerator to that result.
3. Write the new numerator over the original denominator.

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Problem 1: 5 ⅓

Step 1: 5 × 3 = 15
Step 2: 15 + 1 = 16
Answer: 16/3

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Problem 2: 2 ⅛

Step 1: 2 × 8 = 16
Step 2: 16 + 1 = 17
Answer: 17/8

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Problem 3: 3 ¾

Step 1: 3 × 4 = 12
Step 2: 12 + 3 = 15
Answer: 15/4

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Problem 4: 3 ²⁄₉

Step 1: 3 × 9 = 27
Step 2: 27 + 2 = 29
Answer: 29/9

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Problem 5: 9 ³⁄₈

Step 1: 9 × 8 = 72
Step 2: 72 + 3 = 75
Answer: 75/8

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Problem 6: 2 ½

Step 1: 2 × 2 = 4
Step 2: 4 + 1 = 5
Answer: 5/2

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Problem 7: 2 ¾

Step 1: 2 × 4 = 8
Step 2: 8 + 3 = 11
Answer: 11/4

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Problem 8: 6 ¹⁰⁄₁₀

Wait — ¹⁰⁄₁₀ is equal to 1, so this is actually 6 + 1 = 7. But let’s do it the proper way anyway:

Step 1: 6 × 10 = 60
Step 2: 60 + 10 = 70
Answer: 70/10 → which simplifies to 7, but since the worksheet says “write as improper fraction”, we leave it as 70/10 unless told to simplify. However, in most cases, teachers expect simplified form if possible. Let’s check the example — they didn’t simplify 17/5, so maybe we don’t need to. But 70/10 reduces to 7/1, which is just 7. Hmm.

Actually, looking at the example: 3 ⅖ became 17/5 — not simplified further. So we’ll keep it as 70/10. But note: 70 ÷ 10 = 7, so it’s a whole number. Still, per instructions, write as improper fraction → 70/10

But wait — maybe the problem meant 6 ¹⁄₁₀? Because 6 ¹⁰⁄₁₀ is unusual. Looking back at the image description — yes, it says “6) 2 ½” and “8) 6 ¹⁰⁄₁₀”. That seems odd. Maybe typo? But we must go with what’s written.

So: 6 ¹⁰⁄₁₀ = (6×10 + 10)/10 = 70/10

But let’s double-check: ¹⁰⁄₁₀ = 1, so 6 + 1 = 7 = 7/1. But again, following procedure: 70/10.

However, in standard math practice, we usually reduce fractions. Since the example didn’t reduce, but 70/10 is clearly reducible, I think it’s safe to assume we should reduce it. Let me see the other problems — none of them have numerators equal to denominators except this one. Probably a trick question or typo. To be safe, I’ll write both:

If not reducing: 70/10
If reducing: 7/1 or just 7

But the instruction says: “Write your answer on the line next to each problem.” and the example shows 17/5 — unreduced. So perhaps we leave it as 70/10.

Actually, let’s look at problem 14: 9 ²⁄₃ — that’s fine. Problem 8 is likely intended to be 6 ¹⁄₁₀? But the text says “6 ¹⁰⁄₁₀”.

Given ambiguity, I’ll proceed with calculation as written: 6 ¹⁰⁄₁₀ = 70/10. But I’ll note that it equals 7.

For consistency with the example (which didn’t reduce), I’ll write 70/10.

But wait — let’s check problem 15: 5 ³⁄₂₀ — that’s fine. No issue.

I think it’s better to reduce when obvious. In real classrooms, teachers would mark 70/10 as correct but prefer 7. Since the worksheet doesn’t specify, and the example didn’t reduce, I’ll stick with unreduced for now.

Actually, re-examining the example: 3 ⅖ → 17/5 — 17 and 5 share no common factors, so it can’t be reduced. Here, 70 and 10 do. So perhaps we should reduce.

To avoid confusion, I’ll calculate correctly and reduce where possible.

So for 6 ¹⁰⁄₁₀:

= (6*10 + 10)/10 = 70/10 = 7/1 = 7

But since it asks for improper fraction, 7/1 is an improper fraction. Or even 70/10 is technically correct but not simplified.

I think the best approach is to simplify all answers to lowest terms, as that’s standard practice unless specified otherwise.

Let me confirm with another source or logic: In the example, they wrote 17/5 — which is already simplified. They didn’t say “do not simplify”. So probably, we should simplify.

Therefore, for problem 8: 70/10 simplifies to 7/1, which is 7. But 7 is a whole number, not typically called an "improper fraction" — though technically 7/1 is improper.

This is messy. Perhaps the problem was meant to be 6 ¹⁄₁₀? Let me assume that for sanity, because 6 ¹⁰⁄₁₀ is redundant.

Looking back at the user's input: "8) 6 ¹⁰⁄₁₀" — it's written as such. I have to go with it.

Final decision: Calculate as per formula, then simplify if possible.

So:

8) 6 ¹⁰⁄₁₀ = (6*10 + 10)/10 = 70/10 = 7/1 → 7

But to match format, perhaps write as 7/1? The example used 17/5, so fraction form.

I think for consistency, I'll write all as fractions, simplified.

So 70/10 = 7/1

Similarly, if any others simplify, we do.

Let's continue and handle each.

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Problem 8: 6 ¹⁰⁄₁₀

As above: (6×10 + 10)/10 = 70/10 = 7/1 → 7/1

But let's see if the worksheet expects unsimplified. Given the example didn't need simplifying, and this does, I'm conflicted.

Perhaps in this context, since it's a basic worksheet, they want the direct result without simplifying. Let's look at problem 13: 5 ⁴⁄₅ — that's fine. Problem 12: 6 ½ — will be 13/2, which is simplified.

I recall that in many elementary worksheets, they accept the unsimplified form as long as the process is correct. But to be precise, I'll provide the simplified version, as it's mathematically better.

After careful thought, I will simplify all answers to lowest terms, as that is standard mathematical practice.

So for 8) 6 ¹⁰⁄₁₀ = 70/10 = 7/1

But 7/1 is 7, and sometimes they write it as 7. However, the instruction says "improper fraction", and 7/1 is improper.

I think it's acceptable.

Let's move on and come back.

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Problem 9: 5 ⁷₁₀

Step 1: 5 × 10 = 50
Step 2: 50 + 7 = 57
Answer: 57/10 (already simplified)

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Problem 10: 9 ½

Step 1: 9 × 2 = 18
Step 2: 18 + 1 = 19
Answer: 19/2

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Problem 11: 9 ⁵⁄₆

Step 1: 9 × 6 = 54
Step 2: 54 + 5 = 59
Answer: 59/6

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Problem 12: 6 ½

Step 1: 6 × 2 = 12
Step 2: 12 + 1 = 13
Answer: 13/2

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Problem 13: 5 ⁴⁄₅

Step 1: 5 × 5 = 25
Step 2: 25 + 4 = 29
Answer: 29/5

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Problem 14: 9 ²⁄₃

Step 1: 9 × 3 = 27
Step 2: 27 + 2 = 29
Answer: 29/3

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Problem 15: 5 ³⁄₂₀

Step 1: 5 × 20 = 100
Step 2: 100 + 3 = 103
Answer: 103/20

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Now back to Problem 8: 6 ¹⁰⁄₁₀

As calculated: (6*10 + 10)/10 = 70/10

Simplify: divide numerator and denominator by 10 → 7/1

So 7/1

But is 7/1 considered an improper fraction? Yes, because numerator > denominator (7>1).

Some might argue it's a whole number, but technically it fits.

To match the format of other answers, which are fractions, I'll write it as 7/1.

Alternatively, if the problem was a typo and meant 6 ¹⁄₁₀, then it would be (6*10 +1)/10 = 61/10, which makes more sense. But since the text says "6 ¹⁰⁄₁₀", I have to go with that.

Upon second thought, in the initial problem list, it's written as "8) 6 ¹⁰⁄₁₀" — and in fractions, having numerator equal to denominator means it's 1, so 6 + 1 = 7. So the improper fraction is 7/1.

I think it's correct.

Now, let's list all answers:

1) 5 ⅓ = 16/3
2) 2 ⅛ = 17/8
3) 3 ¾ = 15/4
4) 3 ²⁄₉ = 29/9
5) 9 ³⁄₈ = 75/8
6) 2 ½ = 5/2
7) 2 ¾ = 11/4
8) 6 ¹⁰⁄₁₀ = 70/10 = 7/1 → but to be consistent, perhaps write 70/10? No, I think simplify.

I found a better way: in the example, they didn't simplify because it wasn't needed. For this, since 70/10 reduces, and to teach good habits, I'll simplify.

So final decision: simplify all fractions to lowest terms.

Thus:

8) 70/10 = 7/1

But let's write it as 7/1 for uniformity.

Some teachers might prefer 7, but the worksheet says "improper fraction", so 7/1 is fine.

Now, compiling all:

1) 16/3
2) 17/8
3) 15/4
4) 29/9
5) 75/8
6) 5/2
7) 11/4
8) 7/1 (or 70/10, but I'll go with 7/1)
9) 57/10
10) 19/2
11) 59/6
12) 13/2
13) 29/5
14) 29/3
15) 103/20

For problem 8, to avoid controversy, I'll calculate it as 70/10 and leave it, since the example didn't simplify. But I feel that's not ideal.

Let me check online or standard practice. Upon quick search in my knowledge, in converting mixed numbers to improper fractions, it's common to leave it as is without simplifying, especially in introductory levels. For example, 2 2/4 would be converted to 10/4, not 5/2, to show the process.

In this case, for 6 10/10, it's 70/10, and they might expect that.

Moreover, in the worksheet, problem 8 is listed as "6 ¹⁰⁄₁₀", which is unusual, so perhaps it's intentional to test if students recognize it's 7, but still write the fraction.

I think for accuracy to the task, I'll provide the direct result from the formula without simplifying, as the example did not simplify.

So for 8) 70/10

Similarly, if any other could be simplified, but in this list, only this one has common factors.

For instance, 75/8 - 75 and 8 share no common factors, so ok.

57/10 - no.

etc.

Only problem 8 has reducible fraction.

So to be consistent with the example (17/5 not simplified), I'll write 70/10 for problem 8.

Final answers:

1) 16/3
2) 17/8
3) 15/4
4) 29/9
5) 75/8
6) 5/2
7) 11/4
8) 70/10
9) 57/10
10) 19/2
11) 59/6
12) 13/2
13) 29/5
14) 29/3
15) 103/20

Yes, this matches the method shown in the example.

So I'll go with that.

Final Answer:
1) 16/3
2) 17/8
3) 15/4
4) 29/9
5) 75/8
6) 5/2
7) 11/4
8) 70/10
9) 57/10
10) 19/2
11) 59/6
12) 13/2
13) 29/5
14) 29/3
15) 103/20