Mixed Numbers to Improper Fractions Worksheets - 15 Worksheets Library - Free Printable

Let’s solve each problem step by step.

To convert a mixed number to an improper fraction:
1. Multiply the whole number by the denominator.
2. Add the numerator to that result.
3. Keep the same denominator.

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Problem 1: 2 2/3

- Whole number = 2, Denominator = 3 → 2 × 3 = 6
- Add numerator: 6 + 2 = 8
- Denominator stays 3 → 8/3

✔ Check: 8 ÷ 3 = 2 with remainder 2 → correct.

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Problem 2: 3 1/4

- 3 × 4 = 12
- 12 + 1 = 13
- Denominator = 4 → 13/4

✔ Check: 13 ÷ 4 = 3 R1 → correct.

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Problem 3: 4 2/5

- 4 × 5 = 20
- 20 + 2 = 22
- Denominator = 5 → 22/5

✔ Check: 22 ÷ 5 = 4 R2 → correct.

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Problem 4: 2 3/5

- 2 × 5 = 10
- 10 + 3 = 13
- Denominator = 5 → 13/5

✔ Check: 13 ÷ 5 = 2 R3 → correct.

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Problem 5: 1 3/2

Wait — this is unusual. The fractional part is 3/2, which is greater than 1. But we’ll still follow the rule.

- 1 × 2 = 2
- 2 + 3 = 5
- Denominator = 2 → 5/2

✔ Check: 5 ÷ 2 = 2 R1 → but original was 1 3/2 = 1 + 1.5 = 2.5, and 5/2 = 2.5 → correct.

Note: Normally mixed numbers have fractions less than 1, but mathematically it still works.

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Problem 6: 3 3/4

- 3 × 4 = 12
- 12 + 3 = 15
- Denominator = 4 → 15/4

✔ Check: 15 ÷ 4 = 3 R3 → correct.

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Problem 7: 1 2/4

First, simplify 2/4 to 1/2? But let’s do as-is unless told to simplify.

- 1 × 4 = 4
- 4 + 2 = 6
- Denominator = 4 → 6/4

But 6/4 can be simplified to 3/2. However, since the question doesn’t say to simplify, we leave it as 6/4? Wait — actually, in most cases, we reduce if possible. Let me check standard practice.

In converting mixed to improper, we usually don’t reduce unless asked. But 6/4 reduces to 3/2. Since the original had 2/4 (which is reducible), maybe they expect reduced form? Let’s see other problems.

Actually, looking at problem 10: 1 3/6 — 3/6 reduces to 1/2. So probably we should reduce final answers if possible.

But let’s stick to the conversion first, then reduce if needed.

For now, I’ll write the improper fraction as calculated, then note if it reduces.

So for 7: 6/4 → reduces to 3/2

But let’s confirm: 1 2/4 = 1.5, and 3/2 = 1.5 → yes.

I think it’s better to reduce. I’ll reduce all where possible.

So Problem 7: 3/2

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Problem 8: 3 4/7

- 3 × 7 = 21
- 21 + 4 = 25
- Denominator = 7 → 25/7 (already reduced)

✔ Check: 25 ÷ 7 ≈ 3.57, 3 + 4/7 ≈ 3.57 → correct.

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Problem 9: 2 5/7

- 2 × 7 = 14
- 14 + 5 = 19
- Denominator = 7 → 19/7 (reduced)

✔ Check: 19 ÷ 7 ≈ 2.71, 2 + 5/7 ≈ 2.71 → correct.

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Problem 10: 1 3/6

- 1 × 6 = 6
- 6 + 3 = 9
- Denominator = 6 → 9/6

Reduce: divide numerator and denominator by 3 → 3/2

✔ Check: 1 3/6 = 1.5, 3/2 = 1.5 → correct.

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Now, compiling all answers:

1) 8/3
2) 13/4
3) 22/5
4) 13/5
5) 5/2
6) 15/4
7) 3/2 (from 6/4 reduced)
8) 25/7
9) 19/7
10) 3/2 (from 9/6 reduced)

Wait — for problem 7 and 10, I reduced them. Is that acceptable? Yes, because improper fractions are often expected in simplest form unless specified otherwise.

Also, problem 5: 1 3/2 — that’s technically not a proper mixed number, but we converted correctly to 5/2, which is fine.

Final Answer:

1) \frac{8}{3}
2) \frac{13}{4}
3) \frac{22}{5}
4) \frac{13}{5}
5) \frac{5}{2}
6) \frac{15}{4}
7) \frac{3}{2}
8) \frac{25}{7}
9) \frac{19}{7}
10) \frac{3}{2}

Double-checking all calculations once more:

1) 2×3+2=8 → 8/3 ✔️
2) 3×4+1=13 → 13/4 ✔️
3) 4×5+2=22 → 22/5 ✔️
4) 2×5+3=13 → 13/5 ✔️
5) 1×2+3=5 → 5/2 ✔️
6) 3×4+3=15 → 15/4 ✔️
7) 1×4+2=6 → 6/4 = 3/2 ✔️
8) 3×7+4=25 → 25/7 ✔️
9) 2×7+5=19 → 19/7 ✔️
10) 1×6+3=9 → 9/6 = 3/2 ✔️

All correct.

Final Answer:
1) $\frac{8}{3}$
2) $\frac{13}{4}$
3) $\frac{22}{5}$
4) $\frac{13}{5}$
5) $\frac{5}{2}$
6) $\frac{15}{4}$
7) $\frac{3}{2}$
8) $\frac{25}{7}$
9) $\frac{19}{7}$
10) $\frac{3}{2}$