Subtracting Fractions & Mixed Numbers - Worksheets - Free Printable

You're working on subtracting mixed numbers with unlike denominators. This requires a few key steps:

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✔ Steps to Subtract Mixed Numbers with Unlike Denominators:

1. Convert mixed numbers to improper fractions (optional, but often helpful).
2. Find the Least Common Denominator (LCD) of the two fractions.
3. Rewrite both fractions with the common denominator.
4. Subtract the fractions — if the top fraction is smaller, you’ll need to borrow from the whole number.
5. Simplify the result and convert back to a mixed number if needed.

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Let’s solve each problem step by step.

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a. 6 ¹⁄₂ − 3 ⁷⁄₈

- LCD of 2 and 8 is 8.
- Convert:
6 ¹⁄₂ = 6 ⁴⁄₈
3 ⁷⁄₈ stays as is.
- Now subtract:
6 ⁴⁄₈ − 3 ⁷⁄₈ → Can’t do 4/8 − 7/8, so borrow 1 from 6 → becomes 5 ¹²⁄₈
- Now: 5 ¹²⁄₈ − 3 ⁷⁄₈ = 2 ⁵⁄₈

✔ Answer: 2 ⁵⁄₈

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b. 9 ³⁄₄ − 5 ²⁄₃

- LCD of 4 and 3 is 12.
- Convert:
9 ³⁄₄ = 9 ⁹⁄₁₂
5 ²⁄₃ = 5 ⁸⁄₁₂
- Subtract: 9 ⁹⁄₁₂ − 5 ⁸⁄₁₂ = 4 ¹⁄₁₂

✔ Answer: 4 ¹⁄₁₂

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c. 7 ⁵⁄₆ − 2 ¹⁄₃

- LCD of 6 and 3 is 6.
- Convert:
7 ⁵⁄₆ stays
2 ¹⁄₃ = 2 ²⁄₆
- Subtract: 7 ⁵⁄₆ − 2 ²⁄₆ = 5 ³⁄₆ → simplify → 5 ¹⁄₂

✔ Answer: 5 ¹⁄₂

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d. 5 ⁷⁄₉ − 3 ¹⁄₃

- LCD of 9 and 3 is 9.
- Convert:
5 ⁷⁄₉ stays
3 ¹⁄₃ = 3 ³⁄₉
- Subtract: 5 ⁷⁄₉ − 3 ³⁄₉ = 2 ⁴⁄₉

✔ Answer: 2 ⁴⁄₉

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e. 8 ⁹⁄₁₂ − 3 ¹⁄₆

- First, simplify ⁹⁄₁₂ → ³⁄₄ → but better to use LCD of 12 and 6 = 12
- Convert:
8 ⁹⁄₁₂ stays
3 ¹⁄₆ = 3 ²⁄₁₂
- Subtract: 8 ⁹⁄₁₂ − 3 ²⁄₁₂ = 5 ⁷⁄₁₂

✔ Answer: 5 ⁷⁄₁₂

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f. 1 ¹⁄₄ − ⁷⁄₈

- LCD of 4 and 8 is 8.
- Convert:
1 ¹⁄₄ = 1 ²⁄₈
- Subtract: 1 ²⁄₈ − ⁷⁄₈ → borrow 1 → becomes ⁸⁄₈ + ²⁄₈ = ¹⁰⁄₈
So: ¹⁰⁄₈ − ⁷⁄₈ = ³⁄₈

✔ Answer: ³⁄₈

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g. 15 ³⁄₅ − 3 ¹⁄₂

- LCD of 5 and 2 is 10.
- Convert:
15 ³⁄₅ = 15 ⁶⁄₁₀
3 ¹⁄₂ = 3 ⁵⁄₁₀
- Subtract: 15 ⁶⁄₁₀ − 3 ⁵⁄₁₀ = 12 ¹⁄₁₀ → which is 12 + 1 + ¹⁄₁₀ = 13 ¹⁄₁₀? Wait — no!

Actually: ¹²⁄₁₀ = 1 ²⁄₁₀ → so 12 ¹⁄₁₀ = 12 + ¹⁄₁₀ = 12 ¹⁄₁₀ — that’s already simplified? But ¹⁄₁₀ is proper.

Wait — 15 ⁶⁄₁₀ − 3 ⁵⁄₁₀ = (15−3) + (⁶⁄₁₀ − ⁵⁄₁₀) = 12 ¹⁄₁₀

But ¹⁄₁₀ is less than 1, so it's fine. However, ¹⁄₁₀ is already simplified.

✔ Answer: 12 ¹⁄₁₀ — or you can write as 12.1, but as a mixed number, it’s correct.

Actually — wait! ¹⁄₁₀ is correct. No simplification needed.

✔ Answer: 12 ¹⁄₁₀

*(Note: Some might expect improper fraction, but mixed number is fine.)*

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h. 3 ⁵⁄₈ − 2 ¹⁄₄

- LCD of 8 and 4 is 8.
- Convert:
3 ⁵⁄₈ stays
2 ¹⁄₄ = 2 ²⁄₈
- Subtract: 3 ⁵⁄₈ − 2 ²⁄₈ = 1 ³⁄₈

✔ Answer: 1 ³⁄₈

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i. 7 ¹¹⁄₁₂ − 2 ¹⁄₂

- LCD of 12 and 2 is 12.
- Convert:
7 ¹¹⁄₁₂ stays
2 ¹⁄₂ = 2 ⁶⁄₁₂
- Subtract: 7 ¹¹⁄₁₂ − 2 ⁶⁄₁₂ = 5 ⁵⁄₁₂

✔ Answer: 5 ⁵⁄₁₂

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j. 19 ³⁄₅ − 12 ³⁄₁₀

- LCD of 5 and 10 is 10.
- Convert:
19 ³⁄₅ = 19 ⁶⁄₁₀
12 ³⁄₁₀ stays
- Subtract: 19 ⁶⁄₁₀ − 12 ³⁄₁₀ = 7 ³⁄₁₀

✔ Answer: 7 ³⁄₁₀

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k. 4 ²⁄₃ − 3 ¹⁄₂

- LCD of 3 and 2 is 6.
- Convert:
4 ²⁄₃ = 4 ⁴⁄₆
3 ¹⁄₂ = 3 ³⁄₆
- Subtract: 4 ⁴⁄₆ − 3 ³⁄₆ = 1 ¹⁄₆

✔ Answer: 1 ¹⁄₆

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l. 5 ⁵⁄₁₂ − 3 ¹⁄₃

- LCD of 12 and 3 is 12.
- Convert:
5 ⁵⁄₁₂ stays
3 ¹⁄₃ = 3 ⁴⁄₁₂
- Subtract: 5 ⁵⁄₁₂ − 3 ⁴⁄₁₂ = 2 ¹⁄₁₂

✔ Answer: 2 ¹⁄₁₂

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## 📝 Final Answers:

a. 2 ⁵⁄₈
b. 4 ¹⁄₁₂
c. 5 ¹⁄₂
d. 2 ⁴⁄₉
e. 5 ⁷⁄₁₂
f. ³⁄₈
g. 12 ¹⁄₁₀
h. 1 ³⁄₈
i. 5 ⁵⁄₁₂
j. 7 ³⁄₁₀
k. 1 ¹⁄₆
l. 2 ¹⁄₁₂

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Let me know if you’d like to see any of these solved with improper fractions instead — sometimes that method avoids borrowing confusion!