Subtracting Fractions & Mixed Numbers - Worksheets - Free Printable

Of course! Let’s solve each of these subtracting mixed numbers with unlike denominators problems step by step. The key steps are:

1. Convert mixed numbers to improper fractions (optional, but helpful).
2. Find a common denominator for the fractions.
3. Subtract the fractions — if the top fraction is smaller, you may need to borrow from the whole number.
4. Simplify the result and convert back to a mixed number if needed.

Let’s go through each problem one by one.

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a. 6 1/2 - 3 7/8

- Convert to improper fractions:
- 6 1/2 = 13/2
- 3 7/8 = 31/8

- Common denominator: LCM of 2 and 8 is 8
- 13/2 = 52/8
- 31/8 stays 31/8

- Subtract: 52/8 - 31/8 = 21/8

- Convert to mixed number: 21 ÷ 8 = 2 R5 → 2 5/8

✔ Answer: 2 5/8

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b. 9 3/4 - 5 2/3

- Common denominator of 4 and 3 is 12
- Convert:
- 9 3/4 = 9 + 9/12 = 9 9/12
- 5 2/3 = 5 + 8/12 = 5 8/12

- Subtract whole numbers and fractions separately:
- Whole: 9 - 5 = 4
- Fraction: 9/12 - 8/12 = 1/12

✔ Answer: 4 1/12

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c. 7 5/6 - 2 1/3

- Common denominator of 6 and 3 is 6
- Convert:
- 7 5/6 stays 7 5/6
- 2 1/3 = 2 2/6

- Subtract:
- Whole: 7 - 2 = 5
- Fraction: 5/6 - 2/6 = 3/6 = 1/2

✔ Answer: 5 1/2

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d. 5 7/9 - 3 1/3

- Common denominator of 9 and 3 is 9
- Convert:
- 5 7/9 stays 5 7/9
- 3 1/3 = 3 3/9

- Subtract:
- Whole: 5 - 3 = 2
- Fraction: 7/9 - 3/9 = 4/9

✔ Answer: 2 4/9

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e. 8 9/12 - 3 1/6

- Simplify 9/12 → 3/4, but let’s use 12 as common denominator.
- 3 1/6 = 3 2/12

- Subtract:
- Whole: 8 - 3 = 5
- Fraction: 9/12 - 2/12 = 7/12

✔ Answer: 5 7/12

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f. 1 1/4 - 7/8

- Convert 1 1/4 to improper: 5/4
- Common denominator of 4 and 8 is 8
- 5/4 = 10/8
- 7/8 stays 7/8

- Subtract: 10/8 - 7/8 = 3/8

✔ Answer: 3/8

*(Note: Since 3/8 < 1, it remains a proper fraction.)*

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g. 15 3/5 - 3 1/2

- Common denominator of 5 and 2 is 10
- Convert:
- 15 3/5 = 15 6/10
- 3 1/2 = 3 5/10

- Subtract:
- Whole: 15 - 3 = 12
- Fraction: 6/10 - 5/10 = 1/10

✔ Answer: 12 1/10

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h. 3 3/8 - 2 1/4

- Common denominator of 8 and 4 is 8
- Convert:
- 3 3/8 stays 3 3/8
- 2 1/4 = 2 2/8

- Subtract:
- Whole: 3 - 2 = 1
- Fraction: 3/8 - 2/8 = 1/8

✔ Answer: 1 1/8

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i. 7 11/12 - 2 1/2

- Common denominator of 12 and 2 is 12
- Convert:
- 7 11/12 stays 7 11/12
- 2 1/2 = 2 6/12

- Subtract:
- Whole: 7 - 2 = 5
- Fraction: 11/12 - 6/12 = 5/12

✔ Answer: 5 5/12

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j. 19 3/5 - 12 3/10

- Common denominator of 5 and 10 is 10
- Convert:
- 19 3/5 = 19 6/10
- 12 3/10 stays 12 3/10

- Subtract:
- Whole: 19 - 12 = 7
- Fraction: 6/10 - 3/10 = 3/10

✔ Answer: 7 3/10

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k. 4 2/3 - 3 1/2

- Common denominator of 3 and 2 is 6
- Convert:
- 4 2/3 = 4 4/6
- 3 1/2 = 3 3/6

- Subtract:
- Whole: 4 - 3 = 1
- Fraction: 4/6 - 3/6 = 1/6

✔ Answer: 1 1/6

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l. 5 5/12 - 3 1/3

- Common denominator of 12 and 3 is 12
- Convert:
- 5 5/12 stays 5 5/12
- 3 1/3 = 3 4/12

- Subtract:
- Whole: 5 - 3 = 2
- Fraction: 5/12 - 4/12 = 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 1/8
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 using the “borrowing” method or visual models!