Subtracting Mixed Numbers Worksheets - 15 Worksheets Library - Free Printable

Let's solve each problem on the worksheet step by step. The task is to subtract mixed numbers with unlike denominators.

We'll follow these steps for each problem:
1. Convert mixed numbers to improper fractions.
2. Find a common denominator.
3. Subtract the fractions.
4. Simplify and convert back to a mixed number if needed.

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Problem 1:

3 1/3 - 1 1/2

- Convert:
$ 3\frac{1}{3} = \frac{10}{3}, \quad 1\frac{1}{2} = \frac{3}{2} $
- LCD of 3 and 2 is 6.
$ \frac{10}{3} = \frac{20}{6}, \quad \frac{3}{2} = \frac{9}{6} $
- Subtract: $ \frac{20}{6} - \frac{9}{6} = \frac{11}{6} $
- Convert: $ \frac{11}{6} = 1\frac{5}{6} $

✔ Answer: 1 5/6

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Problem 2:

4 3/5 - 2 1/3

- Convert:
$ 4\frac{3}{5} = \frac{23}{5}, \quad 2\frac{1}{3} = \frac{7}{3} $
- LCD of 5 and 3 is 15.
$ \frac{23}{5} = \frac{69}{15}, \quad \frac{7}{3} = \frac{35}{15} $
- Subtract: $ \frac{69}{15} - \frac{35}{15} = \frac{34}{15} $
- Convert: $ \frac{34}{15} = 2\frac{4}{15} $

✔ Answer: 2 4/15

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Problem 3:

3 1/2 - 2 1/5

- Convert:
$ 3\frac{1}{2} = \frac{7}{2}, \quad 2\frac{1}{5} = \frac{11}{5} $
- LCD of 2 and 5 is 10.
$ \frac{7}{2} = \frac{35}{10}, \quad \frac{11}{5} = \frac{22}{10} $
- Subtract: $ \frac{35}{10} - \frac{22}{10} = \frac{13}{10} $
- Convert: $ \frac{13}{10} = 1\frac{3}{10} $

✔ Answer: 1 3/10

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Problem 4:

2 2/3 - 1 1/5

- Convert:
$ 2\frac{2}{3} = \frac{8}{3}, \quad 1\frac{1}{5} = \frac{6}{5} $
- LCD of 3 and 5 is 15.
$ \frac{8}{3} = \frac{40}{15}, \quad \frac{6}{5} = \frac{18}{15} $
- Subtract: $ \frac{40}{15} - \frac{18}{15} = \frac{22}{15} $
- Convert: $ \frac{22}{15} = 1\frac{7}{15} $

✔ Answer: 1 7/15

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Problem 5:

4 1/6 - 3 1/5

- Convert:
$ 4\frac{1}{6} = \frac{25}{6}, \quad 3\frac{1}{5} = \frac{16}{5} $
- LCD of 6 and 5 is 30.
$ \frac{25}{6} = \frac{125}{30}, \quad \frac{16}{5} = \frac{96}{30} $
- Subtract: $ \frac{125}{30} - \frac{96}{30} = \frac{29}{30} $

✔ Answer: 29/30

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Problem 6:

2 3/4 - 1 1/5

- Convert:
$ 2\frac{3}{4} = \frac{11}{4}, \quad 1\frac{1}{5} = \frac{6}{5} $
- LCD of 4 and 5 is 20.
$ \frac{11}{4} = \frac{55}{20}, \quad \frac{6}{5} = \frac{24}{20} $
- Subtract: $ \frac{55}{20} - \frac{24}{20} = \frac{31}{20} $
- Convert: $ \frac{31}{20} = 1\frac{11}{20} $

✔ Answer: 1 11/20

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Problem 7:

3 1/5 - 2 1/3

- Convert:
$ 3\frac{1}{5} = \frac{16}{5}, \quad 2\frac{1}{3} = \frac{7}{3} $
- LCD of 5 and 3 is 15.
$ \frac{16}{5} = \frac{48}{15}, \quad \frac{7}{3} = \frac{35}{15} $
- Subtract: $ \frac{48}{15} - \frac{35}{15} = \frac{13}{15} $

✔ Answer: 13/15

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Problem 8:

5 1/3 - 2 2/5

- Convert:
$ 5\frac{1}{3} = \frac{16}{3}, \quad 2\frac{2}{5} = \frac{12}{5} $
- LCD of 3 and 5 is 15.
$ \frac{16}{3} = \frac{80}{15}, \quad \frac{12}{5} = \frac{36}{15} $
- Subtract: $ \frac{80}{15} - \frac{36}{15} = \frac{44}{15} $
- Convert: $ \frac{44}{15} = 2\frac{14}{15} $

✔ Answer: 2 14/15

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Problem 9:

4 2/5 - 2 3/4

- Convert:
$ 4\frac{2}{5} = \frac{22}{5}, \quad 2\frac{3}{4} = \frac{11}{4} $
- LCD of 5 and 4 is 20.
$ \frac{22}{5} = \frac{88}{20}, \quad \frac{11}{4} = \frac{55}{20} $
- Subtract: $ \frac{88}{20} - \frac{55}{20} = \frac{33}{20} $
- Convert: $ \frac{33}{20} = 1\frac{13}{20} $

✔ Answer: 1 13/20

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Problem 10:

3 3/5 - 1 1/4

- Convert:
$ 3\frac{3}{5} = \frac{18}{5}, \quad 1\frac{1}{4} = \frac{5}{4} $
- LCD of 5 and 4 is 20.
$ \frac{18}{5} = \frac{72}{20}, \quad \frac{5}{4} = \frac{25}{20} $
- Subtract: $ \frac{72}{20} - \frac{25}{20} = \frac{47}{20} $
- Convert: $ \frac{47}{20} = 2\frac{7}{20} $

✔ Answer: 2 7/20

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Problem 11:

4 1/5 - 3 2/7

- Convert:
$ 4\frac{1}{5} = \frac{21}{5}, \quad 3\frac{2}{7} = \frac{23}{7} $
- LCD of 5 and 7 is 35.
$ \frac{21}{5} = \frac{147}{35}, \quad \frac{23}{7} = \frac{115}{35} $
- Subtract: $ \frac{147}{35} - \frac{115}{35} = \frac{32}{35} $

✔ Answer: 32/35

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Problem 12:

2 2/5 - 1 1/3

- Convert:
$ 2\frac{2}{5} = \frac{12}{5}, \quad 1\frac{1}{3} = \frac{4}{3} $
- LCD of 5 and 3 is 15.
$ \frac{12}{5} = \frac{36}{15}, \quad \frac{4}{3} = \frac{20}{15} $
- Subtract: $ \frac{36}{15} - \frac{20}{15} = \frac{16}{15} $
- Convert: $ \frac{16}{15} = 1\frac{1}{15} $

✔ Answer: 1 1/15

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Problem 13:

3 3/5 - 2 2/3

- Convert:
$ 3\frac{3}{5} = \frac{18}{5}, \quad 2\frac{2}{3} = \frac{8}{3} $
- LCD of 5 and 3 is 15.
$ \frac{18}{5} = \frac{54}{15}, \quad \frac{8}{3} = \frac{40}{15} $
- Subtract: $ \frac{54}{15} - \frac{40}{15} = \frac{14}{15} $

✔ Answer: 14/15

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Problem 14:

3 4/5 - 1 1/3

- Convert:
$ 3\frac{4}{5} = \frac{19}{5}, \quad 1\frac{1}{3} = \frac{4}{3} $
- LCD of 5 and 3 is 15.
$ \frac{19}{5} = \frac{57}{15}, \quad \frac{4}{3} = \frac{20}{15} $
- Subtract: $ \frac{57}{15} - \frac{20}{15} = \frac{37}{15} $
- Convert: $ \frac{37}{15} = 2\frac{7}{15} $

✔ Answer: 2 7/15

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Problem 15:

3 3/4 - 2 3/5

- Convert:
$ 3\frac{3}{4} = \frac{15}{4}, \quad 2\frac{3}{5} = \frac{13}{5} $
- LCD of 4 and 5 is 20.
$ \frac{15}{4} = \frac{75}{20}, \quad \frac{13}{5} = \frac{52}{20} $
- Subtract: $ \frac{75}{20} - \frac{52}{20} = \frac{23}{20} $
- Convert: $ \frac{23}{20} = 1\frac{3}{20} $

✔ Answer: 1 3/20

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Problem 16:

2 3/4 - 1 1/5

- Convert:
$ 2\frac{3}{4} = \frac{11}{4}, \quad 1\frac{1}{5} = \frac{6}{5} $
- LCD of 4 and 5 is 20.
$ \frac{11}{4} = \frac{55}{20}, \quad \frac{6}{5} = \frac{24}{20} $
- Subtract: $ \frac{55}{20} - \frac{24}{20} = \frac{31}{20} $
- Convert: $ \frac{31}{20} = 1\frac{11}{20} $

✔ Answer: 1 11/20

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 1 5/6 |
| 2 | 2 4/15 |
| 3 | 1 3/10 |
| 4 | 1 7/15 |
| 5 | 29/30 |
| 6 | 1 11/20 |
| 7 | 13/15 |
| 8 | 2 14/15 |
| 9 | 1 13/20 |
| 10 | 2 7/20 |
| 11 | 32/35 |
| 12 | 1 1/15 |
| 13 | 14/15 |
| 14 | 2 7/15 |
| 15 | 1 3/20 |
| 16 | 1 11/20 |

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🔍 Summary of Key Steps:

- Always convert mixed numbers to improper fractions.
- Find the least common denominator (LCD).
- Rewrite both fractions with the LCD.
- Subtract the numerators.
- Simplify and convert back to mixed number if necessary.

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