Subtracting Fractions with the Same Denominator - Free Printable

Let's solve each problem step by step. We are adding and subtracting positive and negative mixed numbers. The key is to convert mixed numbers to improper fractions, handle the signs carefully, perform the operations, and then simplify the result.

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1. $ 2\frac{6}{7} + (-3\frac{3}{4}) $

Convert to improper fractions:

- $ 2\frac{6}{7} = \frac{2 \times 7 + 6}{7} = \frac{14 + 6}{7} = \frac{20}{7} $
- $ -3\frac{3}{4} = -\left(\frac{3 \times 4 + 3}{4}\right) = -\frac{15}{4} $

Now add:
$ \frac{20}{7} + \left(-\frac{15}{4}\right) = \frac{20}{7} - \frac{15}{4} $

Find common denominator: LCM of 7 and 4 is 28

- $ \frac{20}{7} = \frac{20 \times 4}{28} = \frac{80}{28} $
- $ \frac{15}{4} = \frac{15 \times 7}{28} = \frac{105}{28} $

So:
$ \frac{80}{28} - \frac{105}{28} = \frac{-25}{28} $

Answer: $ \boxed{-\frac{25}{28}} $

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2. $ 7\frac{1}{6} - 2\frac{5}{8} $

Convert:

- $ 7\frac{1}{6} = \frac{7 \times 6 + 1}{6} = \frac{42 + 1}{6} = \frac{43}{6} $
- $ 2\frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8} $

Subtract:
$ \frac{43}{6} - \frac{21}{8} $

LCM of 6 and 8 is 24

- $ \frac{43}{6} = \frac{43 \times 4}{24} = \frac{172}{24} $
- $ \frac{21}{8} = \frac{21 \times 3}{24} = \frac{63}{24} $

$ \frac{172}{24} - \frac{63}{24} = \frac{109}{24} $

Convert to mixed number:
$ \frac{109}{24} = 4\frac{13}{24} $ (since $ 24 \times 4 = 96 $, $ 109 - 96 = 13 $)

Answer: $ \boxed{4\frac{13}{24}} $

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3. $ -5\frac{1}{2} + 1\frac{5}{6} $

Convert:

- $ -5\frac{1}{2} = -\frac{11}{2} $
- $ 1\frac{5}{6} = \frac{11}{6} $

Add:
$ -\frac{11}{2} + \frac{11}{6} $

LCM of 2 and 6 is 6

- $ -\frac{11}{2} = -\frac{33}{6} $
- $ \frac{11}{6} = \frac{11}{6} $

$ -\frac{33}{6} + \frac{11}{6} = -\frac{22}{6} = -\frac{11}{3} $

Simplify: $ -\frac{11}{3} = -3\frac{2}{3} $

Answer: $ \boxed{-3\frac{2}{3}} $

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4. $ 3\frac{1}{10} - (-4\frac{1}{10}) $

Subtracting a negative is adding:

$ 3\frac{1}{10} + 4\frac{1}{10} = (3 + 4) + \left(\frac{1}{10} + \frac{1}{10}\right) = 7\frac{2}{10} = 7\frac{1}{5} $

Answer: $ \boxed{7\frac{1}{5}} $

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5. $ -4\frac{2}{5} + 3\frac{3}{10} $

Convert:

- $ -4\frac{2}{5} = -\frac{22}{5} $
- $ 3\frac{3}{10} = \frac{33}{10} $

Add:
$ -\frac{22}{5} + \frac{33}{10} $

LCM of 5 and 10 is 10

- $ -\frac{22}{5} = -\frac{44}{10} $
- $ \frac{33}{10} = \frac{33}{10} $

$ -\frac{44}{10} + \frac{33}{10} = -\frac{11}{10} = -1\frac{1}{10} $

Answer: $ \boxed{-1\frac{1}{10}} $

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6. $ -2\frac{3}{5} - 5\frac{1}{2} $

Convert:

- $ -2\frac{3}{5} = -\frac{13}{5} $
- $ 5\frac{1}{2} = \frac{11}{2} $

Now:
$ -\frac{13}{5} - \frac{11}{2} $

LCM of 5 and 2 is 10

- $ -\frac{13}{5} = -\frac{26}{10} $
- $ \frac{11}{2} = \frac{55}{10} $

$ -\frac{26}{10} - \frac{55}{10} = -\frac{81}{10} = -8\frac{1}{10} $

Answer: $ \boxed{-8\frac{1}{10}} $

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7. $ -3\frac{1}{2} + (-5\frac{1}{3}) $

Both negative: add absolute values

Convert:

- $ -3\frac{1}{2} = -\frac{7}{2} $
- $ -5\frac{1}{3} = -\frac{16}{3} $

Add:
$ -\frac{7}{2} - \frac{16}{3} = -\left( \frac{7}{2} + \frac{16}{3} \right) $

LCM of 2 and 3 is 6

- $ \frac{7}{2} = \frac{21}{6} $
- $ \frac{16}{3} = \frac{32}{6} $

Sum: $ \frac{53}{6} $ → $ -\frac{53}{6} = -8\frac{5}{6} $

Answer: $ \boxed{-8\frac{5}{6}} $

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8. $ 4\frac{1}{3} + (-1\frac{1}{2}) $

Convert:

- $ 4\frac{1}{3} = \frac{13}{3} $
- $ -1\frac{1}{2} = -\frac{3}{2} $

Add:
$ \frac{13}{3} - \frac{3}{2} $

LCM of 3 and 2 is 6

- $ \frac{13}{3} = \frac{26}{6} $
- $ \frac{3}{2} = \frac{9}{6} $

$ \frac{26}{6} - \frac{9}{6} = \frac{17}{6} = 2\frac{5}{6} $

Answer: $ \boxed{2\frac{5}{6}} $

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9. $ -5\frac{3}{4} - (-2\frac{3}{8}) $

Subtracting a negative = adding:

$ -5\frac{3}{4} + 2\frac{3}{8} $

Convert:

- $ -5\frac{3}{4} = -\frac{23}{4} $
- $ 2\frac{3}{8} = \frac{19}{8} $

Add:
$ -\frac{23}{4} + \frac{19}{8} $

LCM of 4 and 8 is 8

- $ -\frac{23}{4} = -\frac{46}{8} $
- $ \frac{19}{8} = \frac{19}{8} $

$ -\frac{46}{8} + \frac{19}{8} = -\frac{27}{8} = -3\frac{3}{8} $

Answer: $ \boxed{-3\frac{3}{8}} $

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10. $ -6\frac{5}{8} - (-3\frac{1}{2}) $

Subtracting negative = adding:

$ -6\frac{5}{8} + 3\frac{1}{2} $

Convert:

- $ -6\frac{5}{8} = -\frac{53}{8} $
- $ 3\frac{1}{2} = \frac{7}{2} $

Add:
$ -\frac{53}{8} + \frac{7}{2} $

LCM of 8 and 2 is 8

- $ \frac{7}{2} = \frac{28}{8} $

$ -\frac{53}{8} + \frac{28}{8} = -\frac{25}{8} = -3\frac{1}{8} $

Answer: $ \boxed{-3\frac{1}{8}} $

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11. $ 2\frac{1}{3} - (-2\frac{1}{4}) $

Subtracting negative = adding:

$ 2\frac{1}{3} + 2\frac{1}{4} $

Convert:

- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 2\frac{1}{4} = \frac{9}{4} $

Add:
$ \frac{7}{3} + \frac{9}{4} $

LCM of 3 and 4 is 12

- $ \frac{7}{3} = \frac{28}{12} $
- $ \frac{9}{4} = \frac{27}{12} $

$ \frac{28}{12} + \frac{27}{12} = \frac{55}{12} = 4\frac{7}{12} $

Answer: $ \boxed{4\frac{7}{12}} $

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12. $ -3\frac{1}{4} + (-4\frac{1}{3}) $

Both negative: add absolute values

Convert:

- $ -3\frac{1}{4} = -\frac{13}{4} $
- $ -4\frac{1}{3} = -\frac{13}{3} $

Add:
$ -\frac{13}{4} - \frac{13}{3} = -\left( \frac{13}{4} + \frac{13}{3} \right) $

LCM of 4 and 3 is 12

- $ \frac{13}{4} = \frac{39}{12} $
- $ \frac{13}{3} = \frac{52}{12} $

Sum: $ \frac{91}{12} $ → $ -\frac{91}{12} = -7\frac{7}{12} $

Answer: $ \boxed{-7\frac{7}{12}} $

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✔ Final Answers:

1. $ -\frac{25}{28} $
2. $ 4\frac{13}{24} $
3. $ -3\frac{2}{3} $
4. $ 7\frac{1}{5} $
5. $ -1\frac{1}{10} $
6. $ -8\frac{1}{10} $
7. $ -8\frac{5}{6} $
8. $ 2\frac{5}{6} $
9. $ -3\frac{3}{8} $
10. $ -3\frac{1}{8} $
11. $ 4\frac{7}{12} $
12. $ -7\frac{7}{12} $

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