Subtracting fractions worksheet with regrouping exercises.

Let's solve each of these subtracting fractions with regrouping problems step by step. The key idea is that when subtracting mixed numbers and the fractional part of the minuend (the first number) is smaller than the fractional part of the subtrahend (the second number), we need to regroup (borrow 1 from the whole number part and convert it into a fraction).

We'll go through each problem carefully.

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1) $ 5\frac{1}{4} - 2\frac{3}{4} $

- Since $ \frac{1}{4} < \frac{3}{4} $, we need to regroup.
- Borrow 1 from 5 → $ 5 = 4 + 1 $
- Convert 1 to $ \frac{4}{4} $, so $ 5\frac{1}{4} = 4 + \frac{4}{4} + \frac{1}{4} = 4\frac{5}{4} $
- Now: $ 4\frac{5}{4} - 2\frac{3}{4} = (4 - 2) + \left(\frac{5}{4} - \frac{3}{4}\right) = 2 + \frac{2}{4} = 2\frac{1}{2} $

✔ Answer: $ 2\frac{1}{2} $

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2) $ 2\frac{2}{4} - 1\frac{3}{4} $

- $ \frac{2}{4} < \frac{3}{4} $ → regroup
- Borrow 1 from 2 → $ 2\frac{2}{4} = 1 + \frac{4}{4} + \frac{2}{4} = 1\frac{6}{4} $
- Now: $ 1\frac{6}{4} - 1\frac{3}{4} = (1 - 1) + \left(\frac{6}{4} - \frac{3}{4}\right) = 0 + \frac{3}{4} = \frac{3}{4} $

✔ Answer: $ \frac{3}{4} $

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3) $ 3\frac{4}{8} - 1\frac{7}{8} $

- $ \frac{4}{8} < \frac{7}{8} $ → regroup
- Borrow 1 from 3 → $ 3\frac{4}{8} = 2 + \frac{8}{8} + \frac{4}{8} = 2\frac{12}{8} $
- Subtract: $ 2\frac{12}{8} - 1\frac{7}{8} = (2 - 1) + \left(\frac{12}{8} - \frac{7}{8}\right) = 1 + \frac{5}{8} = 1\frac{5}{8} $

✔ Answer: $ 1\frac{5}{8} $

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4) $ 4\frac{1}{8} - 2\frac{2}{8} $

- $ \frac{1}{8} < \frac{2}{8} $ → regroup
- Borrow 1 from 4 → $ 4\frac{1}{8} = 3 + \frac{8}{8} + \frac{1}{8} = 3\frac{9}{8} $
- Subtract: $ 3\frac{9}{8} - 2\frac{2}{8} = (3 - 2) + \left(\frac{9}{8} - \frac{2}{8}\right) = 1 + \frac{7}{8} = 1\frac{7}{8} $

✔ Answer: $ 1\frac{7}{8} $

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5) $ 9\frac{1}{9} - 7\frac{4}{9} $

- $ \frac{1}{9} < \frac{4}{9} $ → regroup
- Borrow 1 from 9 → $ 9\frac{1}{9} = 8 + \frac{9}{9} + \frac{1}{9} = 8\frac{10}{9} $
- Subtract: $ 8\frac{10}{9} - 7\frac{4}{9} = (8 - 7) + \left(\frac{10}{9} - \frac{4}{9}\right) = 1 + \frac{6}{9} = 1\frac{2}{3} $

✔ Answer: $ 1\frac{2}{3} $

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6) $ 2\frac{2}{5} - 1\frac{4}{5} $

- $ \frac{2}{5} < \frac{4}{5} $ → regroup
- Borrow 1 from 2 → $ 2\frac{2}{5} = 1 + \frac{5}{5} + \frac{2}{5} = 1\frac{7}{5} $
- Subtract: $ 1\frac{7}{5} - 1\frac{4}{5} = (1 - 1) + \left(\frac{7}{5} - \frac{4}{5}\right) = 0 + \frac{3}{5} = \frac{3}{5} $

✔ Answer: $ \frac{3}{5} $

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7) $ 2\frac{2}{9} - 1\frac{3}{9} $

- $ \frac{2}{9} < \frac{3}{9} $ → regroup
- Borrow 1 from 2 → $ 2\frac{2}{9} = 1 + \frac{9}{9} + \frac{2}{9} = 1\frac{11}{9} $
- Subtract: $ 1\frac{11}{9} - 1\frac{3}{9} = (1 - 1) + \left(\frac{11}{9} - \frac{3}{9}\right) = 0 + \frac{8}{9} = \frac{8}{9} $

✔ Answer: $ \frac{8}{9} $

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8) $ 9\frac{1}{8} - 2\frac{4}{8} $

- $ \frac{1}{8} < \frac{4}{8} $ → regroup
- Borrow 1 from 9 → $ 9\frac{1}{8} = 8 + \frac{8}{8} + \frac{1}{8} = 8\frac{9}{8} $
- Subtract: $ 8\frac{9}{8} - 2\frac{4}{8} = (8 - 2) + \left(\frac{9}{8} - \frac{4}{8}\right) = 6 + \frac{5}{8} = 6\frac{5}{8} $

✔ Answer: $ 6\frac{5}{8} $

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9) $ 2\frac{3}{6} - 1\frac{5}{6} $

- Simplify fractions first: $ \frac{3}{6} = \frac{1}{2}, \frac{5}{6} $ stays
- But keep as sixths for subtraction: $ \frac{3}{6} < \frac{5}{6} $ → regroup
- Borrow 1 from 2 → $ 2\frac{3}{6} = 1 + \frac{6}{6} + \frac{3}{6} = 1\frac{9}{6} $
- Subtract: $ 1\frac{9}{6} - 1\frac{5}{6} = (1 - 1) + \left(\frac{9}{6} - \frac{5}{6}\right) = 0 + \frac{4}{6} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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10) $ 8\frac{1}{5} - 1\frac{3}{5} $

- $ \frac{1}{5} < \frac{3}{5} $ → regroup
- Borrow 1 from 8 → $ 8\frac{1}{5} = 7 + \frac{5}{5} + \frac{1}{5} = 7\frac{6}{5} $
- Subtract: $ 7\frac{6}{5} - 1\frac{3}{5} = (7 - 1) + \left(\frac{6}{5} - \frac{3}{5}\right) = 6 + \frac{3}{5} = 6\frac{3}{5} $

✔ Answer: $ 6\frac{3}{5} $

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11) $ 2\frac{1}{8} - 1\frac{3}{8} $

- $ \frac{1}{8} < \frac{3}{8} $ → regroup
- Borrow 1 from 2 → $ 2\frac{1}{8} = 1 + \frac{8}{8} + \frac{1}{8} = 1\frac{9}{8} $
- Subtract: $ 1\frac{9}{8} - 1\frac{3}{8} = (1 - 1) + \left(\frac{9}{8} - \frac{3}{8}\right) = 0 + \frac{6}{8} = \frac{3}{4} $

✔ Answer: $ \frac{3}{4} $

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12) $ 9\frac{1}{9} - 7\frac{2}{9} $

- $ \frac{1}{9} < \frac{2}{9} $ → regroup
- Borrow 1 from 9 → $ 9\frac{1}{9} = 8 + \frac{9}{9} + \frac{1}{9} = 8\frac{10}{9} $
- Subtract: $ 8\frac{10}{9} - 7\frac{2}{9} = (8 - 7) + \left(\frac{10}{9} - \frac{2}{9}\right) = 1 + \frac{8}{9} = 1\frac{8}{9} $

✔ Answer: $ 1\frac{8}{9} $

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13) $ 3\frac{1}{5} - 2\frac{2}{5} $

- $ \frac{1}{5} < \frac{2}{5} $ → regroup
- Borrow 1 from 3 → $ 3\frac{1}{5} = 2 + \frac{5}{5} + \frac{1}{5} = 2\frac{6}{5} $
- Subtract: $ 2\frac{6}{5} - 2\frac{2}{5} = (2 - 2) + \left(\frac{6}{5} - \frac{2}{5}\right) = 0 + \frac{4}{5} = \frac{4}{5} $

✔ Answer: $ \frac{4}{5} $

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14) $ 4\frac{1}{5} - 3\frac{3}{5} $

- $ \frac{1}{5} < \frac{3}{5} $ → regroup
- Borrow 1 from 4 → $ 4\frac{1}{5} = 3 + \frac{5}{5} + \frac{1}{5} = 3\frac{6}{5} $
- Subtract: $ 3\frac{6}{5} - 3\frac{3}{5} = (3 - 3) + \left(\frac{6}{5} - \frac{3}{5}\right) = 0 + \frac{3}{5} = \frac{3}{5} $

✔ Answer: $ \frac{3}{5} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 2\frac{1}{2} $ |
| 2 | $ \frac{3}{4} $ |
| 3 | $ 1\frac{5}{8} $ |
| 4 | $ 1\frac{7}{8} $ |
| 5 | $ 1\frac{2}{3} $ |
| 6 | $ \frac{3}{5} $ |
| 7 | $ \frac{8}{9} $ |
| 8 | $ 6\frac{5}{8} $ |
| 9 | $ \frac{2}{3} $ |
| 10 | $ 6\frac{3}{5} $ |
| 11 | $ \frac{3}{4} $ |
| 12 | $ 1\frac{8}{9} $ |
| 13 | $ \frac{4}{5} $ |
| 14 | $ \frac{3}{5} $ |

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Let me know if you'd like this in a printable format or need explanations for any specific problem!