Subtraction of fractions worksheet with mixed number problems for practice.

Let's solve each subtraction problem involving mixed numbers (whole numbers and fractions). We'll follow these steps for each:

1. Convert mixed numbers to improper fractions if needed.
2. Find a common denominator.
3. Subtract the fractions.
4. Simplify and convert back to a mixed number if necessary.

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

Convert to improper fractions:
- $ 4\frac{1}{2} = \frac{9}{2} $
- $ 2\frac{3}{4} = \frac{11}{4} $

Find common denominator: LCM of 2 and 4 is 4
- $ \frac{9}{2} = \frac{18}{4} $
- $ \frac{18}{4} - \frac{11}{4} = \frac{7}{4} = 1\frac{3}{4} $

✔ Answer: $ 1\frac{3}{4} $

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2. $ 20\frac{2}{4} - 19\frac{7}{10} $

Simplify $ \frac{2}{4} = \frac{1}{2} $, so:
- $ 20\frac{1}{2} = \frac{41}{2} $
- $ 19\frac{7}{10} = \frac{197}{10} $

Common denominator: LCM of 2 and 10 is 10
- $ \frac{41}{2} = \frac{205}{10} $
- $ \frac{205}{10} - \frac{197}{10} = \frac{8}{10} = \frac{4}{5} $

✔ Answer: $ \frac{4}{5} $

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3. $ 20\frac{4}{5} - 7\frac{1}{5} $

Same denominators:
- $ 20\frac{4}{5} - 7\frac{1}{5} = (20 - 7) + \left(\frac{4}{5} - \frac{1}{5}\right) = 13 + \frac{3}{5} $

✔ Answer: $ 13\frac{3}{5} $

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4. $ 10\frac{3}{9} - 8\frac{1}{4} $

Simplify $ \frac{3}{9} = \frac{1}{3} $, so:
- $ 10\frac{1}{3} = \frac{31}{3} $
- $ 8\frac{1}{4} = \frac{33}{4} $

Common denominator: LCM of 3 and 4 is 12
- $ \frac{31}{3} = \frac{124}{12} $
- $ \frac{33}{4} = \frac{99}{12} $
- $ \frac{124}{12} - \frac{99}{12} = \frac{25}{12} = 2\frac{1}{12} $

✔ Answer: $ 2\frac{1}{12} $

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5. $ 15\frac{1}{6} - 13\frac{7}{10} $

Convert:
- $ 15\frac{1}{6} = \frac{91}{6} $
- $ 13\frac{7}{10} = \frac{137}{10} $

LCM of 6 and 10 is 30
- $ \frac{91}{6} = \frac{455}{30} $
- $ \frac{137}{10} = \frac{411}{30} $
- $ \frac{455}{30} - \frac{411}{30} = \frac{44}{30} = \frac{22}{15} = 1\frac{7}{15} $

✔ Answer: $ 1\frac{7}{15} $

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6. $ 19\frac{1}{4} - 17\frac{4}{8} $

Simplify $ \frac{4}{8} = \frac{1}{2} $, so:
- $ 19\frac{1}{4} = \frac{77}{4} $
- $ 17\frac{1}{2} = \frac{35}{2} $

LCM of 4 and 2 is 4
- $ \frac{35}{2} = \frac{70}{4} $
- $ \frac{77}{4} - \frac{70}{4} = \frac{7}{4} = 1\frac{3}{4} $

✔ Answer: $ 1\frac{3}{4} $

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7. $ 12\frac{2}{8} - 10\frac{5}{6} $

Simplify $ \frac{2}{8} = \frac{1}{4} $, so:
- $ 12\frac{1}{4} = \frac{49}{4} $
- $ 10\frac{5}{6} = \frac{65}{6} $

LCM of 4 and 6 is 12
- $ \frac{49}{4} = \frac{147}{12} $
- $ \frac{65}{6} = \frac{130}{12} $
- $ \frac{147}{12} - \frac{130}{12} = \frac{17}{12} = 1\frac{5}{12} $

✔ Answer: $ 1\frac{5}{12} $

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8. $ 12\frac{7}{8} - 2\frac{1}{6} $

Convert:
- $ 12\frac{7}{8} = \frac{103}{8} $
- $ 2\frac{1}{6} = \frac{13}{6} $

LCM of 8 and 6 is 24
- $ \frac{103}{8} = \frac{309}{24} $
- $ \frac{13}{6} = \frac{52}{24} $
- $ \frac{309}{24} - \frac{52}{24} = \frac{257}{24} = 10\frac{17}{24} $

✔ Answer: $ 10\frac{17}{24} $

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9. $ 8\frac{9}{12} - 8\frac{3}{5} $

Simplify $ \frac{9}{12} = \frac{3}{4} $, so:
- $ 8\frac{3}{4} = \frac{35}{4} $
- $ 8\frac{3}{5} = \frac{43}{5} $

LCM of 4 and 5 is 20
- $ \frac{35}{4} = \frac{175}{20} $
- $ \frac{43}{5} = \frac{172}{20} $
- $ \frac{175}{20} - \frac{172}{20} = \frac{3}{20} $

✔ Answer: $ \frac{3}{20} $

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10. $ 17\frac{1}{3} - 1\frac{1}{4} $

Convert:
- $ 17\frac{1}{3} = \frac{52}{3} $
- $ 1\frac{1}{4} = \frac{5}{4} $

LCM of 3 and 4 is 12
- $ \frac{52}{3} = \frac{208}{12} $
- $ \frac{5}{4} = \frac{15}{12} $
- $ \frac{208}{12} - \frac{15}{12} = \frac{193}{12} = 16\frac{1}{12} $

✔ Answer: $ 16\frac{1}{12} $

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11. $ 19\frac{7}{10} - 16\frac{2}{3} $

Convert:
- $ 19\frac{7}{10} = \frac{197}{10} $
- $ 16\frac{2}{3} = \frac{50}{3} $

LCM of 10 and 3 is 30
- $ \frac{197}{10} = \frac{591}{30} $
- $ \frac{50}{3} = \frac{500}{30} $
- $ \frac{591}{30} - \frac{500}{30} = \frac{91}{30} = 3\frac{1}{30} $

✔ Answer: $ 3\frac{1}{30} $

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12. $ 13\frac{1}{2} - 10\frac{7}{8} $

Convert:
- $ 13\frac{1}{2} = \frac{27}{2} $
- $ 10\frac{7}{8} = \frac{87}{8} $

LCM of 2 and 8 is 8
- $ \frac{27}{2} = \frac{108}{8} $
- $ \frac{108}{8} - \frac{87}{8} = \frac{21}{8} = 2\frac{5}{8} $

✔ Answer: $ 2\frac{5}{8} $

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✔ Final Answers:

1. $ 1\frac{3}{4} $
2. $ \frac{4}{5} $
3. $ 13\frac{3}{5} $
4. $ 2\frac{1}{12} $
5. $ 1\frac{7}{15} $
6. $ 1\frac{3}{4} $
7. $ 1\frac{5}{12} $
8. $ 10\frac{17}{24} $
9. $ \frac{3}{20} $
10. $ 16\frac{1}{12} $
11. $ 3\frac{1}{30} $
12. $ 2\frac{5}{8} $

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