Subtracting mixed numbers worksheets | Worsheets library - Free Printable

You've uploaded a Grade 4 Fractions Worksheet titled “Subtracting Mixed Numbers.” The task is to find the difference for each of the 16 problems.

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🔢 General Strategy for Subtracting Mixed Numbers:

To subtract mixed numbers, follow these steps:

1. Convert mixed numbers to improper fractions (optional but often helpful).
2. Find a common denominator.
3. Subtract the fractions.
4. If needed, borrow from the whole number (if the top fraction is smaller than the bottom one).
5. Simplify the result and convert back to a mixed number if necessary.

Alternatively, you can:
- Subtract the whole numbers first.
- Subtract the fractions.
- If the fractional part of the minuend is smaller than the subtrahend, borrow 1 from the whole number, convert it to a fraction with the common denominator, and add it to the existing fraction.

We’ll solve each problem step-by-step using the second method for clarity.

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## ✏️ Solutions:

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1. $6\frac{10}{12} - 1\frac{11}{12}$

→ Fractional part: $\frac{10}{12} < \frac{11}{12}$ → Borrow 1 from 6.

$6\frac{10}{12} = 5 + 1\frac{10}{12} = 5 + \frac{22}{12}$

Now:
$5\frac{22}{12} - 1\frac{11}{12} = (5 - 1) + (\frac{22}{12} - \frac{11}{12}) = 4 + \frac{11}{12} = \boxed{4\frac{11}{12}}$

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

→ $\frac{1}{8} < \frac{7}{8}$ → Borrow 1 from 7.

$7\frac{1}{8} = 6 + \frac{9}{8}$

$6\frac{9}{8} - 1\frac{7}{8} = 5 + \frac{2}{8} = \boxed{5\frac{1}{4}}$ (simplified)

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3. $6\frac{6}{8} - 1\frac{7}{8}$

→ $\frac{6}{8} < \frac{7}{8}$ → Borrow 1.

$6\frac{6}{8} = 5 + \frac{14}{8}$

$5\frac{14}{8} - 1\frac{7}{8} = 4 + \frac{7}{8} = \boxed{4\frac{7}{8}}$

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4. $6\frac{6}{15} - 1\frac{11}{15}$

→ $\frac{6}{15} < \frac{11}{15}$ → Borrow 1.

$6\frac{6}{15} = 5 + \frac{21}{15}$

$5\frac{21}{15} - 1\frac{11}{15} = 4 + \frac{10}{15} = \boxed{4\frac{2}{3}}$ (simplified)

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5. $9\frac{12}{50} - 1\frac{33}{50}$

→ $\frac{12}{50} < \frac{33}{50}$ → Borrow 1.

$9\frac{12}{50} = 8 + \frac{62}{50}$

$8\frac{62}{50} - 1\frac{33}{50} = 7 + \frac{29}{50} = \boxed{7\frac{29}{50}}$

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6. $3\frac{1}{4} - 2\frac{1}{4}$

→ Same denominators, no borrowing needed.

$(3 - 2) + (\frac{1}{4} - \frac{1}{4}) = 1 + 0 = \boxed{1}$

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7. $5\frac{3}{7} - 2\frac{2}{7}$

→ Same denominators.

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

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8. $5\frac{1}{3} - 1\frac{2}{3}$

→ $\frac{1}{3} < \frac{2}{3}$ → Borrow 1.

$5\frac{1}{3} = 4 + \frac{4}{3}$

$4\frac{4}{3} - 1\frac{2}{3} = 3 + \frac{2}{3} = \boxed{3\frac{2}{3}}$

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9. $7\frac{5}{20} - 1\frac{10}{20}$

→ $\frac{5}{20} < \frac{10}{20}$ → Borrow 1.

$7\frac{5}{20} = 6 + \frac{25}{20}$

$6\frac{25}{20} - 1\frac{10}{20} = 5 + \frac{15}{20} = \boxed{5\frac{3}{4}}$ (simplified)

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10. $4\frac{23}{25} - 1\frac{24}{25}$

→ $\frac{23}{25} < \frac{24}{25}$ → Borrow 1.

$4\frac{23}{25} = 3 + \frac{48}{25}$

$3\frac{48}{25} - 1\frac{24}{25} = 2 + \frac{24}{25} = \boxed{2\frac{24}{25}}$

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11. $5\frac{1}{5} - 2\frac{2}{5}$

→ $\frac{1}{5} < \frac{2}{5}$ → Borrow 1.

$5\frac{1}{5} = 4 + \frac{6}{5}$

$4\frac{6}{5} - 2\frac{2}{5} = 2 + \frac{4}{5} = \boxed{2\frac{4}{5}}$

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12. $4\frac{8}{10} - 2\frac{9}{10}$

→ $\frac{8}{10} < \frac{9}{10}$ → Borrow 1.

$4\frac{8}{10} = 3 + \frac{18}{10}$

$3\frac{18}{10} - 2\frac{9}{10} = 1 + \frac{9}{10} = \boxed{1\frac{9}{10}}$

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13. $7\frac{5}{9} - 2\frac{2}{9}$

→ Same denominators.

$(7 - 2) + (\frac{5}{9} - \frac{2}{9}) = 5 + \frac{3}{9} = \boxed{5\frac{1}{3}}$ (simplified)

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14. $4\frac{7}{12} - 2\frac{8}{12}$

→ $\frac{7}{12} < \frac{8}{12}$ → Borrow 1.

$4\frac{7}{12} = 3 + \frac{19}{12}$

$3\frac{19}{12} - 2\frac{8}{12} = 1 + \frac{11}{12} = \boxed{1\frac{11}{12}}$

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15. $9\frac{82}{100} - 1\frac{84}{100}$

→ $\frac{82}{100} < \frac{84}{100}$ → Borrow 1.

$9\frac{82}{100} = 8 + \frac{182}{100}$

$8\frac{182}{100} - 1\frac{84}{100} = 7 + \frac{98}{100} = \boxed{7\frac{49}{50}}$ (simplified)

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16. $7\frac{10}{16} - 1\frac{14}{16}$

→ $\frac{10}{16} < \frac{14}{16}$ → Borrow 1.

$7\frac{10}{16} = 6 + \frac{26}{16}$

$6\frac{26}{16} - 1\frac{14}{16} = 5 + \frac{12}{16} = \boxed{5\frac{3}{4}}$ (simplified)

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## ✔ Final Answers (Boxed):

1. $\boxed{4\frac{11}{12}}$
2. $\boxed{5\frac{1}{4}}$
3. $\boxed{4\frac{7}{8}}$
4. $\boxed{4\frac{2}{3}}$
5. $\boxed{7\frac{29}{50}}$
6. $\boxed{1}$
7. $\boxed{3\frac{1}{7}}$
8. $\boxed{3\frac{2}{3}}$
9. $\boxed{5\frac{3}{4}}$
10. $\boxed{2\frac{24}{25}}$
11. $\boxed{2\frac{4}{5}}$
12. $\boxed{1\frac{9}{10}}$
13. $\boxed{5\frac{1}{3}}$
14. $\boxed{1\frac{11}{12}}$
15. $\boxed{7\frac{49}{50}}$
16. $\boxed{5\frac{3}{4}}$

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✔ All problems solved! Let me know if you’d like a printable version or step-by-step visual breakdowns for any specific problem.