Mixed Operations - Fractions worksheet with 18 problems for practice.

Here's the complete solution to all 18 problems on the “Mixed Operations - Fractions” worksheet. I’ll solve each one step by step, showing the work clearly.

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General Strategy:

- For addition/subtraction: Convert mixed numbers to improper fractions, find common denominators, then add or subtract.
- For multiplication: Convert mixed numbers to improper fractions, multiply numerators and denominators, then simplify.
- Always reduce final answers to lowest terms and convert back to mixed numbers if needed.

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## ✔ Problem-by-Problem Solutions:

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1. $9\frac{3}{5} - 4\frac{4}{5}$

→ Convert to improper fractions:
$9\frac{3}{5} = \frac{48}{5}, \quad 4\frac{4}{5} = \frac{24}{5}$

→ Subtract: $\frac{48}{5} - \frac{24}{5} = \frac{24}{5} = 4\frac{4}{5}$

✔ Answer: $4\frac{4}{5}$

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2. $9\frac{2}{3} + 3\frac{1}{3}$

→ Both have denominator 3:
$\frac{29}{3} + \frac{10}{3} = \frac{39}{3} = 13$

✔ Answer: $13$

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

→ $\frac{7}{3} + \frac{16}{3} = \frac{23}{3} = 7\frac{2}{3}$

✔ Answer: $7\frac{2}{3}$

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4. $9\frac{2}{4} + 1\frac{2}{4}$ → Simplify first: $9\frac{1}{2} + 1\frac{1}{2}$

→ $\frac{19}{2} + \frac{3}{2} = \frac{22}{2} = 11$

✔ Answer: $11$

*(Note: $9\frac{2}{4} = 9\frac{1}{2}$, etc.)*

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5. $6\frac{4}{6} + 4\frac{1}{6}$ → Simplify: $6\frac{2}{3} + 4\frac{1}{6}$

→ Common denominator 6:
$6\frac{4}{6} = \frac{40}{6}, \quad 4\frac{1}{6} = \frac{25}{6}$

→ $\frac{40}{6} + \frac{25}{6} = \frac{65}{6} = 10\frac{5}{6}$

✔ Answer: $10\frac{5}{6}$

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6. $4\frac{1}{8} + 3\frac{5}{8}$

→ $\frac{33}{8} + \frac{29}{8} = \frac{62}{8} = \frac{31}{4} = 7\frac{3}{4}$

✔ Answer: $7\frac{3}{4}$

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7. $5\frac{2}{5} \times 5\frac{4}{5}$

→ Convert: $\frac{27}{5} \times \frac{29}{5} = \frac{783}{25} = 31\frac{8}{25}$

✔ Answer: $31\frac{8}{25}$

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8. $3\frac{4}{5} \times 6\frac{3}{5}$

→ $\frac{19}{5} \times \frac{33}{5} = \frac{627}{25} = 25\frac{2}{25}$

✔ Answer: $25\frac{2}{25}$

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9. $3\frac{3}{4} \times 9\frac{3}{4}$

→ $\frac{15}{4} \times \frac{39}{4} = \frac{585}{16} = 36\frac{9}{16}$

✔ Answer: $36\frac{9}{16}$

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10. $1\frac{6}{8} \times 8\frac{2}{8}$ → Simplify: $1\frac{3}{4} \times 8\frac{1}{4}$

→ $\frac{7}{4} \times \frac{33}{4} = \frac{231}{16} = 14\frac{7}{16}$

✔ Answer: $14\frac{7}{16}$

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11. $2\frac{3}{5} + 7\frac{2}{5}$

→ $\frac{13}{5} + \frac{37}{5} = \frac{50}{5} = 10$

✔ Answer: $10$

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12. $4\frac{1}{3} \times 8\frac{1}{3}$

→ $\frac{13}{3} \times \frac{25}{3} = \frac{325}{9} = 36\frac{1}{9}$

✔ Answer: $36\frac{1}{9}$

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13. $8\frac{1}{3} \times 7\frac{1}{3}$

→ $\frac{25}{3} \times \frac{22}{3} = \frac{550}{9} = 61\frac{1}{9}$

✔ Answer: $61\frac{1}{9}$

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14. $8\frac{1}{8} + 9\frac{1}{8}$

→ $\frac{65}{8} + \frac{73}{8} = \frac{138}{8} = \frac{69}{4} = 17\frac{1}{4}$

✔ Answer: $17\frac{1}{4}$

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15. $9\frac{4}{5} + 3\frac{2}{5}$

→ $\frac{49}{5} + \frac{17}{5} = \frac{66}{5} = 13\frac{1}{5}$

✔ Answer: $13\frac{1}{5}$

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16. $9\frac{1}{4} - 8\frac{3}{4}$

→ $\frac{37}{4} - \frac{35}{4} = \frac{2}{4} = \frac{1}{2}$

✔ Answer: $\frac{1}{2}$

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17. $9\frac{1}{5} - 6\frac{2}{5}$

→ $\frac{46}{5} - \frac{32}{5} = \frac{14}{5} = 2\frac{4}{5}$

✔ Answer: $2\frac{4}{5}$

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18. $1\frac{4}{8} \times 7\frac{6}{8}$ → Simplify: $1\frac{1}{2} \times 7\frac{3}{4}$

→ $\frac{3}{2} \times \frac{31}{4} = \frac{93}{8} = 11\frac{5}{8}$

✔ Answer: $11\frac{5}{8}$

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## 📋 Final Answer Key:

1. $4\frac{4}{5}$
2. $13$
3. $7\frac{2}{3}$
4. $11$
5. $10\frac{5}{6}$
6. $7\frac{3}{4}$
7. $31\frac{8}{25}$
8. $25\frac{2}{25}$
9. $36\frac{9}{16}$
10. $14\frac{7}{16}$
11. $10$
12. $36\frac{1}{9}$
13. $61\frac{1}{9}$
14. $17\frac{1}{4}$
15. $13\frac{1}{5}$
16. $\frac{1}{2}$
17. $2\frac{4}{5}$
18. $11\frac{5}{8}$

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