Students can practice their arithmetic skills with this structured worksheet covering everything from simple unit fractions to complex mixed numbers.

Let's solve each problem step-by-step, following the instructions: add or subtract fractions, simplify answers, and convert to mixed numbers where possible.

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✔ Section A: Add and Subtract Unit Fractions

These are fractions with numerator 1 (e.g., $ \frac{1}{2}, \frac{1}{3} $). We need to find a common denominator before adding or subtracting.

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#### 1) $ \frac{1}{8} + \frac{1}{2} $

- LCM of 8 and 2 is 8.
- $ \frac{1}{2} = \frac{4}{8} $
- $ \frac{1}{8} + \frac{4}{8} = \frac{5}{8} $

✔ Answer: $ \frac{5}{8} $

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#### 2) $ \frac{1}{20} + \frac{1}{5} $

- LCM of 20 and 5 is 20.
- $ \frac{1}{5} = \frac{4}{20} $
- $ \frac{1}{20} + \frac{4}{20} = \frac{5}{20} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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#### 3) $ \frac{1}{7} - \frac{1}{14} $

- LCM of 7 and 14 is 14.
- $ \frac{1}{7} = \frac{2}{14} $
- $ \frac{2}{14} - \frac{1}{14} = \frac{1}{14} $

✔ Answer: $ \frac{1}{14} $

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#### 4) $ \frac{1}{5} - \frac{1}{15} $

- LCM of 5 and 15 is 15.
- $ \frac{1}{5} = \frac{3}{15} $
- $ \frac{3}{15} - \frac{1}{15} = \frac{2}{15} $

✔ Answer: $ \frac{2}{15} $

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#### 5) $ \frac{1}{40} + \frac{1}{2} $

- LCM of 40 and 2 is 40.
- $ \frac{1}{2} = \frac{20}{40} $
- $ \frac{1}{40} + \frac{20}{40} = \frac{21}{40} $

✔ Answer: $ \frac{21}{40} $

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#### 6) $ \frac{1}{2} - \frac{1}{3} $

- LCM of 2 and 3 is 6.
- $ \frac{1}{2} = \frac{3}{6}, \frac{1}{3} = \frac{2}{6} $
- $ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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#### 7) $ \frac{1}{5} + \frac{1}{4} $

- LCM of 5 and 4 is 20.
- $ \frac{1}{5} = \frac{4}{20}, \frac{1}{4} = \frac{5}{20} $
- $ \frac{4}{20} + \frac{5}{20} = \frac{9}{20} $

✔ Answer: $ \frac{9}{20} $

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#### 8) $ \frac{1}{7} - \frac{1}{11} $

- LCM of 7 and 11 is 77.
- $ \frac{1}{7} = \frac{11}{77}, \frac{1}{11} = \frac{7}{77} $
- $ \frac{11}{77} - \frac{7}{77} = \frac{4}{77} $

✔ Answer: $ \frac{4}{77} $

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#### 9) $ \frac{1}{15} + \frac{1}{2} $

- LCM of 15 and 2 is 30.
- $ \frac{1}{15} = \frac{2}{30}, \frac{1}{2} = \frac{15}{30} $
- $ \frac{2}{30} + \frac{15}{30} = \frac{17}{30} $

✔ Answer: $ \frac{17}{30} $

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#### 10) $ \frac{1}{12} + \frac{1}{5} $

- LCM of 12 and 5 is 60.
- $ \frac{1}{12} = \frac{5}{60}, \frac{1}{5} = \frac{12}{60} $
- $ \frac{5}{60} + \frac{12}{60} = \frac{17}{60} $

✔ Answer: $ \frac{17}{60} $

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#### 11) $ \frac{1}{5} + \frac{1}{8} $

- LCM of 5 and 8 is 40.
- $ \frac{1}{5} = \frac{8}{40}, \frac{1}{8} = \frac{5}{40} $
- $ \frac{8}{40} + \frac{5}{40} = \frac{13}{40} $

✔ Answer: $ \frac{13}{40} $

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#### 12) $ \frac{1}{9} - \frac{1}{10} $

- LCM of 9 and 10 is 90.
- $ \frac{1}{9} = \frac{10}{90}, \frac{1}{10} = \frac{9}{90} $
- $ \frac{10}{90} - \frac{9}{90} = \frac{1}{90} $

✔ Answer: $ \frac{1}{90} $

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✔ Section B: Add and Subtract Non-Unit Fractions

Now we have numerators other than 1.

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#### 1) $ \frac{1}{15} + \frac{2}{5} $

- $ \frac{2}{5} = \frac{6}{15} $
- $ \frac{1}{15} + \frac{6}{15} = \frac{7}{15} $

✔ Answer: $ \frac{7}{15} $

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#### 2) $ \frac{2}{3} - \frac{1}{21} $

- LCM of 3 and 21 is 21.
- $ \frac{2}{3} = \frac{14}{21} $
- $ \frac{14}{21} - \frac{1}{21} = \frac{13}{21} $

✔ Answer: $ \frac{13}{21} $

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#### 3) $ \frac{1}{4} + \frac{5}{12} $

- LCM of 4 and 12 is 12.
- $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{3}{12} + \frac{5}{12} = \frac{8}{12} = \frac{2}{3} $

✔ Answer: $ \frac{2}{3} $

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#### 4) $ \frac{1}{2} - \frac{7}{16} $

- LCM of 2 and 16 is 16.
- $ \frac{1}{2} = \frac{8}{16} $
- $ \frac{8}{16} - \frac{7}{16} = \frac{1}{16} $

✔ Answer: $ \frac{1}{16} $

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#### 5) $ \frac{3}{5} + \frac{1}{2} $

- LCM of 5 and 2 is 10.
- $ \frac{3}{5} = \frac{6}{10}, \frac{1}{2} = \frac{5}{10} $
- $ \frac{6}{10} + \frac{5}{10} = \frac{11}{10} = 1\frac{1}{10} $

✔ Answer: $ 1\frac{1}{10} $

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#### 6) $ \frac{1}{6} + \frac{9}{10} $

- LCM of 6 and 10 is 30.
- $ \frac{1}{6} = \frac{5}{30}, \frac{9}{10} = \frac{27}{30} $
- $ \frac{5}{30} + \frac{27}{30} = \frac{32}{30} = \frac{16}{15} = 1\frac{1}{15} $

✔ Answer: $ 1\frac{1}{15} $

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#### 7) $ \frac{3}{7} - \frac{2}{5} $

- LCM of 7 and 5 is 35.
- $ \frac{3}{7} = \frac{15}{35}, \frac{2}{5} = \frac{14}{35} $
- $ \frac{15}{35} - \frac{14}{35} = \frac{1}{35} $

✔ Answer: $ \frac{1}{35} $

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#### 8) $ \frac{7}{11} + \frac{2}{3} $

- LCM of 11 and 3 is 33.
- $ \frac{7}{11} = \frac{21}{33}, \frac{2}{3} = \frac{22}{33} $
- $ \frac{21}{33} + \frac{22}{33} = \frac{43}{33} = 1\frac{10}{33} $

✔ Answer: $ 1\frac{10}{33} $

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#### 9) $ \frac{4}{5} - \frac{5}{8} $

- LCM of 5 and 8 is 40.
- $ \frac{4}{5} = \frac{32}{40}, \frac{5}{8} = \frac{25}{40} $
- $ \frac{32}{40} - \frac{25}{40} = \frac{7}{40} $

✔ Answer: $ \frac{7}{40} $

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#### 10) $ \frac{3}{10} + \frac{6}{7} $

- LCM of 10 and 7 is 70.
- $ \frac{3}{10} = \frac{21}{70}, \frac{6}{7} = \frac{60}{70} $
- $ \frac{21}{70} + \frac{60}{70} = \frac{81}{70} = 1\frac{11}{70} $

✔ Answer: $ 1\frac{11}{70} $

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#### 11) $ \frac{7}{9} + \frac{3}{8} $

- LCM of 9 and 8 is 72.
- $ \frac{7}{9} = \frac{56}{72}, \frac{3}{8} = \frac{27}{72} $
- $ \frac{56}{72} + \frac{27}{72} = \frac{83}{72} = 1\frac{11}{72} $

✔ Answer: $ 1\frac{11}{72} $

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#### 12) $ \frac{3}{4} - \frac{6}{15} $

- Simplify $ \frac{6}{15} = \frac{2}{5} $
- Now: $ \frac{3}{4} - \frac{2}{5} $
- LCM of 4 and 5 is 20.
- $ \frac{3}{4} = \frac{15}{20}, \frac{2}{5} = \frac{8}{20} $
- $ \frac{15}{20} - \frac{8}{20} = \frac{7}{20} $

✔ Answer: $ \frac{7}{20} $

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✔ Section C: Add and Subtract Mixed Numbers and Improper Fractions

We'll convert mixed numbers to improper fractions when needed, then simplify.

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#### 1) $ 3 + \frac{56}{9} $

- Convert 3 to ninths: $ 3 = \frac{27}{9} $
- $ \frac{27}{9} + \frac{56}{9} = \frac{83}{9} $
- $ \frac{83}{9} = 9\frac{2}{9} $ (since $ 9 \times 9 = 81 $, remainder 2)

✔ Answer: $ 9\frac{2}{9} $

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#### 2) $ 7\frac{2}{3} + 5 $

- $ 7\frac{2}{3} = \frac{23}{3} $
- $ 5 = \frac{15}{3} $
- $ \frac{23}{3} + \frac{15}{3} = \frac{38}{3} = 12\frac{2}{3} $

✔ Answer: $ 12\frac{2}{3} $

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#### 3) $ 1\frac{1}{3} + 2\frac{1}{5} $

- Convert to improper:
- $ 1\frac{1}{3} = \frac{4}{3} $
- $ 2\frac{1}{5} = \frac{11}{5} $
- LCM of 3 and 5 is 15.
- $ \frac{4}{3} = \frac{20}{15}, \frac{11}{5} = \frac{33}{15} $
- $ \frac{20}{15} + \frac{33}{15} = \frac{53}{15} = 3\frac{8}{15} $

✔ Answer: $ 3\frac{8}{15} $

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

- $ 2\frac{1}{4} = \frac{9}{4}, 3\frac{1}{2} = \frac{7}{2} $
- LCM of 4 and 2 is 4.
- $ \frac{7}{2} = \frac{14}{4} $
- $ \frac{9}{4} + \frac{14}{4} = \frac{23}{4} = 5\frac{3}{4} $

✔ Answer: $ 5\frac{3}{4} $

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#### 5) $ 8\frac{1}{3} + 4\frac{2}{5} $

- $ 8\frac{1}{3} = \frac{25}{3}, 4\frac{2}{5} = \frac{22}{5} $
- LCM of 3 and 5 is 15.
- $ \frac{25}{3} = \frac{125}{15}, \frac{22}{5} = \frac{66}{15} $
- $ \frac{125}{15} + \frac{66}{15} = \frac{191}{15} = 12\frac{11}{15} $

✔ Answer: $ 12\frac{11}{15} $

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#### 6) $ 5\frac{8}{11} + 3\frac{7}{9} $

- $ 5\frac{8}{11} = \frac{63}{11}, 3\frac{7}{9} = \frac{34}{9} $
- LCM of 11 and 9 is 99.
- $ \frac{63}{11} = \frac{567}{99}, \frac{34}{9} = \frac{374}{99} $
- $ \frac{567}{99} + \frac{374}{99} = \frac{941}{99} $
- Divide: $ 99 \times 9 = 891 $, remainder $ 50 $
- So $ \frac{941}{99} = 9\frac{50}{99} $

✔ Answer: $ 9\frac{50}{99} $

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#### 7) $ \frac{17}{8} - 1 $

- $ 1 = \frac{8}{8} $
- $ \frac{17}{8} - \frac{8}{8} = \frac{9}{8} = 1\frac{1}{8} $

✔ Answer: $ 1\frac{1}{8} $

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#### 8) $ \frac{21}{9} - 2 $

- Simplify $ \frac{21}{9} = \frac{7}{3} $
- $ 2 = \frac{6}{3} $
- $ \frac{7}{3} - \frac{6}{3} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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#### 9) $ 5 - 2\frac{3}{5} $

- $ 2\frac{3}{5} = \frac{13}{5} $
- $ 5 = \frac{25}{5} $
- $ \frac{25}{5} - \frac{13}{5} = \frac{12}{5} = 2\frac{2}{5} $

✔ Answer: $ 2\frac{2}{5} $

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#### 10) $ 3\frac{1}{10} - 1\frac{2}{3} $

- $ 3\frac{1}{10} = \frac{31}{10}, 1\frac{2}{3} = \frac{5}{3} $
- LCM of 10 and 3 is 30.
- $ \frac{31}{10} = \frac{93}{30}, \frac{5}{3} = \frac{50}{30} $
- $ \frac{93}{30} - \frac{50}{30} = \frac{43}{30} = 1\frac{13}{30} $

✔ Answer: $ 1\frac{13}{30} $

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#### 11) $ 9\frac{5}{8} - 4\frac{6}{7} $

- $ 9\frac{5}{8} = \frac{77}{8}, 4\frac{6}{7} = \frac{34}{7} $
- LCM of 8 and 7 is 56.
- $ \frac{77}{8} = \frac{539}{56}, \frac{34}{7} = \frac{272}{56} $
- $ \frac{539}{56} - \frac{272}{56} = \frac{267}{56} $
- $ 56 \times 4 = 224 $, remainder $ 43 $
- So $ \frac{267}{56} = 4\frac{43}{56} $

✔ Answer: $ 4\frac{43}{56} $

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#### 12) $ 4\frac{2}{11} - 2\frac{8}{9} $

- $ 4\frac{2}{11} = \frac{46}{11}, 2\frac{8}{9} = \frac{26}{9} $
- LCM of 11 and 9 is 99.
- $ \frac{46}{11} = \frac{414}{99}, \frac{26}{9} = \frac{286}{99} $
- $ \frac{414}{99} - \frac{286}{99} = \frac{128}{99} $
- $ 99 \times 1 = 99 $, remainder $ 29 $
- So $ \frac{128}{99} = 1\frac{29}{99} $

✔ Answer: $ 1\frac{29}{99} $

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## ✔ Final Answers Summary

Section A

1. $ \frac{5}{8} $
2. $ \frac{1}{4} $
3. $ \frac{1}{14} $
4. $ \frac{2}{15} $
5. $ \frac{21}{40} $
6. $ \frac{1}{6} $
7. $ \frac{9}{20} $
8. $ \frac{4}{77} $
9. $ \frac{17}{30} $
10. $ \frac{17}{60} $
11. $ \frac{13}{40} $
12. $ \frac{1}{90} $

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Section B

1. $ \frac{7}{15} $
2. $ \frac{13}{21} $
3. $ \frac{2}{3} $
4. $ \frac{1}{16} $
5. $ 1\frac{1}{10} $
6. $ 1\frac{1}{15} $
7. $ \frac{1}{35} $
8. $ 1\frac{10}{33} $
9. $ \frac{7}{40} $
10. $ 1\frac{11}{70} $
11. $ 1\frac{11}{72} $
12. $ \frac{7}{20} $

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Section C

1. $ 9\frac{2}{9} $
2. $ 12\frac{2}{3} $
3. $ 3\frac{8}{15} $
4. $ 5\frac{3}{4} $
5. $ 12\frac{11}{15} $
6. $ 9\frac{50}{99} $
7. $ 1\frac{1}{8} $
8. $ \frac{1}{3} $
9. $ 2\frac{2}{5} $
10. $ 1\frac{13}{30} $
11. $ 4\frac{43}{56} $
12. $ 1\frac{29}{99} $

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