Math worksheet for practicing fraction operations including addition, subtraction, multiplication, and division.

Let's solve each problem step by step from the worksheet. We'll go through addition, subtraction, multiplication, and division of fractions and mixed numbers.

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Add the mixed numbers:

#### 22. $ 4 \frac{1}{9} + 3 \frac{5}{12} $

Step 1: Convert to improper fractions.

- $ 4 \frac{1}{9} = \frac{4 \times 9 + 1}{9} = \frac{36 + 1}{9} = \frac{37}{9} $
- $ 3 \frac{5}{12} = \frac{3 \times 12 + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12} $

Step 2: Find a common denominator. LCM of 9 and 12 is 36.

- $ \frac{37}{9} = \frac{37 \times 4}{36} = \frac{148}{36} $
- $ \frac{41}{12} = \frac{41 \times 3}{36} = \frac{123}{36} $

Step 3: Add:

- $ \frac{148}{36} + \frac{123}{36} = \frac{271}{36} $

Step 4: Convert to mixed number:

- $ 271 \div 36 = 7 $ remainder $ 19 $ → $ 7 \frac{19}{36} $

✔ Answer: $ 7 \frac{19}{36} $

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#### 23. $ 3 \frac{2}{3} + 4 \frac{1}{8} $

Convert to improper fractions:

- $ 3 \frac{2}{3} = \frac{11}{3} $
- $ 4 \frac{1}{8} = \frac{33}{8} $

LCM of 3 and 8 is 24.

- $ \frac{11}{3} = \frac{88}{24} $
- $ \frac{33}{8} = \frac{99}{24} $

Add: $ \frac{88 + 99}{24} = \frac{187}{24} $

Convert: $ 187 \div 24 = 7 $ remainder $ 19 $ → $ 7 \frac{19}{24} $

✔ Answer: $ 7 \frac{19}{24} $

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Subtract the fractions:

#### 24. $ \frac{5}{6} - \frac{1}{3} $

Common denominator: 6

- $ \frac{1}{3} = \frac{2}{6} $
- $ \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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#### 25. $ \frac{7}{9} - \frac{5}{8} $

LCM of 9 and 8 is 72.

- $ \frac{7}{9} = \frac{56}{72} $
- $ \frac{5}{8} = \frac{45}{72} $
- $ \frac{56 - 45}{72} = \frac{11}{72} $

✔ Answer: $ \frac{11}{72} $

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#### 26. $ \frac{11}{10} - \frac{3}{5} $

Convert $ \frac{3}{5} = \frac{6}{10} $

- $ \frac{11}{10} - \frac{6}{10} = \frac{5}{10} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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Subtract the mixed numbers:

#### 27. $ 5 \frac{2}{3} - 4 \frac{1}{2} $

Convert:

- $ 5 \frac{2}{3} = \frac{17}{3} $
- $ 4 \frac{1}{2} = \frac{9}{2} $

LCM of 3 and 2 is 6.

- $ \frac{17}{3} = \frac{34}{6} $
- $ \frac{9}{2} = \frac{27}{6} $
- $ \frac{34 - 27}{6} = \frac{7}{6} = 1 \frac{1}{6} $

✔ Answer: $ 1 \frac{1}{6} $

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#### 28. $ 8 \frac{1}{6} - 5 \frac{3}{4} $

Convert:

- $ 8 \frac{1}{6} = \frac{49}{6} $
- $ 5 \frac{3}{4} = \frac{23}{4} $

LCM of 6 and 4 is 12.

- $ \frac{49}{6} = \frac{98}{12} $
- $ \frac{23}{4} = \frac{69}{12} $
- $ \frac{98 - 69}{12} = \frac{29}{12} = 2 \frac{5}{12} $

✔ Answer: $ 2 \frac{5}{12} $

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Multiply the fractions:

#### 29. $ \frac{2}{3} \times \frac{1}{2} $

Multiply numerators and denominators:

- $ \frac{2 \times 1}{3 \times 2} = \frac{2}{6} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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#### 30. $ \frac{1}{5} \times \frac{10}{13} $

- $ \frac{1 \times 10}{5 \times 13} = \frac{10}{65} = \frac{2}{13} $ (simplify by dividing numerator and denominator by 5)

✔ Answer: $ \frac{2}{13} $

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#### 31. $ \frac{4}{7} \times 1 \frac{1}{6} $

First, convert mixed number:

- $ 1 \frac{1}{6} = \frac{7}{6} $

Now multiply:

- $ \frac{4}{7} \times \frac{7}{6} = \frac{4 \times 7}{7 \times 6} = \frac{28}{42} = \frac{2}{3} $ (divide numerator and denominator by 14)

✔ Answer: $ \frac{2}{3} $

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Divide the fractions:

#### 32. $ 1 \frac{1}{4} \div \frac{10}{12} $

Convert $ 1 \frac{1}{4} = \frac{5}{4} $

$ \frac{10}{12} = \frac{5}{6} $ (simplified)

So: $ \frac{5}{4} \div \frac{5}{6} = \frac{5}{4} \times \frac{6}{5} = \frac{30}{20} = \frac{3}{2} = 1 \frac{1}{2} $

✔ Answer: $ 1 \frac{1}{2} $

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#### 33. $ \frac{3}{4} \div \frac{1}{8} $

Invert and multiply:

- $ \frac{3}{4} \times \frac{8}{1} = \frac{24}{4} = 6 $

✔ Answer: $ 6 $

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#### 34. $ \frac{1}{15} \div \frac{2}{5} $

Invert and multiply:

- $ \frac{1}{15} \times \frac{5}{2} = \frac{5}{30} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 22. | $ 7 \frac{19}{36} $ |
| 23. | $ 7 \frac{19}{24} $ |
| 24. | $ \frac{1}{2} $ |
| 25. | $ \frac{11}{72} $ |
| 26. | $ \frac{1}{2} $ |
| 27. | $ 1 \frac{1}{6} $ |
| 28. | $ 2 \frac{5}{12} $ |
| 29. | $ \frac{1}{3} $ |
| 30. | $ \frac{2}{13} $ |
| 31. | $ \frac{2}{3} $ |
| 32. | $ 1 \frac{1}{2} $ |
| 33. | $ 6 $ |
| 34. | $ \frac{1}{6} $ |

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