Addition, Subtraction, Multiplication, and Division of Fractions ... - Free Printable

Sure! Let’s solve each problem step by step, with clear explanations. The worksheet contains 14 problems across five operations: adding mixed numbers, subtracting fractions, subtracting mixed numbers, multiplying fractions, and dividing fractions.

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Add the mixed numbers

22. \( 4\frac{2}{7} + 3\frac{1}{14} \)

✔ Step 1: Convert to improper fractions or add whole parts and fractional parts separately.

Whole numbers: \( 4 + 3 = 7 \)

Fractions: \( \frac{2}{7} + \frac{1}{14} \)

Find common denominator → LCM of 7 and 14 is 14.

\( \frac{2}{7} = \frac{4}{14} \), so \( \frac{4}{14} + \frac{1}{14} = \frac{5}{14} \)

✔ Final answer: \( 7\frac{5}{14} \)

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23. \( 3\frac{3}{8} + 4\frac{1}{8} \)

Whole numbers: \( 3 + 4 = 7 \)

Fractions: \( \frac{3}{8} + \frac{1}{8} = \frac{4}{8} = \frac{1}{2} \)

✔ Final answer: \( 7\frac{1}{2} \)

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Subtract the fractions

24. \( \frac{5}{6} - \frac{1}{3} \)

Common denominator: 6

\( \frac{1}{3} = \frac{2}{6} \)

So, \( \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \)

✔ Final answer: \( \frac{1}{2} \)

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25. \( \frac{7}{9} - \frac{2}{8} \)

Simplify \( \frac{2}{8} = \frac{1}{4} \)

Now find LCD of 9 and 4 → 36

\( \frac{7}{9} = \frac{28}{36} \), \( \frac{1}{4} = \frac{9}{36} \)

\( \frac{28}{36} - \frac{9}{36} = \frac{19}{36} \)

✔ Final answer: \( \frac{19}{36} \)

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26. \( \frac{9}{10} - \frac{2}{5} \)

Common denominator: 10

\( \frac{2}{5} = \frac{4}{10} \)

\( \frac{9}{10} - \frac{4}{10} = \frac{5}{10} = \frac{1}{2} \)

✔ Final answer: \( \frac{1}{2} \)

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Subtract the mixed numbers

27. \( 5\frac{2}{3} - 4\frac{2}{3} \)

Whole numbers: \( 5 - 4 = 1 \)

Fractions: \( \frac{2}{3} - \frac{2}{3} = 0 \)

✔ Final answer: \( 1 \)

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28. \( 8\frac{2}{3} - 5\frac{2}{3} \)

Whole numbers: \( 8 - 5 = 3 \)

Fractions: \( \frac{2}{3} - \frac{2}{3} = 0 \)

✔ Final answer: \( 3 \)

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Multiply the fractions

29. \( \frac{2}{3} \times \frac{1}{8} \)

Multiply numerators: \( 2 \times 1 = 2 \)

Multiply denominators: \( 3 \times 8 = 24 \)

Simplify: \( \frac{2}{24} = \frac{1}{12} \)

✔ Final answer: \( \frac{1}{12} \)

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30. \( \frac{1}{5} \times \frac{10}{13} \)

Multiply: \( \frac{1 \times 10}{5 \times 13} = \frac{10}{65} \)

Simplify: divide numerator and denominator by 5 → \( \frac{2}{13} \)

✔ Final answer: \( \frac{2}{13} \)

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31. \( \frac{3}{4} \times \frac{1}{15} \)

Multiply: \( \frac{3 \times 1}{4 \times 15} = \frac{3}{60} \)

Simplify: divide by 3 → \( \frac{1}{20} \)

✔ Final answer: \( \frac{1}{20} \)

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Divide the fractions

Remember: To divide fractions, multiply by the reciprocal.

32. \( \frac{10}{12} \div \frac{12}{12} \)

Note: \( \frac{12}{12} = 1 \), so any number divided by 1 is itself.

\( \frac{10}{12} \div 1 = \frac{10}{12} = \frac{5}{6} \) (simplified)

✔ Final answer: \( \frac{5}{6} \)

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33. \( \frac{3}{4} \div \frac{1}{16} \)

Multiply by reciprocal: \( \frac{3}{4} \times \frac{16}{1} = \frac{48}{4} = 12 \)

✔ Final answer: \( 12 \)

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34. \( \frac{1}{15} \div \frac{2}{3} \)

Multiply by reciprocal: \( \frac{1}{15} \times \frac{3}{2} = \frac{3}{30} = \frac{1}{10} \)

✔ Final answer: \( \frac{1}{10} \)

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## ✔ Final Answers Summary:

22. \( \boxed{7\frac{5}{14}} \)
23. \( \boxed{7\frac{1}{2}} \)
24. \( \boxed{\frac{1}{2}} \)
25. \( \boxed{\frac{19}{36}} \)
26. \( \boxed{\frac{1}{2}} \)
27. \( \boxed{1} \)
28. \( \boxed{3} \)
29. \( \boxed{\frac{1}{12}} \)
30. \( \boxed{\frac{2}{13}} \)
31. \( \boxed{\frac{1}{20}} \)
32. \( \boxed{\frac{5}{6}} \)
33. \( \boxed{12} \)
34. \( \boxed{\frac{1}{10}} \)

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