Math worksheet for practicing order of operations with fractions.

Let's solve each expression step by step using the order of operations (PEMDAS):
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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1. $ \frac{3}{4} + \frac{1}{4} + \left(\frac{1}{3}\right)^2 $

- First, evaluate the exponent:
$ \left(\frac{1}{3}\right)^2 = \frac{1}{9} $
- Now add:
$ \frac{3}{4} + \frac{1}{4} = 1 $
Then: $ 1 + \frac{1}{9} = \frac{9}{9} + \frac{1}{9} = \frac{10}{9} $

✔ Answer: $ \frac{10}{9} $

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2. $ \left(\frac{5}{6}\right)^2 + \left(\frac{5}{6} - \frac{4}{5}\right) $

- Evaluate exponent:
$ \left(\frac{5}{6}\right)^2 = \frac{25}{36} $
- Simplify inside parentheses:
$ \frac{5}{6} - \frac{4}{5} $ → common denominator is 30
$ \frac{25}{30} - \frac{24}{30} = \frac{1}{30} $
- Now add:
$ \frac{25}{36} + \frac{1}{30} $ → LCD of 36 and 30 is 180
$ \frac{25}{36} = \frac{125}{180},\quad \frac{1}{30} = \frac{6}{180} $
$ \frac{125}{180} + \frac{6}{180} = \frac{131}{180} $

✔ Answer: $ \frac{131}{180} $

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3. $ \frac{1}{9} \times \frac{5}{6} + \left(\frac{1}{2}\right)^3 $

- Multiply: $ \frac{1}{9} \times \frac{5}{6} = \frac{5}{54} $
- Exponent: $ \left(\frac{1}{2}\right)^3 = \frac{1}{8} $
- Add: $ \frac{5}{54} + \frac{1}{8} $ → LCD of 54 and 8 is 216
$ \frac{5}{54} = \frac{20}{216},\quad \frac{1}{8} = \frac{27}{216} $
$ \frac{20}{216} + \frac{27}{216} = \frac{47}{216} $

✔ Answer: $ \frac{47}{216} $

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4. $ \frac{7}{8} \div \left( \frac{2}{3} - \left(\frac{1}{3}\right)^2 \right) $

- First, exponent: $ \left(\frac{1}{3}\right)^2 = \frac{1}{9} $
- Subtract inside parentheses:
$ \frac{2}{3} - \frac{1}{9} = \frac{6}{9} - \frac{1}{9} = \frac{5}{9} $
- Now divide: $ \frac{7}{8} \div \frac{5}{9} = \frac{7}{8} \times \frac{9}{5} = \frac{63}{40} $

✔ Answer: $ \frac{63}{40} $

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5. $ \left(\frac{2}{5} + \frac{2}{3}\right) \times \left(\frac{1}{9}\right)^2 $

- Add inside parentheses:
$ \frac{2}{5} + \frac{2}{3} $ → LCD = 15
$ \frac{6}{15} + \frac{10}{15} = \frac{16}{15} $
- Exponent: $ \left(\frac{1}{9}\right)^2 = \frac{1}{81} $
- Multiply: $ \frac{16}{15} \times \frac{1}{81} = \frac{16}{1215} $

✔ Answer: $ \frac{16}{1215} $

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6. $ \left(\frac{5}{6} - \left(\frac{1}{3}\right)^2\right) \times \frac{1}{2} $

- Exponent: $ \left(\frac{1}{3}\right)^2 = \frac{1}{9} $
- Subtract: $ \frac{5}{6} - \frac{1}{9} $ → LCD = 18
$ \frac{15}{18} - \frac{2}{18} = \frac{13}{18} $
- Multiply: $ \frac{13}{18} \times \frac{1}{2} = \frac{13}{36} $

✔ Answer: $ \frac{13}{36} $

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7. $ \frac{3}{4} - \frac{1}{6} \div \left(\frac{4}{5}\right)^2 $

- Exponent: $ \left(\frac{4}{5}\right)^2 = \frac{16}{25} $
- Division: $ \frac{1}{6} \div \frac{16}{25} = \frac{1}{6} \times \frac{25}{16} = \frac{25}{96} $
- Now subtract: $ \frac{3}{4} - \frac{25}{96} $ → LCD = 96
$ \frac{3}{4} = \frac{72}{96} $
$ \frac{72}{96} - \frac{25}{96} = \frac{47}{96} $

✔ Answer: $ \frac{47}{96} $

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8. $ \left(\frac{1}{3}\right)^2 \div \frac{4}{9} + \frac{1}{6} $

- Exponent: $ \left(\frac{1}{3}\right)^2 = \frac{1}{9} $
- Divide: $ \frac{1}{9} \div \frac{4}{9} = \frac{1}{9} \times \frac{9}{4} = \frac{1}{4} $
- Add: $ \frac{1}{4} + \frac{1}{6} $ → LCD = 12
$ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $

✔ Answer: $ \frac{5}{12} $

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9. $ \left(\frac{3}{4}\right)^2 \times \frac{2}{5} + \frac{1}{2} $

- Exponent: $ \left(\frac{3}{4}\right)^2 = \frac{9}{16} $
- Multiply: $ \frac{9}{16} \times \frac{2}{5} = \frac{18}{80} = \frac{9}{40} $
- Add: $ \frac{9}{40} + \frac{1}{2} = \frac{9}{40} + \frac{20}{40} = \frac{29}{40} $

✔ Answer: $ \frac{29}{40} $

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✔ Final Answers:

1. $ \frac{10}{9} $
2. $ \frac{131}{180} $
3. $ \frac{47}{216} $
4. $ \frac{63}{40} $
5. $ \frac{16}{1215} $
6. $ \frac{13}{36} $
7. $ \frac{47}{96} $
8. $ \frac{5}{12} $
9. $ \frac{29}{40} $

Let me know if you'd like these as mixed numbers or decimals!