This worksheet provides essential practice with evaluating numerical expressions that combine fractions and whole numbers using proper order of operations.

Sure! Let’s evaluate each of the 10 numerical expressions step by step, following the order of operations (PEMDAS/BODMAS):
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right).

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1) \( 8 - \frac{3}{2} \times 4 + \frac{1}{3} \)

- First, multiplication: \( \frac{3}{2} \times 4 = \frac{12}{2} = 6 \)
- Now expression becomes: \( 8 - 6 + \frac{1}{3} \)
- Left to right: \( 8 - 6 = 2 \), then \( 2 + \frac{1}{3} = \frac{7}{3} \)

✔ Answer: \( \frac{7}{3} \) or \( 2\frac{1}{3} \)

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2) \( 5 + \frac{5}{8} \div 21 \)

- Division first: \( \frac{5}{8} \div 21 = \frac{5}{8} \times \frac{1}{21} = \frac{5}{168} \)
- Now add: \( 5 + \frac{5}{168} = \frac{840}{168} + \frac{5}{168} = \frac{845}{168} \)

✔ Answer: \( \frac{845}{168} \) (can be simplified? GCD of 845 and 168 is 1 → already simplified)

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3) \( \frac{1}{4} \times 9 \times \frac{2}{3} \)

- Multiply left to right: \( \frac{1}{4} \times 9 = \frac{9}{4} \)
- Then \( \frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2} \)

✔ Answer: \( \frac{3}{2} \) or \( 1\frac{1}{2} \)

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4) \( 8 \times 5 - \frac{9}{2} \times \frac{3}{4} \)

- Multiplication first:
- \( 8 \times 5 = 40 \)
- \( \frac{9}{2} \times \frac{3}{4} = \frac{27}{8} \)
- Now subtract: \( 40 - \frac{27}{8} = \frac{320}{8} - \frac{27}{8} = \frac{293}{8} \)

✔ Answer: \( \frac{293}{8} \) or \( 36\frac{5}{8} \)

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5) \( 64 \div 6 - \frac{7}{9} \times \frac{3}{7} \)

- Division and multiplication first:
- \( 64 \div 6 = \frac{64}{6} = \frac{32}{3} \)
- \( \frac{7}{9} \times \frac{3}{7} = \frac{21}{63} = \frac{1}{3} \) (simplify by canceling 7 and 3)
- Now subtract: \( \frac{32}{3} - \frac{1}{3} = \frac{31}{3} \)

✔ Answer: \( \frac{31}{3} \) or \( 10\frac{1}{3} \)

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6) \( 4 \times \frac{1}{7} \div 5 \)

- Left to right: multiplication then division
- \( 4 \times \frac{1}{7} = \frac{4}{7} \)
- \( \frac{4}{7} \div 5 = \frac{4}{7} \times \frac{1}{5} = \frac{4}{35} \)

✔ Answer: \( \frac{4}{35} \)

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7) \( \frac{5}{6} \times 18 - \frac{4}{3} \)

- First, multiplication: \( \frac{5}{6} \times 18 = \frac{90}{6} = 15 \)
- Then subtract: \( 15 - \frac{4}{3} = \frac{45}{3} - \frac{4}{3} = \frac{41}{3} \)

✔ Answer: \( \frac{41}{3} \) or \( 13\frac{2}{3} \)

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8) \( 2 - \frac{4}{9} \times \frac{3}{8} + 1 \)

- Multiplication first: \( \frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6} \)
- Now expression: \( 2 - \frac{1}{6} + 1 \)
- Left to right: \( 2 - \frac{1}{6} = \frac{12}{6} - \frac{1}{6} = \frac{11}{6} \)
- Then \( \frac{11}{6} + 1 = \frac{11}{6} + \frac{6}{6} = \frac{17}{6} \)

✔ Answer: \( \frac{17}{6} \) or \( 2\frac{5}{6} \)

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9) \( 82 - 9 \times \frac{7}{6} + \frac{5}{2} \)

- Multiplication first: \( 9 \times \frac{7}{6} = \frac{63}{6} = \frac{21}{2} \)
- Expression becomes: \( 82 - \frac{21}{2} + \frac{5}{2} \)
- Combine fractions: \( -\frac{21}{2} + \frac{5}{2} = -\frac{16}{2} = -8 \)
- Now: \( 82 - 8 = 74 \)

✔ Answer: \( 74 \)

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10) \( 1 + 4 \times \frac{9}{8} \)

- Multiplication first: \( 4 \times \frac{9}{8} = \frac{36}{8} = \frac{9}{2} \)
- Add: \( 1 + \frac{9}{2} = \frac{2}{2} + \frac{9}{2} = \frac{11}{2} \)

✔ Answer: \( \frac{11}{2} \) or \( 5\frac{1}{2} \)

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## ✔ Final Answers:

1. \( \frac{7}{3} \)
2. \( \frac{845}{168} \)
3. \( \frac{3}{2} \)
4. \( \frac{293}{8} \)
5. \( \frac{31}{3} \)
6. \( \frac{4}{35} \)
7. \( \frac{41}{3} \)
8. \( \frac{17}{6} \)
9. \( 74 \)
10. \( \frac{11}{2} \)

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