Evaluating Numerical Expressions | Fractions worksheet with ten problems to solve.

Let's evaluate each of the numerical expressions involving fractions step by step. We'll follow 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) $ 8 - \frac{3}{4} \times 4 + \frac{1}{3} $

Step 1: Multiply first:
$ \frac{3}{4} \times 4 = 3 $

Now substitute:
$ 8 - 3 + \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} $

✔ Answer: $ \frac{16}{3} $ or $ 5\frac{1}{3} $

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2) $ 5 + \frac{5}{8} + 21 $

Add whole numbers:
$ 5 + 21 = 26 $

Then add fraction:
$ 26 + \frac{5}{8} = 26\frac{5}{8} $

✔ Answer: $ 26\frac{5}{8} $

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3) $ \frac{1}{4} + 9 \times \frac{2}{3} $

Step 1: Multiply:
$ 9 \times \frac{2}{3} = \frac{18}{3} = 6 $

Now add:
$ \frac{1}{4} + 6 = 6\frac{1}{4} $

✔ Answer: $ 6\frac{1}{4} $

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

Step 1: Multiply:
$ 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} $

Convert to mixed number:
$ \frac{293}{8} = 36\frac{5}{8} $

✔ Answer: $ 36\frac{5}{8} $

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5) $ 64 + 6 - \frac{7}{9} \times \frac{3}{7} $

Step 1: Multiply:
$ \frac{7}{9} \times \frac{3}{7} = \frac{21}{63} = \frac{1}{3} $

Now simplify:
$ 64 + 6 = 70 $
$ 70 - \frac{1}{3} = 69\frac{2}{3} $

✔ Answer: $ 69\frac{2}{3} $

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6) $ 4 \times \frac{1}{2} + 5 $

Step 1: Multiply:
$ 4 \times \frac{1}{2} = 2 $

Now add:
$ 2 + 5 = 7 $

✔ Answer: $ 7 $

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

Step 1: Multiply:
$ \frac{5}{6} \times 18 = \frac{5 \times 18}{6} = \frac{90}{6} = 15 $

Now subtract:
$ 15 - \frac{4}{3} = \frac{45}{3} - \frac{4}{3} = \frac{41}{3} $

Convert to mixed number:
$ \frac{41}{3} = 13\frac{2}{3} $

✔ Answer: $ 13\frac{2}{3} $

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

Step 1: Multiply:
$ \frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6} $

Now compute:
$ 2 - \frac{1}{6} + 1 = (2 + 1) - \frac{1}{6} = 3 - \frac{1}{6} = 2\frac{5}{6} $

✔ Answer: $ 2\frac{5}{6} $

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

Step 1: Multiply:
$ 9 \times \frac{7}{6} = \frac{63}{6} = 10.5 $ or $ \frac{21}{2} $

Now:
$ 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} $

Step 1: Multiply:
$ 4 \times \frac{9}{8} = \frac{36}{8} = \frac{9}{2} = 4.5 $

Now add:
$ 1 + \frac{9}{2} = \frac{2}{2} + \frac{9}{2} = \frac{11}{2} = 5\frac{1}{2} $

✔ Answer: $ 5\frac{1}{2} $

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✔ Final Answers:

1) $ \frac{16}{3} $ or $ 5\frac{1}{3} $
2) $ 26\frac{5}{8} $
3) $ 6\frac{1}{4} $
4) $ 36\frac{5}{8} $
5) $ 69\frac{2}{3} $
6) $ 7 $
7) $ 13\frac{2}{3} $
8) $ 2\frac{5}{6} $
9) $ 74 $
10) $ 5\frac{1}{2} $

Let me know if you'd like these shown as improper fractions or decimals!