301 Moved Permanently - Free Printable

Let's solve each of the 10 multiple-choice questions step by step, evaluating expressions involving rational numbers (fractions). We'll simplify each expression carefully and select the correct answer.

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1) $ 6 - \frac{2}{5} - \frac{7}{6} $

We need to subtract the fractions from 6. First, convert 6 into a fraction with a common denominator.

The least common denominator (LCD) of 5 and 6 is 30.

Convert all terms:
- $ 6 = \frac{180}{30} $
- $ \frac{2}{5} = \frac{12}{30} $
- $ \frac{7}{6} = \frac{35}{30} $

Now compute:
$$
\frac{180}{30} - \frac{12}{30} - \frac{35}{30} = \frac{180 - 12 - 35}{30} = \frac{133}{30}
$$

✔ Answer: A) $ \frac{133}{30} $

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2) $ \frac{3}{2} \times 2 \times \frac{1}{2} $

Multiply step-by-step:
$$
\frac{3}{2} \times 2 = 3 \\
3 \times \frac{1}{2} = \frac{3}{2}
$$

✔ Answer: D) $ \frac{3}{2} $

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3) $ 6 \times 2 \div \frac{3}{5} $

First, do multiplication and division left to right:
- $ 6 \times 2 = 12 $
- Now divide: $ 12 \div \frac{3}{5} = 12 \times \frac{5}{3} = \frac{60}{3} = 20 $

✔ Answer: B) 20

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

First add inside parentheses:
- $ 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} $

Now multiply:
- $ \frac{8}{3} \times \frac{1}{5} = \frac{8}{15} $

✔ Answer: D) $ \frac{8}{15} $

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5) $ 2 \times \frac{9}{5} \times \frac{1}{5} $

Multiply all together:
- $ 2 \times \frac{9}{5} = \frac{18}{5} $
- $ \frac{18}{5} \times \frac{1}{5} = \frac{18}{25} $

✔ Answer: A) $ \frac{18}{25} $

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

First simplify inside the parentheses:
- $ \frac{5}{3} - 1 = \frac{5}{3} - \frac{3}{3} = \frac{2}{3} $

Now multiply:
- $ 2 \times \frac{2}{3} = \frac{4}{3} $

✔ Answer: D) $ \frac{4}{3} $

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7) $ \frac{3}{2}\left(1 - \frac{1}{2}\right) $

Simplify inside parentheses:
- $ 1 - \frac{1}{2} = \frac{1}{2} $

Now multiply:
- $ \frac{3}{2} \times \frac{1}{2} = \frac{3}{4} $

✔ Answer: C) $ \frac{3}{4} $

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8) $ \frac{5}{3} \div \left(\frac{1}{2} + \frac{1}{2}\right) $

Simplify inside parentheses:
- $ \frac{1}{2} + \frac{1}{2} = 1 $

Now divide:
- $ \frac{5}{3} \div 1 = \frac{5}{3} $

✔ Answer: B) $ \frac{5}{3} $

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

First add inside parentheses:
- LCD of 4 and 2 is 4
- $ \frac{1}{4} + \frac{6}{4} = \frac{7}{4} $

Now divide by 2:
- $ \frac{7}{4} \div 2 = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} $

✔ Answer: C) $ \frac{7}{8} $

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10) $ \left(6 \times \frac{4}{5}\right) \div \frac{5}{6} $

First compute inside parentheses:
- $ 6 \times \frac{4}{5} = \frac{24}{5} $

Now divide:
- $ \frac{24}{5} \div \frac{5}{6} = \frac{24}{5} \times \frac{6}{5} = \frac{144}{25} $

✔ Answer: C) $ \frac{144}{25} $

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✔ Final Answers:

| Q | Answer |
|---|--------|
| 1 | A) $ \frac{133}{30} $ |
| 2 | D) $ \frac{3}{2} $ |
| 3 | B) 20 |
| 4 | D) $ \frac{8}{15} $ |
| 5 | A) $ \frac{18}{25} $ |
| 6 | D) $ \frac{4}{3} $ |
| 7 | C) $ \frac{3}{4} $ |
| 8 | B) $ \frac{5}{3} $ |
| 9 | C) $ \frac{7}{8} $ |
|10 | C) $ \frac{144}{25} $ |

Let me know if you'd like these explained in a video or worksheet format!