QuestionAugust 26, 2025

8. (-(1)/(2)+1(1)/(8))cdot (2(2)/(3)-3(1)/(3))cdot 7.5

8. (-(1)/(2)+1(1)/(8))cdot (2(2)/(3)-3(1)/(3))cdot 7.5
8. (-(1)/(2)+1(1)/(8))cdot (2(2)/(3)-3(1)/(3))cdot 7.5

Solution
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Answer

-\frac{25}{8} Explanation 1. Simplify the first expression Convert -\frac{1}{2} to -\frac{4}{8} and 1\frac{1}{8} to \frac{9}{8}. Add them: -\frac{4}{8} + \frac{9}{8} = \frac{5}{8}. 2. Simplify the second expression Convert 2\frac{2}{3} to \frac{8}{3} and 3\frac{1}{3} to \frac{10}{3}. Subtract them: \frac{8}{3} - \frac{10}{3} = -\frac{2}{3}. 3. Multiply the simplified expressions Multiply \frac{5}{8} \cdot (-\frac{2}{3}) \cdot 7.5: First, \frac{5}{8} \cdot (-\frac{2}{3}) = -\frac{10}{24} = -\frac{5}{12}. Then, -\frac{5}{12} \cdot 7.5 = -\frac{5 \times 7.5}{12} = -\frac{37.5}{12}. 4. Simplify the final result Simplify -\frac{37.5}{12} to -\frac{75}{24}, which reduces to -\frac{25}{8}.

Explanation

1. Simplify the first expression<br /> Convert $-\frac{1}{2}$ to $-\frac{4}{8}$ and $1\frac{1}{8}$ to $\frac{9}{8}$. Add them: $-\frac{4}{8} + \frac{9}{8} = \frac{5}{8}$.<br /><br />2. Simplify the second expression<br /> Convert $2\frac{2}{3}$ to $\frac{8}{3}$ and $3\frac{1}{3}$ to $\frac{10}{3}$. Subtract them: $\frac{8}{3} - \frac{10}{3} = -\frac{2}{3}$.<br /><br />3. Multiply the simplified expressions<br /> Multiply $\frac{5}{8} \cdot (-\frac{2}{3}) \cdot 7.5$: <br /> First, $\frac{5}{8} \cdot (-\frac{2}{3}) = -\frac{10}{24} = -\frac{5}{12}$.<br /> Then, $-\frac{5}{12} \cdot 7.5 = -\frac{5 \times 7.5}{12} = -\frac{37.5}{12}$.<br /><br />4. Simplify the final result<br /> Simplify $-\frac{37.5}{12}$ to $-\frac{75}{24}$, which reduces to $-\frac{25}{8}$.
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