Question

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compute:

\\-1\frac{2}{3} \cdot 2\frac{1}{7}\\

answer

Explanation:

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<reasoning>

Convert mixed numbers to improper fractions

Convert each mixed number into an improper fraction:
\[
-1\frac{2}{3} = -\frac{1 \cdot 3 + 2}{3} = -\frac{5}{3}
\]
\[
2\frac{1}{7} = \frac{2 \cdot 7 + 1}{7} = \frac{15}{7}
\]

Multiply the improper fractions

Multiply the numerators and denominators:
\[
-\frac{5}{3} \cdot \frac{15}{7} = -\frac{5 \cdot 15}{3 \cdot 7}
\]

Simplify the expression

Using the Fraction Division knowledge point, simplify by dividing out common factors:
\[
-\frac{5 \cdot
ot{15}^5}{
ot{3}_1 \cdot 7} = -\frac{5 \cdot 5}{1 \cdot 7} = -\frac{25}{7}
\]

Convert back to a mixed number

Convert the improper fraction back to a mixed number:
\[
-\frac{25}{7} = -3\frac{4}{7}
\]
</reasoning>

<answer>
\(-3\frac{4}{7}\)
</answer>

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Answer:

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}
</pre_analysis>

<reasoning>

Convert mixed numbers to improper fractions

Convert each mixed number into an improper fraction:
\[
-1\frac{2}{3} = -\frac{1 \cdot 3 + 2}{3} = -\frac{5}{3}
\]
\[
2\frac{1}{7} = \frac{2 \cdot 7 + 1}{7} = \frac{15}{7}
\]

Multiply the improper fractions

Multiply the numerators and denominators:
\[
-\frac{5}{3} \cdot \frac{15}{7} = -\frac{5 \cdot 15}{3 \cdot 7}
\]

Simplify the expression

Using the Fraction Division knowledge point, simplify by dividing out common factors:
\[
-\frac{5 \cdot
ot{15}^5}{
ot{3}_1 \cdot 7} = -\frac{5 \cdot 5}{1 \cdot 7} = -\frac{25}{7}
\]

Convert back to a mixed number

Convert the improper fraction back to a mixed number:
\[
-\frac{25}{7} = -3\frac{4}{7}
\]
</reasoning>

<answer>
\(-3\frac{4}{7}\)
</answer>

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"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Multiplying Mixed Numbers"
]
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