Question

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compute:

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

answer

Explanation:

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:

$$ -\frac{25}{7} = -3\frac{4}{7} $$

Answer:

\(-3\frac{4}{7}\)