Question

math 8
equations, systems, and fractions review
find each product.

1. $2 \cdot \frac{5}{3} \cdot \frac{7}{6}$
2. $4 \cdot \frac{1}{6} \cdot \frac{3}{2}$
3. $\frac{1}{5} \cdot \frac{2}{3} \cdot \frac{2}{5}$
4. $\frac{1}{6} \cdot \frac{4}{5} \cdot \frac{1}{4}$
5. $\frac{1}{6} \cdot \frac{3}{2} \cdot \frac{7}{6}$
6. $\frac{5}{3} \cdot \frac{1}{3} \cdot \frac{3}{2}$

name ______
date ______

Explanation:

Step1: Multiply all numerators/denominators

$2 \cdot \frac{5}{3} \cdot \frac{7}{6} = \frac{2 \times 5 \times 7}{1 \times 3 \times 6} = \frac{70}{18}$

Step2: Simplify the fraction

$\frac{70}{18} = \frac{35}{9}$

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Step1: Multiply all numerators/denominators

$4 \cdot \frac{1}{6} \cdot \frac{3}{2} = \frac{4 \times 1 \times 3}{1 \times 6 \times 2} = \frac{12}{12}$

Step2: Simplify the fraction

$\frac{12}{12} = 1$

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Step1: Multiply all numerators/denominators

$\frac{1}{5} \cdot \frac{2}{3} \cdot \frac{2}{5} = \frac{1 \times 2 \times 2}{5 \times 3 \times 5} = \frac{4}{75}$

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Step1: Multiply all numerators/denominators

$\frac{1}{6} \cdot \frac{4}{5} \cdot \frac{1}{4} = \frac{1 \times 4 \times 1}{6 \times 5 \times 4} = \frac{4}{120}$

Step2: Simplify the fraction

$\frac{4}{120} = \frac{1}{30}$

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Step1: Multiply all numerators/denominators

$\frac{1}{6} \cdot \frac{3}{2} \cdot \frac{7}{6} = \frac{1 \times 3 \times 7}{6 \times 2 \times 6} = \frac{21}{72}$

Step2: Simplify the fraction

$\frac{21}{72} = \frac{7}{24}$

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Step1: Multiply all numerators/denominators

$\frac{5}{3} \cdot \frac{1}{3} \cdot \frac{3}{2} = \frac{5 \times 1 \times 3}{3 \times 3 \times 2} = \frac{15}{18}$

Step2: Simplify the fraction

$\frac{15}{18} = \frac{5}{6}$

Answer:

1. $\frac{35}{9}$
2. $1$
3. $\frac{4}{75}$
4. $\frac{1}{30}$
5. $\frac{7}{24}$
6. $\frac{5}{6}$