To multiply the fractions \( \frac{2}{5} \), \( \frac{2}{3} \), and \( \frac{7}{8} \), follow these steps:
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Multiply the numerators (top parts): \[ 2 \times 2 \times 7 = 4 \times 7 = 28 \]
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Multiply the denominators (bottom parts): \[ 5 \times 3 \times 8 = 15 \times 8 = 120 \]
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Combine the results into a single fraction: \[ \frac{28}{120} \]
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Simplify the fraction: To simplify, find the greatest common divisor (GCD) of 28 and 120. The factors are:
- \( 28 = 2^2 \times 7 \)
- \( 120 = 2^3 \times 3 \times 5 \)
The GCD is \( 4 \) (which is \( 2^2 \)).
Now divide the numerator and the denominator by their GCD: \[ \frac{28 \div 4}{120 \div 4} = \frac{7}{30} \]
So, the final answer is: \[ \frac{7}{30} \]