Questions: Multiply. (Enter a reduced fraction. If an 4 1/5 · 7 6/7

Multiply. (Enter a reduced fraction. If an 4 1/5 · 7 6/7
Transcript text: Multiply. (Enter a reduced fraction. If an \[ 4 \frac{1}{5} \cdot 7 \frac{6}{7} \]
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Solution

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Solution Steps

To multiply mixed numbers, first convert them to improper fractions. Then, multiply the numerators together and the denominators together. Finally, simplify the resulting fraction if possible.

Step 1: Convert Mixed Numbers to Improper Fractions

To multiply the mixed numbers \(4 \frac{1}{5}\) and \(7 \frac{6}{7}\), first convert them to improper fractions.

For \(4 \frac{1}{5}\): \[ 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5} \]

For \(7 \frac{6}{7}\): \[ 7 \frac{6}{7} = \frac{7 \times 7 + 6}{7} = \frac{55}{7} \]

Step 2: Multiply the Improper Fractions

Multiply the numerators and the denominators of the improper fractions: \[ \frac{21}{5} \times \frac{55}{7} = \frac{21 \times 55}{5 \times 7} = \frac{1155}{35} \]

Step 3: Simplify the Resulting Fraction

Simplify \(\frac{1155}{35}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 35: \[ \frac{1155}{35} = \frac{1155 \div 35}{35 \div 35} = \frac{33}{1} = 33 \]

Final Answer

The product of \(4 \frac{1}{5}\) and \(7 \frac{6}{7}\) is \(\boxed{33}\).

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