To multiply the mixed number \( 7 \frac{1}{3} \) by \( \frac{4}{5} \), we first need to convert the mixed number into an improper fraction.
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Convert \( 7 \frac{1}{3} \) into an improper fraction: \[ 7 \frac{1}{3} = 7 \times 3 + 1 = 21 + 1 = 22 \] So, \( 7 \frac{1}{3} = \frac{22}{3} \).
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Now, multiply \( \frac{4}{5} \) by \( \frac{22}{3} \): \[ \frac{4}{5} \times \frac{22}{3} = \frac{4 \times 22}{5 \times 3} = \frac{88}{15}. \]
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Now, we convert \( \frac{88}{15} \) back into a mixed number:
- Divide \( 88 \) by \( 15 \): \[ 88 \div 15 = 5 \quad \text{(since } 15 \times 5 = 75\text{)} \]
- Find the remainder: \[ 88 - 75 = 13. \]
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Therefore, \( \frac{88}{15} \) can be expressed as the mixed number: \[ 5 \frac{13}{15}. \]
So, the product of \( \frac{4}{5} \times 7 \frac{1}{3} \) is \( 5 \frac{13}{15} \).
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