To multiply \( \frac{4}{5} \) by \( 7 \frac{1}{3} \), we first need to convert the mixed number into an improper fraction.
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Convert \( 7 \frac{1}{3} \) to an improper fraction: \[ 7 \frac{1}{3} = 7 \times 3 + 1 = 21 + 1 = 22 \] Therefore, \( 7 \frac{1}{3} = \frac{22}{3} \).
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Now, we 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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Next, we convert \( \frac{88}{15} \) into a mixed number. To do this, we divide 88 by 15:
- \( 15 \) goes into \( 88 \) \( 5 \) times (since \( 15 \times 5 = 75 \)).
- Subtract \( 75 \) from \( 88 \) to get the remainder: \( 88 - 75 = 13 \).
Thus, the mixed number is: \[ 5 \frac{13}{15} \]
Therefore, the product of \( \frac{4}{5} \) and \( 7 \frac{1}{3} \) is \( 5 \frac{13}{15} \).