multiply 4/5 by 7 1/3. convert the product to be a mixed number

Answer 1

To multiply \( \frac{4}{5} \) by \( 7 \frac{1}{3} \), we first need to convert the mixed number \( 7 \frac{1}{3} \) into an improper fraction.

1. Convert \( 7 \frac{1}{3} \):

   • Multiply the whole number \( 7 \) by the denominator \( 3 \): \( 7 \times 3 = 21 \).
   • Add the numerator \( 1 \): \( 21 + 1 = 22 \).
   • Therefore, \( 7 \frac{1}{3} = \frac{22}{3} \).

2. Now multiply \( \frac{4}{5} \) by \( \frac{22}{3} \): \[ \frac{4}{5} \times \frac{22}{3} = \frac{4 \times 22}{5 \times 3} = \frac{88}{15}. \]

3. Convert \( \frac{88}{15} \) to a mixed number:

   • Divide \( 88 \) by \( 15 \):
     • \( 88 \div 15 = 5 \) (the quotient).
     • To find the remainder, calculate \( 88 - (15 \times 5) = 88 - 75 = 13 \).
   • Therefore, \( \frac{88}{15} = 5 \frac{13}{15} \).

So the product of \( \frac{4}{5} \) and \( 7 \frac{1}{3} \) is \( 5 \frac{13}{15} \).