1. **State the problem:** Calculate the product of the mixed fractions $1 \frac{7}{8}$ and $2 \frac{7}{15}$ and express the result as a reduced mixed fraction. 2. **Convert mixed fractions to improper fractions:** - $1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{15}{8}$ - $2 \frac{7}{15} = \frac{2 \times 15 + 7}{15} = \frac{37}{15}$ 3. **Multiply the improper fractions:** $$\frac{15}{8} \times \frac{37}{15} = \frac{15 \times 37}{8 \times 15} = \frac{555}{120}$$ 4. **Simplify the fraction:** - The numerator is 555 and the denominator is 120. - Find the greatest common divisor (GCD) of 555 and 120. - $555 = 3 \times 5 \times 37$ - $120 = 2^3 \times 3 \times 5$ - GCD is $3 \times 5 = 15$ - Divide numerator and denominator by 15: $$\frac{555 \div 15}{120 \div 15} = \frac{37}{8}$$ 5. **Convert the improper fraction back to a mixed fraction:** - Divide 37 by 8: $$37 \div 8 = 4 \text{ remainder } 5$$ - So, $$\frac{37}{8} = 4 \frac{5}{8}$$ **Final answer:** $$1 \frac{7}{8} \times 2 \frac{7}{15} = 4 \frac{5}{8}$$