Multiply Mixed 4D4C9D

1. **State the problem:** Multiply the mixed numbers $1\ 3/4$ and $6\ 4/5$ and simplify the answer as a mixed number. 2. **Convert mixed numbers to improper fractions:** - $1\ 3/4 = \frac{7}{4}$ because $1 \times 4 + 3 = 7$ - $6\ 4/5 = \frac{34}{5}$ because $6 \times 5 + 4 = 34$ 3. **Multiply the improper fractions:** $$\frac{7}{4} \times \frac{34}{5} = \frac{7 \times 34}{4 \times 5} = \frac{238}{20}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of $238$ and $20$. - $238 = 2 \times 7 \times 17$ - $20 = 2 \times 2 \times 5$ The GCD is $2$. Divide numerator and denominator by $2$: $$\frac{\cancel{2} \times 119}{\cancel{2} \times 10} = \frac{119}{10}$$ 5. **Convert the improper fraction back to a mixed number:** Divide $119$ by $10$: - Quotient: $11$ - Remainder: $9$ So, $$\frac{119}{10} = 11\ \frac{9}{10}$$ **Final answer:** $11\ 9/10$