1. **State the problem:** Multiply the mixed numbers $5 \frac{3}{4}$ and $4 \frac{1}{7}$. 2. **Convert mixed numbers to improper fractions:** $5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$ $4 \frac{1}{7} = \frac{4 \times 7 + 1}{7} = \frac{28 + 1}{7} = \frac{29}{7}$ 3. **Multiply the improper fractions:** $$\frac{23}{4} \times \frac{29}{7} = \frac{23 \times 29}{4 \times 7} = \frac{667}{28}$$ 4. **Simplify the fraction if possible:** Since 667 and 28 have no common factors other than 1, the fraction is in simplest form. 5. **Convert the improper fraction back to a mixed number:** Divide 667 by 28: $$667 \div 28 = 23 \text{ remainder } 23$$ So, $$\frac{667}{28} = 23 \frac{23}{28}$$ **Final answer:** $$5 \frac{3}{4} \times 4 \frac{1}{7} = 23 \frac{23}{28}$$