Fraction Products 977D39

1. **Problem 7:** Calculate $\left(1 - \frac{3}{4}\right)\left(3 - \frac{1}{2}\right)$. 2. Simplify inside the parentheses: $$1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$$ $$3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{5}{2}$$ 3. Multiply the simplified terms: $$\left(\frac{1}{4}\right)\left(\frac{5}{2}\right) = \frac{1 \times 5}{4 \times 2} = \frac{5}{8}$$ --- 4. **Problem 8:** Calculate $\left(\frac{7}{8}\right)\left(\frac{4}{5}\right)\left(\frac{4}{7} - \frac{3}{4}\right)$. 5. Simplify inside the parentheses: Find common denominator for $\frac{4}{7}$ and $\frac{3}{4}$ which is $28$: $$\frac{4}{7} = \frac{16}{28}, \quad \frac{3}{4} = \frac{21}{28}$$ $$\frac{4}{7} - \frac{3}{4} = \frac{16}{28} - \frac{21}{28} = -\frac{5}{28}$$ 6. Multiply all terms: $$\left(\frac{7}{8}\right)\left(\frac{4}{5}\right)\left(-\frac{5}{28}\right) = - \frac{7 \times 4 \times 5}{8 \times 5 \times 28}$$ Cancel common factors: $$- \frac{\cancel{7} \times 4 \times \cancel{5}}{8 \times \cancel{5} \times 28} = - \frac{4}{8 \times 28}$$ Simplify $\frac{4}{8} = \frac{\cancel{4}}{\cancel{8} \times 2} = \frac{1}{2}$: $$- \frac{1}{2 \times 28} = - \frac{1}{56}$$ --- **Final answers:** - Problem 7: $\frac{5}{8}$ - Problem 8: $-\frac{1}{56}$