1. The problem is to find equivalent fractions for the given multiplications. 2. Recall that multiplying fractions is done by multiplying numerators and denominators: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. For the first fraction: $$\frac{1}{2} \times \frac{4}{8} = \frac{1 \times 4}{2 \times 8} = \frac{4}{16}$$ 4. Simplify $\frac{4}{16}$ by dividing numerator and denominator by 4: $$\frac{\cancel{4}}{\cancel{16}} = \frac{1}{4}$$ 5. For the second fraction, the problem is $\frac{3}{4} \times \frac{?}{?} = \frac{9}{12}$ (from the graph description: 3 parts out of 4 and 9 parts out of 12). 6. To find the missing fraction, set: $$\frac{3}{4} \times \frac{x}{y} = \frac{9}{12}$$ 7. Multiply both sides by $\frac{4}{3}$: $$\frac{3}{4} \times \frac{x}{y} \times \frac{4}{3} = \frac{9}{12} \times \frac{4}{3}$$ 8. Simplify left side: $$\cancel{\frac{3}{4}} \times \frac{x}{y} \times \cancel{\frac{4}{3}} = \frac{x}{y}$$ 9. Calculate right side: $$\frac{9}{12} \times \frac{4}{3} = \frac{9 \times 4}{12 \times 3} = \frac{36}{36} = 1$$ 10. So $\frac{x}{y} = 1$, meaning the missing fraction is $\frac{12}{12}$ to keep the denominator consistent with the graph. 11. For the third fraction: $$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$$ 12. For the fourth fraction: $$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$$ Final answers: $$\frac{1}{2} \times \frac{4}{8} = \frac{4}{16}$$ $$\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}$$ $$\frac{4}{5} \times \frac{2}{2} = \frac{8}{10}$$ $$\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}$$