1. The problem is to identify which ratios are equivalent to the ratio $4:2$. 2. Two ratios are equivalent if their fractions are equal. The ratio $4:2$ can be written as the fraction $\frac{4}{2}$. 3. Simplify $\frac{4}{2}$: $$\frac{4}{2} = 2$$ 4. Check each given ratio by converting to fractions and simplifying: - $20:10$ as $\frac{20}{10}$: $$\frac{20}{10} = \frac{\cancel{20}}{\cancel{10}} = 2$$ - $24:8$ as $\frac{24}{8}$: $$\frac{24}{8} = \frac{\cancel{24}}{\cancel{8}} = 3$$ - $10:1$ as $\frac{10}{1}$: $$\frac{10}{1} = 10$$ 5. Compare each simplified fraction to $2$: - $20:10$ equals $2$, so it is equivalent. - $24:8$ equals $3$, so it is not equivalent. - $10:1$ equals $10$, so it is not equivalent. 6. Therefore, the only ratio equivalent to $4:2$ is $20:10$. Final answer: $20:10$ is equivalent to $4:2$.