1. **State the problem:** We need to determine if each statement about unit rates is true or false. 2. **Recall the formula for unit rate:** The unit rate of a ratio $\frac{a}{b} : \frac{c}{d}$ is found by dividing the first ratio by the second ratio: $$\text{Unit rate} = \frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ 3. **Evaluate each statement:** - Statement 1: The ratio $\frac{5}{8} : \frac{10}{9}$ has a unit rate of $\frac{9}{16}$. Calculate unit rate: $$\frac{5}{8} \div \frac{10}{9} = \frac{5}{8} \times \frac{9}{10} = \frac{5 \times 9}{8 \times 10} = \frac{45}{80}$$ Simplify $\frac{45}{80}$: $$\frac{45}{80} = \frac{\cancel{5}9}{\cancel{5}16} = \frac{9}{16}$$ This matches the given unit rate, so **True**. - Statement 2: The ratio $\frac{4}{7} : \frac{8}{21}$ has a unit rate of $\frac{3}{2}$. Calculate unit rate: $$\frac{4}{7} \div \frac{8}{21} = \frac{4}{7} \times \frac{21}{8} = \frac{4 \times 21}{7 \times 8} = \frac{84}{56}$$ Simplify $\frac{84}{56}$: $$\frac{84}{56} = \frac{\cancel{28}3}{\cancel{28}2} = \frac{3}{2}$$ This matches the given unit rate, so **True**. - Statement 3: The unit rate of $\frac{1}{2}$ is $\frac{14}{27}$. The unit rate of a single number $\frac{1}{2}$ is itself, so $\frac{1}{2} \neq \frac{14}{27}$. So this statement is **False**. - Statement 4: The ratio $\frac{3}{12}$ is $\frac{1}{8}$. Simplify $\frac{3}{12}$: $$\frac{3}{12} = \frac{\cancel{3}1}{\cancel{3}4} = \frac{1}{4}$$ Since $\frac{1}{4} \neq \frac{1}{8}$, this statement is **False**. **Final answers:** - Statement 1: True - Statement 2: True - Statement 3: False - Statement 4: False