If a:b = 3:5 and b:c = 4:7, then a:c =

To find the ratio $a:c$, we can express the given ratios as fractions and multiply them. 1. **Express ratios as fractions:** Given $a:b = 3:5$, we can write this as: $$\frac{a}{b} = \frac{3}{5}$$ Given $b:c = 4:7$, we can write this as: $$\frac{b}{c} = \frac{4}{7}$$ 2. **Multiply the fractions:** To isolate $a$ and $c$, we multiply $\frac{a}{b}$ by $\frac{b}{c}$ because the '$b$' terms will cancel out: $$\frac{a}{c} = \frac{a}{b} \times \frac{b}{c}$$ 3. **Substitute the values:** $$\frac{a}{c} = \frac{3}{5} \times \frac{4}{7}$$ $$\frac{a}{c} = \frac{3 \times 4}{5 \times 7} = \frac{12}{35}$$ 4. **Final Ratio:** The ratio $a:c$ is $12:35$.