Question

Find $a:c$ when

$\left(1\right)a:b=2:5$ and $b:c=4:7$

$\left(2\right)a:b=1\frac{1}{2}:1\frac{2}{3}$ and $b:c=1\frac{2}{3}:5$ .

Answer 1

Given:

(1) $\frac{a}{b}=\frac{2}{5},\frac{b}{c}=\frac{4}{7}$

$\frac{a}{c}=\frac{a}{b}\times \frac{b}{c}=\frac{2}{5}\times \frac{4}{7}=\frac{8}{35}$

$a:c=8:35$

(2) $\frac{a}{b}=\frac{1\frac{1}{2}}{1\frac{2}{3}},\frac{b}{c}=\frac{1\frac{2}{3}}{5}$

$\frac{a}{b}=\frac{\frac{3}{2}}{\frac{5}{3}},\frac{b}{c}=\frac{\frac{5}{3}}{5}$

$\frac{a}{b}=\frac{9}{10},\frac{b}{c}=\frac{1}{3}$

$\frac{a}{c}=\frac{a}{b}\times \frac{b}{c}=\frac{9}{10}\times \frac{1}{3}=\frac{3}{10}$

$a:c=3:10$