If a : b = 5 : 6 and b : c = 2.8 : 3.5, find a : c.

Given:

a : b = 5 : 6

b : c = 2.8 : 3.5

Multiply by 10 to remove decimals in the second ratio.

b : c = (2.8 x 10) : (3.5 x 10) = 28 : 35

b : c = 4 : 5 $\quad$ [Dividing by 7]

$a : b = \dfrac{a}{b} = \dfrac{5}{6} \\[1em] b : c = \dfrac{b}{c} = \dfrac{4}{5}$

Now,

$a : c = \dfrac{a}{c} = \left( \dfrac{a}{b} \times \frac{b}{c} \right) \\[1em] = \left( \dfrac{5}{6} \times \dfrac{4}{5} \right) \\[1em] = \left( \dfrac{1}{6} \times \dfrac{4}{1} \right) \\[1em] = \dfrac{4}{6} \\[1em] = \dfrac{2}{3} \\[1em] = 2 : 3$

∴ a : c = 2 : 3