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

If p : q = $1\dfrac{1}{3} : 1\dfrac{1}{2}$ and q : r = $\dfrac{1}{2} : \dfrac{1}{3}$, find p : r.

If l : m = $2\dfrac{1}{2} : 1\dfrac{2}{3}$ and m : n = $1\dfrac{1}{4} : 3\dfrac{1}{2}$, find l : m : n.

Which ratio is greater?

(i) (3 : 4) or (5 : 7)

The given ratios are 3 : 4 and 5 : 7, which are equivalent to the fractions $\dfrac{3}{4}$ and $\dfrac{5}{7}$ respectively.

Let us find the L.C.M. of 4 and 7:

$\begin{array}{l|rr} 2 & 4, & 7 \ \hline 2 & 2, & 7 \ \hline 7 & 1, & 7 \ \hline & 1, & 1 \end{array}$

L.C.M. = 2 x 2 x 7 = 28.

$∴ 3 : 4 = \dfrac{3}{4} = \dfrac{3 \times 7}{4 \times 7} = \dfrac{21}{28}$

$5 : 7 = \dfrac{5}{7} = \dfrac{5 \times 4}{7 \times 4} = \dfrac{20}{28}$

Clearly, $\dfrac{21}{28} \gt \dfrac{20}{28}$.

Hence, (3 : 4) > (5 : 7).

(ii) (11 : 21) or (19 : 28)