Question

Write these ratios in ascending order :

$3:4,1:2,2:3$

Answer 1

Write these ratios in ascending order:

First of all, write all the ratios in the $\frac{p}{q}$ form

$\frac{3}{4},\frac{1}{2},\frac{2}{3}$

Now take the L.C.M. of the number written on the denominator

i.e. L.C.M. of $\left(4,2,3\right)=12$

Multiply both numerator and denominator of the fractions of step 1 with a certain number to make it $40$ in the each denominator

i.e. $\frac{3\times 3}{4\times 3}=\frac{9}{12},\frac{1\times 6}{2\times 6}=\frac{6}{12},\frac{2\times 4}{3\times 4}=\frac{8}{12}$

Since the denominator of each fraction is equal so that we can compare the fractions according to their numerator, we get

$\frac{6}{12}<\frac{8}{12}<\frac{9}{12}$

Therefore, $\frac{1}{2}<\frac{2}{3}<\frac{3}{4}$.