Question

Write these ratios in ascending order :

$1:4,4:20,20:120$

Answer 1

Write these ratios in ascending order:

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

$\frac{1}{4},\frac{4}{20},\frac{20}{120}$

$\frac{1}{4},\frac{1}{5},\frac{1}{6}$

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

i.e. L.C.M. of $\left(4,5,6\right)=60$

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. $\frac{1\times 15}{4\times 15}=\frac{15}{60},\frac{1\times 12}{5\times 12}=\frac{12}{60},\frac{1\times 10}{6\times 10}=\frac{10}{60}$

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

$\frac{10}{60}<\frac{12}{60}<\frac{15}{60}$

Therefore, $\frac{20}{120}<\frac{4}{20}<\frac{1}{4}$.