If p:q=2/3:3 and p:r=3/4:2/3 calculate the ratio p:q:r. Giving the answer in its simplest form

Given

if p:q=2/3:3 and p:r=3/4:1/2, calculate the ratio p:q:r giving your answer in its simplest form

We need to find the ratio p:q:r

Given p:q = 2/3 : 3 = 2/3 / 3 = 2/9

and p : r = 3/4 : 1/2 = 3/4 / 1/2 = 3/2

Now p/q = 2/9 and p/r = 3/2

We need to make p equal numerators so we get

p/q = 2/9 x 3/3 = 6/27 and

p/r = 2/3 x 3/2 = 6/4

Therefore p : q : r = 6 : 27 : 4