Ratio and Rate

Q1. Prove that 1/a : 1/b = 4:3

As a:b:c=6:8:9
Let a = 6k, b = 8k c = 9k , where k is a constant

then, 1/a : 1/b
= (1/a)/(1/b)
= (1/6k)/(1/8k)
= (1/3)/(1/4)
= 4/3

therefore 1/a : 1/b = 4:3