Question

Given that 12a=20b, find the ratio of a to b in simplest form.

Answer 1

The ratio is \[\frac{ 12a }{ 20b }\] To reduce the fraction to it's lowest form, find the greatest common factor and divide the numerator and denominator by that factor.

The factors of 12 are 1*12; 2*6; and 3*4

The factors of of 20 are 1*20; 2*10; 4*5

So 4 is the biggest factor that is a factor of 12 and 20.

So divide the numerator and denominator by 4.

So 12 divided by 4 is 3, and 20 divided by 4 is 5. So in simplest form, the ratio is:
\[\frac{ 3a }{ 5b }\]