# Math Help - Ratios

1. ## Ratios

If the ratio of 2a to 3b is 1:4, what is the ratio of 4a to 3b?

How can I show that it's 1:2? (What's the algebra behind it?)

2. Originally Posted by harold
If the ratio of 2a to 3b is 1:4, what is the ratio of 4a to 3b?

How can I show that it's 1:2? (What's the algebra behind it?)
Hello,

$\frac{2a}{3b} = \frac{1}{4}$

Multiply by 2 each side of the equation to obtain the desired ratio :

$\frac{2a}{3b} \times 2 = \frac{1}{4} \times 2$

$\frac{4a}{3b} = \frac{2}{4}$

Simplify :

$\frac{4a}{3b} = \frac{1}{2}$