ratios: why is the ratio of this equation like so?

Question

The equation is w = 3m

and the ratio of w is to m is 3 : 1

Shouldn't it be 1 : 3?

could you please explain the reasoning?

Answer 1

The ratio of w to m is $w : m = \frac{w}{m} = \frac{3m}{m} = \frac{3}{1} = 3:1.$

Answer 2

I believe what is needed is more arithmetic than pure algebra. So here we go:

If $w=3m$ then when $m = 1, w=3(1)=3$; therefore, the ratio of $w$ to $m$ is 3:1. Likewise, when $m=2, w=3(2)=6$. Note that the value of $w$ is always three times the value of $m$.

Answer 3

$$a:b=\frac{a}{b}$$ $$w=3m$$ $$\frac{w}{m}=\frac{3m}{m}=3$$ $$\frac{w}{m}=w:m=3$$