State True or False:

The ratios 1:4 and 2:3 are equivalent.

The above statement is False.

To check this, we need to know whether $\frac{1}{4}=\frac{2}{3}$.

We have,

$\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}$

and $\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$

We find that $\frac{3}{12}<\frac{8}{12}$, which means that $\frac{1}{4}<\frac{2}{3}$.

Therefore, the ratio 1:4 is not equivalent to the ratio 2:3.