# How do you determine whether the ratios are equivalent: 5/6; 15/18?

Nov 4, 2016

Use:

$\frac{a}{b} = \frac{c}{d} \text{ " <=> " } a d = b c$

#### Explanation:

If $b \ne 0$ and $d \ne 0$ then:

$\frac{a}{b} = \frac{c}{d} \text{ " <=> " } a d = b c$

In our example, (with $a = 5$, $b = 6$, $c = 15$, $d = 18$) we find:

$5 \cdot 18 = 90 = 6 \cdot 15$

Therefore:

$\frac{5}{6} = \frac{15}{18}$