# How could you use cross products to check the solution to this proportion 12/30=5/x?

Oct 27, 2016

$12 \times 12.5 = 30 \times 5$
$\text{ } 150 = 150$

#### Explanation:

You will have to have a solution first ..

Cross multiplying is a way of finding the solution, but we will use that to check later. Let's use another method to find $x$

$\frac{12}{30} = \frac{5}{x}$

Notice that $12 \div 2.4 = 5$

$\frac{12 \div 2.4}{30 \div 2.4} = \frac{5}{12.5} \text{ } \rightarrow x = 12.5$

To check whether this is correct: cross-multiply...

$\frac{\textcolor{\lim e}{12}}{\textcolor{b l u e}{30}} = \frac{\textcolor{b l u e}{5}}{\textcolor{\lim e}{12.5}}$

Is color(lime)(12 xx 12.5) = color(blue)(30xx5)?

We find: $\textcolor{\lim e}{150} = \textcolor{b l u e}{150}$

Therefore we have the correct solution for $x$

This is true for any equivalent fractions:

$\frac{7}{5} = \frac{21}{15} \text{ } \frac{4}{11} = \frac{20}{55}$

$105 = 105 \text{ } 220 = 220$