Question

Use cross products to solve each proportion.

$\frac{2}{y}=\frac{8}{9}$

Short answer

Given proportion is simplified to $y=\frac{9}{4}$

Step-by-step solution

- Cross product between two proportions

Let $\frac{a}{b}$ and $\frac{c}{d}$ be two equal proportions that is $\frac{a}{b}=\frac{c}{d}$

Then cross product is defined as multiplication of denominator of one proportion with the numerator of other proportion, that is $ad=bc$

- Substitution

Substitute 2 for a, y for b, 8 for c, and 9 for d into $ad=bc$gives

$2\times 9=y\times 8$$2\times 9=y\times 8$

- Simplify 2×9=y×8

To simplify this expression multiply both the numbers of left side and then divide it from number on the right as shown below

$\begin{array}{c}18=8y\\ y=\frac{18}{8}\\ y=\frac{9}{4}\end{array}$