Question

Use cross products to solve each proportion.

$\frac{2}{3}=\frac{a}{42}$

Short answer

Given proportion is simplified to $a=28$

Step-by-step solution

- Cross product between two proportions

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

Then cross product is defined as multiplication of denominator of one proportion with the numerator of other proportion, that is $a\text{'}d\text{'}=b\text{'}c\text{'}$

- Substitution

Substitute 2 for $a\text{'}$, 3 for $b\text{'}$, $a$for $c\text{'}$, and 42 for $d\text{'}$ into $a\text{'}d\text{'}=b\text{'}c\text{'}$ gives

$2\times 42=3\times a$

- Simplify 2×42=3×a

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

$\begin{array}{c}84=3a\\ a=\frac{84}{3}\\ a=28\end{array}$