# Proportions

A proportion is a comparison of two equal ratios , that can also be written as an equation of this form:

$\frac{a}{b}=\frac{c}{d}$

This is read $a$ is to $b$ as $c$ is to $d$ . In this equation, $b$ and $c$ are called the means , and $a$ and $d$ are called the extremes .

These can be solved by taking cross products (also known using the means-extremes property or cross multiplication).

Example 1:

Solve the proportion: $\frac{x}{3}=\frac{6}{9}$ .

Take the cross product and solve the resulting equation.

$\begin{array}{l}9x=6\cdot 3\\ 9x=18\\ x=2\end{array}$

Example 2:

If there are $36$ packets of peanuts in $4$ boxes, how many boxes will you need to have $99$ packets?

First, write a proportion. Note that the numbers of packets are the numerators, and the numbers of boxes are the denominators.

$\frac{36}{4}=\frac{99}{x}$

Take the cross product and solve the resulting equation.

$\begin{array}{l}36x=99\cdot 4\\ 36x=396\end{array}$

Divide both sides by $36$ .

$x=11$