# Formulas

A formula is an equation that relates two or more real-life quantities.

Example 1:

To convert temperature from Celsius units to Fahrenheit, use the formula:

$F=\frac{9}{5}C+32$

So, $20$ degrees Celsius is the same as

$\frac{9}{5}\cdot 20+32=36+32=68°F$

Solving the formula for another variable:

The formula above is useful if you know the Celsius temperature, and you want to know the Fahrenheit temperature. What if it's the other way around?

We have to solve for $C$ alone on one side. To do this, treat all the other variables in the equation (in this case only $F$ ) as numbers, and operate on both sides of the equation.

First, subtract $32$ from both sides.

$F-32=\frac{9}{5}C$

Now divide both sides by $\frac{9}{5}$ (which is the same as multiplying by $\frac{5}{9}$ ).

$\frac{5}{9}\left(F-32\right)=C$

Simplifying, we get:

$C=\frac{5}{9}F-\frac{160}{9}$

Example 2:

The formula for the area of a trapezoid is

$A=\frac{1}{2}h\left({b}_{1}+{b}_{2}\right)$ ,

where $h$ is the height and ${b}_{1}$ and ${b}_{2}$ are the base lengths.

You might be asked to solve this formula for the height, in other words, to get $h$ alone on one side.

Treat all the other variables as fixed numbers, and start by multiplying by $2$ .

$2A=h\left({b}_{1}+{b}_{2}\right)$

Now divide both sides by $\left({b}_{1}+{b}_{2}\right)$ .

$\frac{2A}{\left({b}_{1}+{b}_{2}\right)}=h$

or

$h=\frac{2A}{\left({b}_{1}+{b}_{2}\right)}$

With this new formula, given the area and the base lengths of a trapezoid, we can calculate the height!