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# Rearranging equations

An equation or formula can be rearranged to change its subject.

The formula for the temperature in Fahrenheit, $\Tred{F}$, in terms of the temperature in Celsius, $\Tblue{C}$ is $$\Tred{F} = \dfrac{9\Tblue{C}}{5} +32.$$ If we want to find $\Tblue{C}$ in terms of $\Tred{F}$, we must rearrange the equation.

To rearrange an equation, we must always do the same to both sides of an equation.

When we start to rearrange $F = 9C/5 +32$, we first subtract $\Tblue{32}$ from both sides. Now we have $F-\Tblue{32} = 9C/5$.

Now we multiply both sides by $\Tgreen{5}$ to get $\Tgreen{5} (F-32)=9C$. Finally we divide both sides by $\Tviolet{9}$ to give us the fully rearranged formula. $$C = \frac{5(F-32)}{9}$$