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