Division in simple equations

Division in simple equations

The opposite of division is multiplication. Therefore, when solving simple equations which involve division you have to multiply both sides of the equation by the denominator.

Example 1

Find the value of x if $x \div 2 = 4$.

Solution

$x \div 2 = 4$

Re-write the equation in fraction form to get the numerator and denominator:

$\frac{x}{2} = 4$

Multiply both sides of the equation by 2 (the denominator). That is:

$2 \times \frac{x}{2} = 4 \times 2$

$x = 8$

Therefore, the value of $x = 8$.

Example 2

Find the value of $m$ if $-2 \div m = 7$.

Solution

$-2 \div m = 7$ can be written as $\frac{-2}{m} = 7$.

Multiply both sides of the equation by $m$ (the denominator). That is:

$m \times \frac{-2}{m} = 7 \times m$

$-2 = 7m$

Divide both sides of the equation by 7 to make $m$ remain alone on one side of the equation:

$\frac{-2}{7} = \frac{7m}{7}$

$\frac{-2}{7} = m$

Therefore, the value of $m = -\frac{2}{7}$.