# How do you solve 45a = 9?

Apr 15, 2018

$a = \frac{1}{5}$

#### Explanation:

$45 a = 9$ Isolate $a$ (divide each side by $45$)
$\left(45 \frac{a}{45}\right) = \left(\frac{9}{45}\right)$ ($\frac{45}{45} = 1$)
$a = \frac{9}{45}$ Simplify 9/45 by dividing by $9$
$a = \frac{\frac{9}{9}}{\frac{45}{9}}$
$a = \frac{1}{5}$

Apr 15, 2018

$a = 0.2$

#### Explanation:

To solve this type of equation, you need to isolate the variable by itself on one side of the equation. The variable in this problem is $a$.

$45 a$ means the same thing as $45 \times a$, so it means multiplication:

Since we see multiplication, we know that we have to use the opposite function, which would be division to isolate $a$.

OPPOSITES:

$\textcolor{red}{\text{addition}}$$\leftrightarrow$$\textcolor{b l u e}{\text{subtraction}}$
$\textcolor{red}{\text{multiplication}}$ $\leftrightarrow$ $\textcolor{b l u e}{\text{division}}$

So we will divide both sides by $45$ to isolate $a$. Since the one side is already being multiplied by $45$, we can cancel the $45$'s:

$\frac{\cancel{45} a}{\cancel{45}} = \frac{9}{45}$

$a = \frac{9}{45}$

Now just divide $9$ by $45$

$a = 0.2$