# How do you solve 13A = 65 ?

Dec 12, 2015

color(blue)(A=5

#### Explanation:

$13 A = 65$

$A = \frac{65}{13}$

color(blue)(A=5

Dec 12, 2015

$A = \frac{65}{13}$

The explanation gives a very detailed introduction to the method for solving this type of question!

#### Explanation:

Given: $\textcolor{b r o w n}{13 A = 65}$

$\textcolor{b r o w n}{\text{The objective is to get A on its own on one side of the equals sign}}$ $\textcolor{b r o w n}{\text{and everything else on the other.}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{There three things that it is very important you remember:}}$

$\textcolor{b l u e}{\text{Point 1:}}$
If we can change the 13 from 13A into the value of 1 we
would have $1 \times A$ which is the same as just $A$.

$\textcolor{b l u e}{\text{Point 2:}}$
What you do to one side of the equals you also do the other.
Consider 4=4. This we know to be true. But suppose we subtracted 1 from only the left side we would have $4 - 1 \ne 4$ but if we did this instead; $4 - 1 = 4 - 1$ then both sides still have the same value.
$\textcolor{w h i t e}{\times \times}$
$\textcolor{b l u e}{\text{Point 3}}$
The same process applies to addition, multiplication, division squaring, taking square roots and so on!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b r o w n}{\text{Changing the 13 into 1}}$

Multiply both sides by $\textcolor{b l u e}{\frac{1}{13}}$

$\textcolor{b l u e}{\frac{1}{13} \times \textcolor{b r o w n}{13 A = 65} \times \frac{1}{13}}$

giving:

$\frac{13}{13} \times A = \frac{65}{13}$

$1 \times A = \frac{65}{13}$

But $1 \times A$ is the same as just $A$ giving

$A = \frac{65}{13}$