# How do you solve the rational equation 2/a = 4?

Feb 7, 2016

$a = \frac{1}{2}$

#### Explanation:

the first step in solving this equation is to 'cross multiply'

hence : 4a = 2

now divide both sides by 4 :$\frac{\cancel{4} a}{\cancel{4}} = \frac{2}{4} = \frac{1}{2}$

Feb 7, 2016

$a = \frac{1}{2}$

#### Explanation:

$\textcolor{R e d}{\text{This is the system behind the shortcuts. The short cuts are very much faster}}$
$\textcolor{g r e e n}{\text{Jim has used the shortcut method but understanding}}$$\textcolor{g r e e n}{\text{what I have shown you will help with harder maths.}}$

Given: $\frac{2}{a} = 4$

Multiply both sides by a giving:

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

To make sure that initially you do not get in a muddle write this as:

$\textcolor{b r o w n}{\frac{a}{1}} \times \textcolor{b l u e}{\frac{2}{a}} = a \times 4$

By the laws of mathematics you can do this next bit:

color(blue)(color(brown)(a)/axx2/(color(brown)(1))=4a

See the way I have swapped the bottom numbers of the fractions around!

But $\frac{a}{a} \text{ is the same as 1 giving}$

$1 \times \frac{2}{1} = 4 a$

And $\frac{2}{1}$ is the same as just $2$

so we end up with:

$2 = 4 a$

Now if I do the same sort of thing with multiply both sides by $\frac{1}{4}$ I end up with:

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

so $a = \frac{1}{2}$