Question

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

Answer 1

`a = 1/2`

Explanation:

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

hence : 4a = 2

now divide both sides by 4 :`(cancel(4) a)/cancel(4) = 2/4 = 1/2`

Answer 2

`a=1/2`

Explanation:

`color(Red)("This is the system behind the shortcuts. The short cuts are very much faster")`
`color(green)("Jim has used the shortcut method but understanding")` `color(green)("what I have shown you will help with harder maths.")`

Given: `2/a=4`

Multiply both sides by a giving:

`axx2/a=axx4`

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

`color(brown)(a/1)xxcolor(blue)(2/a)=axx4`

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 `a/a" is the same as 1 giving"`

`1xx2/1=4a`

And `2/1` is the same as just `2`

so we end up with:

`2=4a`

Now if I do the same sort of thing with multiply both sides by `1/4` I end up with:

`2/4=a`

so `a=1/2`