Question

How do you solve `\frac { 8} { u } = \frac { 3} { 5}`?

Answer 1

`u = 40/3 = 13 1/3`

Explanation:

Given:

`8/u = 3/5`

We want to isolate `u` by transforming this equation.

Here are a couple of methods.

`color(white)()`
Cross multiplication

Move the denominators of both sides to the numerators of the other side, turning the division into multiplication.

[ This is effectively multiplying both sides of the equation by `5u` ]

So:

`8/u = 3/5" "rarr" "8xx5 = 3xxu`

That is:

`40 = 3u`

Then divide both sides by `3` to find:

`40/3 = u`

That is:

`u = 40/3 = 13 1/3`

`color(white)()`
Method using reciprocals

Given:

`8/u = 3/5`

Take the reciprocal of both sides of the equation to get:

`u/8 = 5/3`

Multiply both sides of the equation by `8` to get:

`u = 8 xx 5/3 = 40/3 = 13 1/3`