Question

How do you simplify `2/9 * 3/5 / (1/2 + 2/3)`?

Answer 1

`4 / 35`

Explanation:

You need to solve the expression in the brackets first:

`1/2 + 2/3`

To do so, you must find the least common multiple (for `2` and `3`, this is `6`) and extend the fractions to it:

`1/2 + 2/3 = (1 * 3) / (2 * 3) + (2 * 2) / (3 * 2) = 3 / 6 + 4 / 6 = 7 / 6`

So, now you have the following:

`2 / 9 * 3 / 5 -: 7/6`

To divide by a fraction you need to multiply by its reciprocal, so basically, you "turn" the fraction `7/6` and replace the division ("`/` or `-:`) by multiplication (`*`):

`2 / 9 * 3 / 5 -: 7/6 = 2 / 9 * 3 / 5 * 6 / 7 = (2 * 3 * 6) / (9 * 5 * 7) = (2 * cancel(color(blue)(3)) * 6) / (cancel(color(blue)(9)) color(blue)(3) * 5 * 7)`

`= (2 * cancel(color(green)(6)) color(green)(2)) / (cancel(color(green)(3)) * 5 * 7) = 4 / 35`