Question

1/5 of the population cycle to work. If 2/3 of these cyclists ride mountain bikes, what fraction of the population cycle with mountain bikes to work?

Answer 1

Explanation:

Let's change the denominator of

`(1)/(5)`

to 15 as it is the lowest common multiple of both denominators, 5 and 3.

`(1)/(5) = (3)/(15)`

Now, think of it this way, there are 15 people cycling and

`(1)/(5)`

of them cycle to work.

`(1)/(5) = (3)/(15)`

`(3)/(15) * 15 = 3`

Out of these 15 cyclists, 3 of them go to work. As

`(2)/(3)`

of these remainders cycle via mountain bikes, we can find how many people ride mountain bikes to work.

`(2)/(3) * 3 = 2`

As there was a total of 15 people at the start and 2 who rode mountain bikes to work, the fraction of the population who rides mountain bikes to work will be

`2 / 15 = (2)/(15)`

Short answer:

`(1)/(5) * (2)/(3) = (2)/(15)`