Explanation:
Let's change the denominator of
![(1)/(5)](https://img.qammunity.org/2020/formulas/mathematics/high-school/cc6oz4h7bewzf3fxxxo1s8n7vxixn6llg0.png)
to 15 as it is the lowest common multiple of both denominators, 5 and 3.
![(1)/(5) = (3)/(15)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ai4m2xwqug5oz3eiirgcv3nen7n9v95p23.png)
Now, think of it this way, there are 15 people cycling and
![(1)/(5)](https://img.qammunity.org/2020/formulas/mathematics/high-school/cc6oz4h7bewzf3fxxxo1s8n7vxixn6llg0.png)
of them cycle to work.
![(1)/(5) = (3)/(15)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ai4m2xwqug5oz3eiirgcv3nen7n9v95p23.png)
![(3)/(15) * 15 = 3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7nqn5lke9x4zza0iftlszzkbismgcte1gr.png)
Out of these 15 cyclists, 3 of them go to work. As
![(2)/(3)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jgft8n5xwx5uidfnxss9gbutm3s8nfmtko.png)
of these remainders cycle via mountain bikes, we can find how many people ride mountain bikes to work.
![(2)/(3) * 3 = 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hf3nr4e27kmrlzyebim9xjqt7qz209pb0y.png)
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)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/6su30435glu6drx7me5d0cp9xw8b0o4ig6.png)
Short answer:
![(1)/(5) * (2)/(3) = (2)/(15)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nwzkuholmiwav6goxs8t36744suix6ej6w.png)