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

Step-by-step explanation:

Let's change the denominator of

$\frac{1}{5}$

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

$\frac{1}{5} = \frac{3}{15}$

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

$\frac{1}{5}$

of them cycle to work.

$\frac{1}{5} = \frac{3}{15}$

$\frac{3}{15} \times 15 = 3$

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

$\frac{2}{3}$

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

$\frac{2}{3} \times 3 = 2$

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

$2 \div 15 = \frac{2}{15}$

Short answer:

$\frac{1}{5} \times \frac{2}{3} = \frac{2}{15}$