To work these questions out, we use the equation below:

**Example 1**

I am going for a 1000m swim. I have swum 400m. What fraction of the race have I swum?

To answer this question, we are going to use the formula above and then simplify.

I am finding the fraction of the race that I have swum. Therefore, the amount that I am interested in is 400m. The total distance of the race is 1000m. I can now sub these values into the equation above (ignoring the units).

The next step is to simplify my answer, which I do by finding common factors in the numerator and the denominator and then dividing the numerator and the denominator by these common factors (I can go straight to the simplified fraction by dividing by the highest common factor for 400 and 1000. However, sometimes it is hard to see what the highest common factor is, so dividing by any common factor can be a good idea to get you started).

A common factor between 400 and 1000 is 100. Therefore, I am going to divide the both the numerator and the denominator by 100.

The fraction above is not yet in its simplest form because there is a common factor of 2 between the numerator and the denominator, so we divide them both by 2.

There are no more common factors between the numerator and the denominator, which means that I have the fraction in its simplest form.

Therefore, I have swum ^{2}/_{5} of the race.

**Example 2**

There are 24 cookies in a bag. My friends and I have eaten 9 cookies. What fraction of the original bag is left?

We are looking for the number of cookies that are left in the bag. There were 24 cookies to start with and my friends and I have eaten 9 cookies. This means that there are 15 cookies left (24 – 9). Therefore, 15 is the amount that I am interested in. The total number of cookies was 24. We sub these values into the formula below.

We now need to simplify and there is a common factor of 3 between the numerator and the denominator, so we divide both of them by 3.

There are no more common factors between 5 and 8, which means that this fraction is in its simplest form. Therefore, my friends and I have ^{5}/_{8} of the bag of cookies left.