Going from a fraction to the whole

The unitary method can be used to solve problems where we are given a fraction of the whole, and wish to find either another faction or the whole itself.

Example 3

There are 51 people at Olivia's barbeque. This is \(\dfrac{3}{5}\) of those invited. How many people were invited?

Solution

The 'part' to use is \(\dfrac{1}{5}\) of those invited so 3 parts are 51 people.

Hence 1 part = 51 ÷ 3 = 17.

The whole is 5 parts.

So the number of people invited = 5 × 17 = 85 people.

Example 4

Conrad is recovering from an operation and has been told to walk 10 000 steps per day. In 45 minutes, he has walked 3000 steps. If he walks at the same rate, how long will it take him to walk the required number of steps?

Solution

Here, the fraction walked is \(\dfrac{3000}{10 000}\) = \(\dfrac{3}{10}\).

So the 'part' is \(\dfrac{1}{10}\).

Three parts are 45 minutes.

Hence 1 part is 45 ÷ 3 = 15 minutes.

So the time it will take him = 15 × 10 = 150 minutes.