# Working with three or more fractions

In this step we work through two further problems where three or more fractions are added together.

## Example

Which of the two shapes below has the largest perimeter? The units for each side are the same and the drawing is not to scale.

### Triangle perimeter

First, convert \(1\frac{1}{10}\) to \(\frac{11}{10}\), and convert \(1\frac{1}{2}\) to \(\frac{3}{2}\), so we are not working with mixed numbers.

The perimeter is equal to \(\frac{3}{4} + \frac{11}{10} + \frac{3}{2}\).

To add these fractions, we look for the lowest common denominator across all three fractions, which is 20.

\(Perimeter_{T} = \frac{15}{20} + \frac{22}{20} + \frac{30}{20}\) \(= \frac{67}{20}\) \(= 3\frac{7}{20}\)

### Quadrilateral perimeter

First, again to change from mixed numbers, convert \(1\frac{1}{6}\) to \(\frac{7}{6}\), and convert \(1\frac{1}{3}\) to \(\frac{4}{3}\).

The perimeter is the sum of all sides, which is \(\frac{7}{6} + \frac{4}{3} + \frac{3}{5} + \frac{7}{10}\).

We look for the lowest common denominator for all four fractions, which is 30.

\(Perimeter_{Q} = \frac{35}{30} + \frac{40}{30} + \frac{18}{30} + \frac{21}{30}\) \(= \frac{114}{30}\) \(= 3\frac{24}{30}\) \(= 3\frac{4}{5}\)

So both are ‘3 and something’. We need to compare the fractional parts of the number. To do this, we again find the lowest common denominator:

\(\frac{7}{20} = \frac{7}{20}\) and \(\frac{4}{5} = \frac{16}{20}\)

\(3\frac{4}{5}\) is bigger than \(3\frac{7}{20}\), so the quadrilateral has the larger perimeter.

Next week we’ll be asking you to create and complete calculations with three or more fractions and different operators.

© National STEM Learning Centre