4.10

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.

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

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.