There are three different situations to explore when adding fractions with the same denominator. Additions can be where:
- the whole is completed (e.g. \(\frac{1}{4}\) + \(\frac{3}{4}\) = 1)
- the total is less than one (e.g. \(\frac{2}{8}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\))
- the total is greater than one, which involves working with improper fractions and mixed numbers (e.g. \(\frac{2}{3}\) + \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\))
Similarly, subtractions can be taking away from:
- one whole (e.g. 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\))
- a fraction less than one (e.g. \(\frac{3}{8}\) – \(\frac{2}{8}\) = \(\frac{1}{8}\))
- a number greater than one (e.g. 1\(\frac{1}{3}\) – \(\frac{2}{3}\) = \(\frac{2}{3}\))
Both additions and subtractions can be modelled with area diagrams or scenarios such as pieces of pizza. However, modelling these operations on a number line allows the use of counting forwards or backwards along the number line as a solution strategy.
The number line counting model can also help avoid the common misconception of adding the denominators as well as the numerators.
