Adding and Subtracting Fractions with Singapore Bar Models

To add or subtract fractions we need to be able to directly compare them. In practice this means that the equal parts each is divided into must be of the same size. That is, they must have the same denominator.

Given two fractions with the same denominator, adding them is simply adding the number of shaded parts together (that is adding the numerators). Similarly, they can be subtracted by taking the difference in the number of shaded parts.

To add fractions where the division is into different numbers of equal parts (i.e. different denominators) is by finding equivalent fractions that have the same denominator, and then adding these. The least common multiple of the two denominators (i.e. the smallest integer that is a multiple of the two denominators) is the appropriate division to use.

For example, the following pair of bar models show how the fractions ¹⁄₂ and ¹⁄₃ can be added by dividing into 6ths, since 6 is the least common multiple of 2 and 3. You can see that the coloured areas in the answer are the same size as the corresponding areas in the original fractions.

The activities on this page involve using Bar Models to add or subtract fractions, and also to work with mixed numbers which arise from the sum of an integer and a fraction.