Fractions as operators
A fraction can be used to 'operate' on a quantity. In other words, the fraction acts as a function.
For example, to find \(\frac{3}{4}\) of something, several combinations of operations could occur. You could:
- divide by 4, then multiply by 3
- multiply by 3, then divide by 4.
The outcome would be a smaller quantity than the original quantity. For example, \(\frac{3}{4} \times\) 12 = 9.
When an improper fraction is the operator, the outcome will be a larger quantity than the original. For example, \(\frac{7}{4} \times\) 12 = 21.
Using the operator model
Using arrays to model fractions as operators provides a bridge between modelling the operations with groups and with area diagrams.