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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.