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.