Two Ways of Thinking about Division

Donna Curry
The Math Practitioner, Vol. 15, No. 3. 2010


We know that division is the inverse of multiplication. We also know that the answer to a division problem can sometimes be found by repeated subtraction e.g., the answer to 18 ÷ 3, determined by seeing how many 3’s can be subtracted from 18.

Many of us, though, have not been taught that there are two ways to look at division: partitive and quotitive. Understanding these two different models of division may help your students visualize division of fractions. Having students understand that there are two ways to look at division does not mean that students need to be taught the terminology, but rather that they understand that division can be represented by different models.