2.5 Dividing fractions
The standard procedure for dividing by a fraction is one of those where learners can get incredibly confused. ‘Turn it upside-down and multiply’ is the common mantra but which fraction (if there are two) and why does it work?
Division is the most difficult of the arithmetic functions, even for whole numbers. It can help to go back to remembering what division means. The grouping method of division is most useful when dealing with fraction division. Watch Video 3 for some useful approaches to teaching division with fractions.
The ‘turn it upside-down and multiply’ method works because turning a fraction upside-down produces its multiplicative inverse. Fractions are unlike the integers in that they have a multiplicative inverse which can be used in fraction division because multiplying is also the inverse of dividing.
In the next section you will meet the mathematical cakes model again as a way to help learners to find percentages of amounts.