Remember my post from June 2013 about a new way to teach dividing fractions? Well the other day I came up with another new method!

You might be wondering why I need a new method anyway, when the normal method (flip it and times it) works so well. Here's why: because that method is not intuitive. Well, it is if you understand reciprocals properly, and that the multiplicative inverse of a is 1/a. We don't normally go into the axioms of fields though, when we teach year 8 fractions.

Here's the way my method works. Say you want to do 3/4 divided by 2/3.

The way I usually think of integer division in my head is to make it into a multiplication. So 20 divided by 4 becomes 4 times something is 20. And then I think of what the something is. I think this is the way many students think about division.

So applying that to my question:

But 2 times something makes 3 and 4 times something makes 4 is quite difficult. So what we'll do is find an equivalent fraction for 3/4 so that 2 goes into the numerator and 3 goes into the denominator.

Then we just have to work out 2 times something is 18 and 3 times something is 24. Easy!

I thought of this method because there was a question in the year 9 MEP textbook that my students came across that was something like 3/4 x = 5/7 and you had to solve for x. But not having done algebra recently, my year 9s didn't think to divide both sides by 3/4. This led to them trying to find the answer by the method above. Interestingly, this year 9 class is the same class (then in year 7) that provided inspiration for the previous blog post on this topic!

What do you think, a waste of time, or a nice way in?

Emma x x x

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