How do you divide a fraction by another fraction?
For example, how would you do something like this:
My guess is you would flip the second fraction upside down and then multiply like so:
If you are a maths teacher, is this how you teach students?
Do you think your students understand why this method works? And, be honest, do you understand why it works?
Well recently in the maths office one of my colleagues showed us a new method he'd thought of.
It works like this:
I think this is a little bit more intuitive.
My colleague got the idea from one of his year sevens who had answered this question without showing any working out:
The answer is quite obviously three. How many quarters are there in three quarters? Three, duh. But I am quite certain many A* students would perform the technique of flipping and timesing without even thinking. My colleague was impressed that this student had used some common sense. He wondered whether the same idea could be applied to fractions with different denominators. It is a little bit less obvious that 21/28 divided by 20/28 is 21/20, but it's not entirely unbelievable. Whereas the "trick" of flipping and timesing can look a little bit like magic to some students.
I haven't tried teaching this method so I can't comment on its effectiveness yet. But as a mathematician it appeals to me. It's quite neat. And in case you were wondering, yes this works with algebraic fractions too.
If you're going to be teaching fractions soon, why not try this out? If you do, please let me know how it goes.
Do you think this is a good method?
This post was written by Emma Cooke, Sidney Stringer Academy, Coventry
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