How to divide fractions
This series of 3 minute math is designed as a quick reminder for some of the main topics. I hope they help to provide a focus and a way forward. If you need any more detail please search the site or contact me – always pleased to answer any questions!
All the very best with your studies.
Transcript from the video:
“Hello and welcome to Three Minute Math. This is all about dividing fractions, so let's jump right into a question.
We'll take something like…
six elevenths divided by twelve thirty-threes
When we're dividing fractions, one of the tricks that we can use is to ‘flip' the numbers and actually multiply, I'll show you what I mean…
We keep the six elevenths but then we multiply and flip the twelve thirty-threes, so we end up with
six elevenths multiplied by thirty-three twelfths
(this is a trick we always use for dividing fractions).
Next, I'm going to reduce these numbers to make them a little bit easier to deal with…
So if I divide the top by six I get one and the bottom by six I get two
then the bottom by eleven giving me one and the top by eleven giving me three
so now if I multiply…
one times three is three divided by
one times two is two
this results is the top-heavy fraction:
two over three
… so I'll convert this back to a mixed number which is
one and one half
which is the answer to this question.
(If you need to know how to perform the multiplication stage, take a look at the Three Minute Math multiplying fractions video).
Okay, so let's make this a little bit trickier now by adding some whole numbers into the question…
three and seven elevenths divided by
two and twelve thirty-threes
this is more typical of a GCSE exam question and the first thing we need to do is convert it to top-heavy fractions.
So, converted our fractions become:
forty elevenths divided by seventy-eight thirty-threes
Exactly as we did earlier, we turn this second fraction upside down and multiply…
…forty elevenths multiplied by thirty-three seventy-eights
Now we're going to reduce these numbers to make them easier to deal with:
Dividing the bottom by eleven gives me one and the top by eleven gives me three
…then I've got forty and seventy-eight. Seventy-eight is a big number to deal with!
However, I can reduce this first number by two which gives me twenty and the seventy-eight becomes thirty-nine.
This is pretty good but I can reduce even further!
If I divide my three by three I get one, and then divide my thirty-nine by three I get thirteen, so now I have:
twenty ones multiplied by one thirteenth which is…
which converted back again is
one whole and seven thirteenths
I hope that's been helpful to you, please do have a look at some of the other videos and I'll look forward to seeing you inside the next three minutes.”
Watch the video on YouTube – How to divide fractions