How to multiply 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:
“Hi and welcome to Three Minute Math. This video is all about multiplying fractions.
So let’s go ahead and look at a particular problem, for example:
Firstly we can multiply the numerators together (the numbers on the top) which gives us:
two times three is six
then we can multiply the denominators, so…
three times four is twelve
this leaves us with
…and we can reduce this by dividing the top and bottom by six, which gives us
That’s fairly straight-forward and perhaps not a bad way to multiply fractions. However, it can be very useful to reduce fractions before we start the multiplication, rather than at the end.
Let me show you how this can be done. If I rewrite the fraction slightly so that it reads:
I’m going to divide the top by two but then I must also then divide the bottom by two, doing this gives me:
Now I’m going to divide the top and bottom by three, which gives me…
So now when I multiply my numbers are a little bit smaller and easier to deal with
the result then is
I still get to the same answer but it just means that I’ve dealt with the reduction a little bit sooner.
While this example is quite straight-forward, handling multiplication in this way can be really useful when you’re dealing with bigger numbers, so let’s take a look at this:
three and three elevenths multiplied by two and eleven twelfths
The first thing we need to do is make sure that we’ve got fractions, or improper fractions – they can also be known as ‘top-heavy’ fractions.
So I convert the first part to
thirty six over eleven
(if you need to know how to do this, please check out some of the other videos)
and I’m going to multiply this by
thirty five over twelve
Before I start I’m going to try to reduce this to make it a little bit easier to deal with.
multiply thirty six by thirty five
…and divide the result by
eleven times twelve
but that’s going to be hard work so I want to make the numbers as small as I can.
I’ll rewrite this as:
thirty six multiplied by thirty five
eleven multiplied by twelve
I can’t do anything about the eleven because it’s a prime number and it’s hard to divide by anything , but I can do something with the twelve and the thirty six.
So, if I reduce the twelve by twelve it becomes one
reduce the thirty six by twelve and it becomes three
Now I have slightly easier numbers to deal with, so…
three times thirty five is one hundred and five
eleven times one is eleven
so the answer to this question, as an improper fraction is:
one hundred and five divided by eleven
I’ll need to convert this back into a mixed number and I do know that
ten times eleven is one hundred and ten
I’ve only got one hundred and five to play with so actually it’s going to be
nine full wholes
and the bit that’s left
nine times eleven is ninety nine
…and the bit that’s left is
so the answer to this question is
nine and six elevenths
This is a fairly easy way of reducing, and making sure that the numbers that you are dealing with are a little bit easier.
I hope that’s been helpful and I look forward to seeing you inside the next three minutes.”
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