Hello and welcome to Working with Fractions.
Today our topic is dividing fractions.
Just like with multiplication, regardless of whether or not the denominators are the same,
you can always divide fractions.
But first, let’s take a quick review of multiplication since it’s important to understanding
how to divide fractions.
Let’s say that we are multiplying 4/5 by 1/4.
So we multiply across the top numbers to give us four, then across the bottom to give us 20.
But wait, we always reduce our fractions at the end, and if you notice, both 4 and 20
are products of 4, so we can really reduce this down to 1/5.
And, with a bit of foresight we may have noticed, as we were multiplying that, oh well,
4 and 4 are the same over here so we could have just done this, and reduced the fraction right away.
Either way that you get to this final answer, just make sure that whenever you’re done
the fraction is fully reduced.
To learn more about this, you can check out our Reducing Fractions video.
But what does this have to do with division?
Well, the really cool thing about dividing fractions is that all you have to do is flip
the second fraction around and then multiply.
This means that you end up multiplying the first numerator by the second denominator on the top,
and the first denominator by the second numerator on the bottom.
Be sure that it’s the second fraction, the divisor, or the number that’s doing the dividing,
that get’s flipped, or else you get the reciprocal of your answer which is
not the same thing as your answer.
I don’t know about you but I’m always a little happier to multiply than to divide.
However this does sound a little too good to be true.
How exactly does it work?
Well, imagine that you have half of a chocolate bar and then your friend comes along and wants
to have part of that too.
Now, being the wonderful person that you are, you want to split it equally.
What we want to do is divide 1/2 by 2/1 in fraction form right.
And, if we cut half of this chocolate bar up, into two pieces you can clearly see that
each person is going to get one fourth of that chocolate bar.
Notice that in order for this to make sense, what we’re really doing is flipping this
upside down so we get 1/2 and 1/2, and then we’re multiplying them.
So, 1 times 1 is 1, 2 times 2 is 4, and there you go, you got 1/4.
Notice that if you want to divide two fractions, it’s the same thing as multiplying the first
fraction by the second fraction turned upside down.
Working with just numbers, let’s say that we have 4/5 divided by 4/3.
What we would do is take the 4/5, flip the 4/3 upside down, giving us 3/4, and then multiply through.
So we have 4 times 3 on the top giving us 12, and then 5 times 4 on the bottom giving us 20.
But wait, we still have to reduce the fractions.
So here’s a tip; when both the numerator and the denominator of your fraction are even,
divide both numbers by 2 until you get an odd number for either.
So if we divide 12 and 20 by 2, we get 6 over 10.
This is still even so we can divide them again, divide by 2, and that gives us 3/5.
Neither is a factor of the other and we still cannot find any other number that both can
be divided by, so there’s your answer, 3/5.
Wow, dividing fractions isn’t that hard at all.
All you have to do is flip the second one over and then multiply and that’s all there is too it.
Nice job, and be sure to check out some of the fun games on Always Icecream and Clever Dragons
to help practice these skills and earn some rewards.
Until next time, good luck!