# Algebraic Fractions: Division

You should all know this when we’re dividing what do we do with the fractions?
With the second one, you flip it so you find the reciprocal, flip it and change the sign to a multiplication sign like this. So you change that to a multiplication sign and you flip this fraction upside down.
So it’s 2y on 15, Okay? And you can see that 15 is 3 times 5 and four is two times two.
Again I just broke it down into some prime factors to see if I can cancel anything out. Okay?
And again guys if you think you can try you don’t have to do it like this.
You can probably go from this step straight to the answer if you can. Okay? But for those who need a bit of guidance again just do what I do.
Because see now you can see that 5 and 5 we can cancel out. And we can see that 2 and 2 we can cancel out. So we just have y on two left times y on three.
So y times y is y squared two times three is six and that’s the answer. Okay?
So that’s what you do when you like when you just cancel things out.

Again we’re dividing so do the same thing. Flip it and change it to a multiplication sign.
We make it down make it into some factors 12 is 6 times 2.
Now I’m not going to break 6 any further although we can. We can probably change it 2 times 3.
But we don’t need to. Because we know that 12 is 6 times 2 and immediately we can see these are common.
So we can kind of cancel those out. And look! x and x we can cancel those out as well. So we just have 2 over 5 left over.
Because there’s nothing there we just cancel the whole thing out it’s just 1 and here we have 2 over 5 left. So 2 over 5 is just the answer. Okay? So very simple!
Again division. We flip it and change it all to multiplication.
So see how x cubed over y x cubed times y squared is x cubed y squared over 1 isn’t it if I wanted to make it into a fraction.
So if I change it to a multiplication sign, that one, if I flip it becomes 1 over x cubed y squared. And that one again flip it and change it to times.
Now we’ll do the same thing. So I know it’s big, sorry. 12 is 6 times 2 and x squared is x times x, isn’t it?

We can see that x cubed is x x x y squared is y y x y cubed is y y y and 18 is six times three. Again I did six times three and six times 2 because I can cancel out the 6’s, can’t I? And then y see I can cancel this y and this y this y and this y this y and also this y so all the y’s just cancel out like that and here x cancel out x cancel out. Okay?
So what do we have left? We have 2 times 1 times x oh sorry I forgot to cancel this x as well. Sorry.
So we don’t have any more for numerals basically so we just have 2 times 1 which is 2 and we have 3 left on the denominator.
So all the pronumerals cancel out. See how I was almost close to making a silly mistake. That’s because there was so much stuff. So when you have three fractions like that.
Be extra careful. Don’t make the mistake that I did by leaving one out.
So that’s the answer. All the pronumerals are cancelled out, which is great! ## Index Notation: Expanded Form to Index Form

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