## You use algebraic fractions all the time…. even without meaning to!

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.

### OK, where are algebraic fractions used?

Algebra is used very frequently in our daily lives. An example might be shopping … you buy 12 items and each bag will only hold 5 items. How many bags do you need?

I’m sure you’ll have worked out 3 bags:

= 2.4 bags or 3 whole bags

This has really used the algebraic fraction where

a = Number of items purchased = 12 items

b = Capacity of a single shopping bag = 5 items/bag

This will allow us to calculate how many bags for *any number of items*. ‘a’ and ‘b’ are general terms and we can use them to calculate any number. It’s not really that important when you’re on a weekly shop (!) – but it could be for the supermarket when they order the bags, or the manufacturer when they are calculating sizes.

Algebra is mainly to do with quantities and scalability. It allows us to create a formula that *applies to any situation.*

### Video Transcript

“Welcome to 3 Minute Maths. In this video, we’re going to be looking at algebra fractions. These come up a lot in fairly high level, GCSE or equivalent type questions and they’re usually A or A*. The way they will be written will be something like:

Simplify divided by .

When you first look at these, it can look a little bit intimidating but actually, if you break it down into its component parts, it’s not too bad.

The main thing with these that you need to remember is that, in keeping with every fraction, whatever you do to the top of the fraction, you’ve got to do to the bottom as well. So, if you divide the top by something, you’ve got to divide the bottom by that same something.

Just as a very brief example, let’s say you’ve got . This can be simplified by dividing the top and bottom by 2. So, if I divide 4 by 2, I get 2. And, if I divide the bottom by 2, I get 3. It’s a little bit easier to deal with than it is to deal with .

You’re going to use the same principle with

but the first thing we’re going to do is look at the top bit, which is called the numerator. The main thing to remember or look at is the top. This particular one is a ‘difference of two squares.’ So, if I factorize that, it’s going to be . (If that’s not quite clear to you then maybe you need to have a look at one of the other videos; there is a video on the difference of two squares.)

If you multiple back you’ll see that it actually does work out to be .

I’m going to do a very similar thing to the expression on the bottom. The way will factor out will be

And again, I can work that backwards if I want. I’ll just to that very briefly: x times x will be x squared, 2x and 5x is 7x, and 5×2 is 10.

In the same way that we’ve done with , where we divided through by 2, what I’m going to do is divide the top and bottom by x+5. If I divide the top and bottom by x+5, then x+5 will cancel out. So, the simplification of will be .

I hope that’s been helpful. Please have a look at the other videos and comment below. And, I’ll put some explanation into the description. I’ll look forward to seeing you inside the next three minutes.”

Visit our store for brilliant toys and games for all ages and abilities. Whether shopping for a birthday or to help your child with fractions and decimals, there’s sure to be a great gift in the Maths Wrap store. Ideal fun toys and games to give your child a great head start !

Shop with confidence – powered by Amazon.

Watch the video on YouTube – Simplifying Algebraic Fractions

live auto says

hi simon it would be happy if u come up with basics algerba .in ur way

(happy smiling)

Pravina Solanki says

great help cheers

Nanaesly Neon says

What if you have p-square minus 4 all over p-square?

Faith Forever says

Thanks this video is brillliant! 🙂 I have an exam tommorow!!

Grant Page says

Have you got any complicated examples of factorising?

Sharif Sircar says

Thanks

Alejandro Navarro says

thanks, that was very useful!, textbooks can’t explain it good enough.

Thanks again!

bedoor abdulla says

Man you just saved my life.

Karen B says

THANK YOU

Ben Slater says

Thanks really helpful

Martyn Smalskys says

I understand the way to simplify algebraic fractions a bit more now

marshall anderson says

very good

Chima Amobi says

hey Simon what you taught (cancelling algebraic fractions) does it apply

even if the plus and minus symbols are arranged PS thanks for the video it

helped 😉

Phoenix Feathers says

GCSEs this year, just done my mocks and this is one of the topics I messed

up on. Thanks for the help!

Trout Fishing Wales says

Thankyou

Morshada Bagum says

Kinda easy with you

Abdullah A says

Tis all good, but can you do Advanced?

James Topp says

oh and yes your 3 minute videos are great!

James Topp says

thank you this video has helped so much my maths exam is in 4 hours and

this is about all i know ahah youve made it really easy to learn!! 🙂

chriser555 says

I’m lost, no link in the description as stated.

purplekawaiilove says

Maths exam tomorrow 🙁 this was so helpful, thanks 🙂

hany nawaseb says

Smart

MrKidReactionz says

could you please explain why you do not divide (x-5) and (x+2) by x-5 like

you did to cancel out the others because i thought you would have to divide

all the numbers by x-5

apart from this minor confusion thanks a lot because it really helped

(subscribed)

SJGSpook says

Best explanation I have seen. Thanks.

WatsonisawesomeMC says

Came across EXACTLY the same question in my maths exam with exactly the

same digits…

matthew bacon says

thx

Simon Deacon says

No prob and glad to help 🙂

reubz poo says

nice one mate

Simon Deacon says

Hi – there’s a couple of videos on the channel. Try How to factorise

algebra formulas – foundation level, How to factorise algebra formulas –

cross method or How to factorise algebra formulas – higher GCSE cross

method. I hope they help and thanks for your comment. All best S

ToniKristian15 says

i wanna know how the steps to factorize a problem…Thank you..

warren marodza says

good video its jus tht rembering all the methods to math problems can be

stressful how do yu do it…

Simon Deacon says

Hi – that’s great and glad it helped 🙂

SamOwenNewton says

Really helps, thanks!