Help needed! Anyone good at algebra??

[tiachica]

Glad it made more sense, and you are right, the letters itself are not relevant just show what belongs together:

3 (2f +4)

I assume you have to expand the calculations, so this would be

3x2f + 3x4

which is:

6f + 12

[pipscariad]

Glad it made more sense, and you are right, the letters itself are not relevant just show what belongs together:

3 (2f +4)

I assume you have to expand the calculations, so this would be

3x2f + 3x4

which is:

6f + 12

Ah. If that is right, I've just had one of those wonderful dawning of comprehension moments. Thank you! (Are you a teacher? You're very good at explaining things - if so, I wish you were teaching my boys. Their maths teacher apparently gives people detention if they don't understand, although I have said in no uncertain terms that if that happens to them, they are to tell me and I will go to see her with the 'light of battle in my eyes', as my dear departed mum would have said!)

[elsie-scot]

Ah. If that is right, I've just had one of those wonderful dawning of comprehension moments. Thank you! (Are you a teacher? You're very good at explaining things - if so, I wish you were teaching my boys. Their maths teacher apparently gives people detention if they don't understand, although I have said in no uncertain terms that if that happens to them, they are to tell me and I will go to see her with the 'light of battle in my eyes', as my dear departed mum would have said!)

Do hope that isn't true. OH had very bad maths teaching, partly because if you didn't understand you got into trouble, still not sure how he got his o'grade (like o'level), failed higher (like a'level) and still pretty much freaks at any maths, and can't get his head around it.

[HotStuff]

3(2f + 4)

the first thing is to note that the multiplication is implied, so if you think of the bit inside the brackets as an apple the answer would be 3 apples.

But in this case each apple is equal to 2f + 4, you could think of it as 2 grapes + 4.

So the three outside the brackets applies to everything inside the brackets.

Therefore:

3 x 2 grapes = 6 grapes
3 x 4 = 12

So the answer is 6 grapes + 12

Or as 1f = 1 grape

6f + 12

[weekendwellies]

wait til they get onto trigonometry.

[Bigmallly]

And Logarithms.............great fun....not......

[Jeanied]

Differential calculus anyone?

[HotStuff]

wait til they get onto trigonometry.

That's easy, all you have to remember is:

"some old hulks carry a huge tub of ale"

[JanieB]

wait til they get onto trigonometry.

And binary and hexadecimals .

These weren't taught when I was at school but are now relevant because of computers.

I learnt it when my older children were at school to keep ahead of their homework. It stood me in good stead when I took my degree in my forties and had to have remedial maths lessons. I still have trouble with calculus. The headmaster of my school didn't think it worth teaching girls academic subjects (a grammar school in the 60's) and I was only allowed to do basic arithmetic. I did pass GCE maths but I had to do the 2 year course in 1 year and didn't have a proper grounding.

Shame 'cos I'm actually very good at maths and science.

[Nicos]

That's easy, all you have to remember is:

"some old hulks carry a huge tub of ale"

SOH CAH TOA!!!...flipping heck- that tweaked a bit of dust from a couple of brain cells!!!!

[organic]

Firstly, the letters don't mean anything in particular and could be changed... to take the original one:
4u+3v+12u-2v
That could be written as 4a+3b+12a-2b or 4r+3y+12r-2y buy not 4a+3c+12c-2d.
Does that make sense to you?
(Actually, in some circumstances the letters really do mean something specific but we can safely ignore that fact for now.)

Now you're starting to get your head around it I'll elaborate a wee bit further on the "just represents something" bit, and since you liked tiachia's fruit example I'll go with that.

Let's talk about crates of apples.

A crate of Cox (number of cox apples = x) apples weighs 5kg (which is 5,000g), each apple weighs 100g (a).
A crate of Bramleys (number of bramley apples = y) also weighs 5kg (again, 5,000g) and each apple weighs 200g (b).
We'll use w to represent 5,000g.

You have 3 crates of Cox and 5 of Bramleys and you want to know how many apples you've got in total (p).

Each time you want to know you could just calculate it with a calculator, pen and paper, slide rule, abacus or fingers and toes... but if you have it in algebra it can be made simpler. The logic leading up to it will look anything but simple, but if you can follow along maybe you'll see the use of all this algebra nonsense... because using the thing at the end is pretty easy.


Dividing the weight of the crate by the weight of the apples it contains will give you the number of apples. So...

x=w/a
y=w/b

The total number of apples (p) in a crate of bramley and a crate of cox is...
p=x+y

So to figure out how many apples are in the 3 crates of cox and 5 crates of bramley...
p=3x+5y



Now - here's where the thing you were trying to do right at the start of the thread comes in.
Let's say the cox and bramley we've been talking about come from your orchard... but you're going to combine them with a neighbour's apples to bring to market.
They've got 4 crates of Cox and 6 crates of Bramley.
So the total number of apples...

p=3x+5y+4x+6y
That should look a lot like the original one you posted (the only real difference is the "p=" part. The one you posted was just the "expression" to the left of the "=" sign. It all works in the same way though.)

So when you reduce that like you did with the first one...
p=7x+11y


So what use is all that?
Well instead of having to calculate how many apples each of you has and add them up you just do this (from right at the start of all this clear-as-mud gobbledygook)...

x=5000/100
so
x=50 (cox per crate)

y=5000/200
so
y=25 (bramleys per crate)

p=7x50+11x25
p=350+275
p=625

So between you, you've got 625 apples.


I know it's all really long winded in explanation, but if you can wrap your head around this you've got enough of a grasp of algebra to pass that part of your GCSEs and then some!
Other real world uses for this kind of thing?

Combined with π you could use it to figure out whether you get more pizza for your money buying one large and two small or those 3 mediums they have on special offer at the pizza place. (Guess who's done something just like that before!)

It wouldn't surprise me even a TINY bit if your eyes had glazed over well before this point, but if not - well done for getting this far. I've taught before, but never maths (or anything else that uses algebra) so this explanation might be a wee bit clumsy.

On the other hand, if you've actually read this far and understood it all - go me! (...and you, of course!)

Class dismissed.

[Jeanied]

Sometimes I lose the will to live.

Help me, I'm drowning by numbers.

I'm no good at maths until it refers to real things.

[organic]

Jeanied - far from what the previous post might have suggested - I'm much the same... and I did A-Level maths!
(Don't ask why - to this day I can't figure it out... I reeeally wish I'd done something a wee bit less academic... photography would be the choice if I had to go back... all the useful maths I learned was in high school - pythagoras and trig being the main bits.)

[weekendwellies]

That's easy, all you have to remember is:

"some old hulks carry a huge tub of ale"

mine was:

sad old henry caught a herring trawling off america

[pipscariad]

wait til they get onto trigonometry.

No...

And Logarithms.............great fun....not......

No...

Differential calculus anyone?

No...

And binary and hexadecimals .

No....

Not sure I can take this *buries head under pillow*.

Sorry Organic, it's too late for me to attempt to tackle your impressively comprehensive reply - I may have to look at it again in the morning (prolly won't make sense then either, but here's hoping!)

Thanks for your replies one and all, now that you've demonstrated that you understand the things I don't, I may call upon you again .