6÷2(1+2)= ?

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it amazes me how many people can't do simple algebraic simplification according to the basic rules of maths.

Brackets are what is IN them not touching.
ab = a*b =a(b)=a*(b)

a(b) is not a shorthand way of saying (a*(b))

so
6/2(1+2)
=6/2(3) = 6/2*3
=3(3) = 3*3
=9

for the answer to be 1 the sum would need to have an extra set of brackets.
6/(2(1+2))
=6/(2(3)) = 6/(2*3)
= 6/(6) = 6/6
=1

and I am a third year engineering student and deal with far more complex algebraic expressions on a day to day basis
 
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Aren't you multiplying a fraction by a whole number?

6/2 (1+2)

6over2 * (1+2)over1 = 18over2 = 9
 
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Who would have thought it could be so complicated! I've really tried to follow all the methods discussed and, at the risk of going off topic, can I just say -





my tiny brain hurts!! :bonk::bonk::bonk: :)


Jean

I *thought* the answer was 9 - now I'm just confused! :)
 
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alastairb said:
it amazes me how many people can't do simple algebraic simplification according to the basic rules of maths.

Brackets are what is IN them not touching.
ab = a*b =a(b)=a*(b)

a(b) is not a shorthand way of saying (a*(b))

so
6/2(1+2)
=6/2(3) = 6/2*3
=3(3) = 3*3
=9

for the answer to be 1 the sum would need to have an extra set of brackets.
6/(2(1+2))
=6/(2(3)) = 6/(2*3)
= 6/(6) = 6/6
=1

and I am a third year engineering student and deal with far more complex algebraic expressions on a day to day basis
Click to expand...

If you are doing algebra, how would you expand out a(b+c) ?

The reality of all of this is that the equation is not written correctly. It should be either:

(6/2)(1+2)

or

6 x (1+2)
________
2

or

6
________
2(1+2)

or

6 ÷ (2(1+2))

The equation as written i.e. 6÷2(1+2) is ambiguous and open to interpretation. I have never seen one written this way.

Applying algebra strictly would give 6 ÷ 2 + 4 = 7 (see post 81)

If you applied plain english...it could be 6 apples divided between a pair of boys (2x1) and 2 pairs of girls (2x2) equals one apple for each person.

If you apply BODMAS strictly you would get 9 ignoring the apparent intent of the equation and the implicit multiplication.

Arguably all of the above could be right depending on your viewpoint. The bottom line though is that the equation is badly written and should be one of those suggested above. An equation would only be written for a set of circumstances and the only unambiguous way to do it is one of the corrected versions.
 
Defiance said:
If you are doing algebra, how would you expand out a(b+c) ?

The reality of all of this is that the equation is not written correctly. It should be either:

(6/2)(1+2)

or

6 x (1+2)
________
2

or

6
________
2(1+2)

or

6 ÷ (2(1+2))

The equation as written i.e. 6÷2(1+2) is ambiguous and open to interpretation. I have never seen one written this way.

Applying algebra strictly would give 6 ÷ 2 + 4 = 7 (see post 81)

If you applied plain english...it could be 6 apples divided between a pair of boys (2x1) and 2 pairs of girls (2x2) equals one apple for each person.

If you apply BODMAS strictly you would get 9 ignoring the apparent intent of the equation and the implicit multiplication.

Arguably all of the above could be right depending on your viewpoint. The bottom line though is that the equation is badly written and should be one of those suggested above. An equation would only be written for a set of circumstances and the only unambiguous way to do it is one of the corrected versions.
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when on its own the same was i expanded a(b) above, so ab+ac

and getting the result of 7 is just wrong, i see no way of justifying it?

i do see how the answer of 1 could be got, but based on maths i don't see it as correct
 
alastairb said:
when on its own the same was i expanded a(b) above, so ab+ac

and getting the result of 7 is just wrong, i see no way of justifying it?

i do see how the answer of 1 could be got, but based on maths i don't see it as correct
Click to expand...

if you expand a(b+c) into ab+ac and apply it to the equation you get

6 ÷ 2 + 4 (algebra is d ÷ ab + ac)

Follow BODMAS priority and you get 7 i.e 6 ÷ 2 = 3 then + 4 = 7

I agree it looks wrong but it's just as plausible as the alternatives.

However it better serves to illustrate how the equation is written incorrectly or unrealistically and certainly not how a mathematician would write it.
 
Peter10d said:
A new campaign for 7, by the looks of it:thinking:
I am sticking with 9, but surely there is one Maths teacher amongst all the TP members that can solve this for once and all:D
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i used to teach maths and science, the answer is 9.
 
Creaxel_photo said:
This certainly is not the way to expand a bracket, if you have a(b+c) you get ab+ac and not what you getting at.

You cannot separate the 2 from the bracket when expanding.

The proof i used is a simple equation, to solve for x.
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Who's expanding anything? I'm simply transposing the equation algebraically - perfectly valid and it disproves the validity of your proof. I didn't bother to simplify the equation further because it's plain to see that the result is valid.

This is basic stuff - anyone who works in any form of engineering that uses formulae will be used to doing this. As long as you do the same thing to both sides of the equation then it's perfectly valid.
 
It's 9. If there is no sign before the brackets it's a multiplication that's what I was taught in maths at school and science at uni it's also what I teach my students so it better be right
 
DemiLion said:
Try learning real mathematics rather than blindly quoting what you've read on the internet.
Click to expand...

I'm more than competant thank you. Did you read the thread? Did you read my quoted extract? No, I thought not.

I was merely providing assistance to those who appear to be getting the basics wrong. Like you!
 
If the answer was intended to be 9 then the equation would be written by anyone above junior school maths as:

3 * 3

at worst it would be written as

3 * (1+2)

There is no logical reason to write it as 6 ÷ 2(1+2)

The latter is clearer written with 2(1+2) as a distributive property (per mathematical convention).

This distributive property has to be resolved before solving the equation.

Only when the distributive property has been resolved can BODMAS be applied.
 
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SIX pages on 1 or 9
.
.
.
. and FOUR pages of ''Unanswered posts''......................:nono:
 
I had to google what a distributive property is, but if you read http://math.about.com/od/algebra/a/distributive.htm which explains what they are, eg breaking up 4*14 into 4*(10+4) = 4*10 + 4*4 then it is not at all valid in this case.

as distributive properties do not break algebraic rules! and if it was written as a mid point through applying a distribute property it would need to have had an extra set of brackets applied.
 
alastairb said:
I had to google what a distributive property is, but if you read http://math.about.com/od/algebra/a/distributive.htm which explains what they are, eg breaking up 4*14 into 4*(10+4) = 4*10 + 4*4 then it is not at all valid in this case.

as distributive properties do not break algebraic rules! and if it was written as a mid point through applying a distribute property it would need to have had an extra set of brackets applied.
Click to expand...

With the greatest of respect if you had to google a distributive property then I'm not sure how you can state categorically whether it is valid or not.

It's not about breaking a sum into component parts as you illustrate above.

As a distributive property is does not require brackets (although nothing would change if they were added).

Also BODMAS is a rule basically created for school kids not as a hard and fast rule for algebra or pure mathematics.
 
Islander said:
No, I was using an example of implied operations.

The answer is 9.

In my previous career I was an electronics engineer and worked in design of complex audio filters and amplifiers in an R&D lab - I used paper to perform operations much harder than this including j notation (imaginary numbers - electrical and electronic engineers use j rather than i to avoid confusion). :p
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I hope I don't buy any of your audio gear then, they'll be way off spec if you get an answer of 9

alastairb said:
it amazes me how many people can't do simple algebraic simplification according to the basic rules of maths.

Brackets are what is IN them not touching.
ab = a*b =a(b)=a*(b)

a(b) is not a shorthand way of saying (a*(b))

so
6/2(1+2)
=6/2(3) = 6/2*3
=3(3) = 3*3
=9

for the answer to be 1 the sum would need to have an extra set of brackets.
6/(2(1+2))
=6/(2(3)) = 6/(2*3)
= 6/(6) = 6/6
=1

and I am a third year engineering student and deal with far more complex algebraic expressions on a day to day basis
Click to expand...

Don't let your maths tutor see this thread then or he'll have to fail you.

Creaxel_photo said:
If we use a simple proof and substitute 1 with 'x' and try the values we get something like this

6/2(x+2)=9
6/2x+4=9
6=9(2x+4)
6=18x+36
-30=18x
x= -(30/18), which definitely isnt 1.

6/2(x+2)=1
6/2x+4=1
6=1(2x+4)
6=2x+4
2=2x
x=1

Well the proof says 1 is correct.
Click to expand...

Finally someone making complete sense for everyone to see, just as Fabs has been trying to explain all along.


The answer is unequivocally 1
 
Critical I said:
Nope. Evaluating brackets first ONLY applies to those numbers IN the brackets.

ab is a convention for writing a*b, hence a(b+c) is the same as a*(b+c). Missing out the operator does not change the order.

a/b(c+d) is simply a/b*(c+d) in shorthand. Missing out the * does not imply it becomes a/(b*(c+d))

And yes I used to teach maths.
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joescrivens said:
i used to teach maths and science, the answer is 9.
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clairelily said:
It's 9. If there is no sign before the brackets it's a multiplication that's what I was taught in maths at school and science at uni it's also what I teach my students so it better be right
Click to expand...

We have three people who actually teach maths agreeing that the answer is 9 :p

I wouldn't want to argue with that ;)
 
joescrivens said:
i used to teach maths and science, the answer is 9.
Click to expand...

Yes, of course.

But in the internet age science and maths are now just a matter of opinion, like religion and politics. We should take a vote.... (no please I am just joking :shake:)
 
Defiance said:
If you did this by algebra the equation looks like this:

a ÷ b(c+d) = e

this would also be written as:

a ÷ bc + bd = e

inserting the numbers back in would be:

6 ÷ 2 + 4 = 7
Click to expand...



Your algebra is wrong - if you expand b(c+d) to give bc+bd it would all have to be under the divide line (if writing out properly over two lines) otherwise you wouldn't be able to multiple out
a____
b(c+d)

would give
a_____
bc + bd


whereas to expand out the below you would need an equals sign something like this
a * (c+d) = y
b

a * (c+d) = by
 
9 without reading the rest of the thread :lol: always solve brackets first, so you essentially you have 3x3=9.
 
The education system was pants when I went to school and fraught with teacher strikes, but I'd put it this way.
If I'm depositing money at the bank, it's 9, if I'm withdrawing it's one but they have to give me nine. If the wife asks me how much I've got it's one and when she asks how much she owes me it's nine.;)

Maybe my teachers weren't that bad after all:thinking::D


For the record I made it 9.
 
Doog said:
The education system was pants when I went to school and fraught with teacher strikes, but I'd put it this way.
If I'm depositing money at the bank, it's 9, if I'm withdrawing it's one but they have to give me nine. If the wife asks me how much I've got it's one and when she asks how much she owes me it's nine.;)

Maybe my teachers weren't that bad after all:thinking::D

For the record I made it 9.
Click to expand...

Haha quality post!
 
Critical I said:
I think you just failed your maths GCSE.
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I asked my 15 year old sister just who is doing GCSE maths higher, she worked it out using the method taught in schools, she made 1.
Myself and my Dad made 9 :bonk:
 
If only any of my cartoon threads received this much attention. :shake:


:naughty: :D ;)


AND my photography threads, come to think of it.
 
Now at 7 pages in length and all you've managed to do is confuse the hell out of me:thinking::thinking:

Does 1+1 still make 2 or is that now wrong as well:shrug:
 
Ploddles said:
I hope I don't buy any of your audio gear then, they'll be way off spec if you get an answer of 9
The answer is unequivocally 1
Click to expand...

Funny that, it worked really well - bang on spec and sold all over the world. :p
 
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