48÷2(9+3)=?

[The Unworthy Gentleman]

If there is no bracket around the 2(9+3) then how is that any different from writing 2*(9+3), moreover did you read my method, because when you rewrite ÷2 as *0.5 it doesn't matter how you do it as it becomes 288.
EDIT; i dont mean to sound like an ass, its just you didnt comment on my solution.

Sorry, I don't like being wrong and often get worked up when people keep telling me I'm wrong.

The ÷2 doesn't become *0.5 because it isn't the function itself. The function is ÷2(9+3) because it is all one thing, the two is merely the coefficient. It would become ÷24 or in the case of multiplication 0.04 2dp.

The coefficient is not 2. Its 48/2. Like in 3*2x = 6x and has so the coefficient 6.

Lord, give me strength. The coefficient is 2, however it would be 48/2 if the equation was written as such (48/2)(9+3), however it isn't it's 48 ÷ 2(9+3) therefore the coefficient of (9+3) is 2.

 

[DaMullet]

No, you're wrong in one step, 48/2(12) is not the same as 48/2*12
You change an exponent to multiplication for no reason what so ever. Doesn't matter if that's how you solve it, exponents exist for a reason damnit!

Blame the schools. Just like with this BODMAS thing giving people wrong ideas, same thing happens when the notation 2x first appears. Many of us were told 2x = 2*x, but weren't told that it's not actually the same thing. So naturally many assumed if x=2, and 2x=4, then 2x= 2*x, instead of 2x=x+x

Shortcuts in education like that early on is why many struggled with maths in the upper classes, myself included.

~Sylv

I actually do blame the schools, so no worries. Smartest thing to do is know that no matter how much you learn its just a drop in the bucket comparied to how much is out there.


Actually, I want to double check my work.

48/2(9+x)=2
48/(18+2x)=2
48=2(18+2x)
48=36+4x
48-36=4x
4x=12
x=3

Yup, still works.

/thread

 

[tahrey]

Just to add my vote...

Correct answer is 2. Start with the deepest level of brackets and work outwards. This is not merely custom but the way it tends to work in science, programming, etc, and how it's taught in school maths lessons. If you happen to do it some other way, you're being wierd and abnormal and should state when posing the question that it's supposed to be worked out some other way.
(Note that driving on a particular side of the road started out mostly as a customary thing, and indeed in many countries it's only demanded that you pass oncoming traffic on a particular side, but you still wouldn't dream of driving around on the opposite side just because "it's only custom")

Having said that, the scientific calculator function on my calculator comes up with 288, but that's because it's thick, and it doesn't emulate the more sophisticated kind of sci calc where you enter the equation in full on a dot matrix top line before pressing enter. It only works on one operation at a time in most cases (i'm not 100% sure how the brackets thing is supposed to work with them, even), so you have to rearrange the order that you type it in. This, too, was part of my high school maths tuition - proper use of simplistic calculation devices.

However I suspect if you were to type it into any old programming language editor and evaluate it, or use it as part of a program, you would get 2.

Even wierder: Microsoft Calculator returns.... 4.
What?!

 

[InfiniteSingularity]

They say BODMAS over here in Aus, or that's what I was taught anyway. Going by that, it's 288. Brackets first, (9+3)=12. So it becomes 48/2(12), or 48/2x12 to put it another way. Whether division comes first or you do division/multiplication at the same time, left to right, it works out the same. 48/2=24. 24*12=288.

eeeuuuuugggghhhh

Brackets Of Division Multiplication Addition Subtraction. OK?

You got the first part - you go from 48/2(9+3) to 48/2(12). What you are forgetting is that there are still brackets that need to be solved, and because of that, you would expand the brackets before anything else. Even though you evaluate 9+3=12 in the brackets, the 12 remains in the brackets, so it still takes priority. Expand first, so you get 48/24=2

Also remember it is a fraction, so it could be better written as

48
------
2(9+3)

That wrong.

48
------ = 48 / (2*(9+3))
2(9+3)

while the original is

48
--- * (9+3)
2

Nope - brackets, including the coefficient, are one term. You are saying that the coefficient is separate. They do not get separated on either side of the division symbol. You are suggesting that 48/2(9+3) is the same as 48(9+3)/2. You are taking the denominator and moving it into the numerator - it does not make sense and does not equate.

If, by your method, we started by expanding the brackets (which is legit, as brackets come first), the answer would be 2. If we evaluated the brackets and used your method, the answer is 288. Different methods for the same question produce different results. That cannot make sense. Expanding the brackets works, that is a fact - what remains in dispute is your method. Therefore, the proven method must deliver the accurate answer

The answer is still 2.

 

[Thomas Rembrandt]

If there is no bracket around the 2(9+3) then how is that any different from writing 2*(9+3), moreover did you read my method, because when you rewrite ÷2 as *0.5 it doesn't matter how you do it as it becomes 288.
EDIT; i dont mean to sound like an ass, its just you didnt comment on my solution.

Sorry, I don't like being wrong and often get worked up when people keep telling me I'm wrong.

The ÷2 doesn't become *0.5 because it isn't the function itself. The function is ÷2(9+3) because it is all one thing, the two is merely the coefficient. It would become ÷24 or in the case of multiplication 0.04 2dp.

The coefficient is not 2. Its 48/2. Like in 3*2x = 6x and has so the coefficient 6.

Lord, give me strength. The coefficient is 2, however it would be 48/2 if the equation was written as such (48/2)(9+3), however it isn't it's 48 ÷ 2(9+3) therefore the coefficient of (9+3) is 2.

Fine, if your interpretation of 2(x+y) is not the same as 2*(x+y) then you'r right, but the international standard is different. You see ÷2(9+3) as one function (apparently) while the standard is 48 op1 2 op2 (9 op3 3) meaning 3 functions, with multiplication and division beeing equal and to be read left to right.

 

[DaMullet]

Even wierder: Microsoft Calculator returns.... 4.
What?!

I'm sorry... 4?

Microsoft scares me

 

[endnuen]

48÷2(9+3)=?
48/(9*2+3*2)
48/(18+6)
48/24

I would say the invisible multiplication between 2 and the left bracket makes it so.

For it to be interpreted as a fraction, when written in a computer format, there would have been need for a bracket around 48/2.
So (48÷2)*(9+3)=?
But since there isn't it isn't.

no you can't use distributive law when you can still simplify your equation in parentheses

I realised as much, and edited that faulty math out.

 

[Daniel Charlton]

Division and multiplication are treated as equals so its just the closest one to the left is done first, the same goes with adding and subtracting

But mathematically there's nothing stopping you from doing it the other way around... and at times that might come up, and it's better to know the real way you do it instead of something you're taught out of convenience in 2nd grade.

This is the real way of working out how to carry out a question

BODMAS

Brackets
Operations
Divide Multiply
Add Subtract

and just to say I got a 1 in SG maths so i think i know how to do the Maths

 

[InfiniteSingularity]

If there is no bracket around the 2(9+3) then how is that any different from writing 2*(9+3), moreover did you read my method, because when you rewrite ÷2 as *0.5 it doesn't matter how you do it as it becomes 288.
EDIT; i dont mean to sound like an ass, its just you didnt comment on my solution.

Sorry, I don't like being wrong and often get worked up when people keep telling me I'm wrong.

The ÷2 doesn't become *0.5 because it isn't the function itself. The function is ÷2(9+3) because it is all one thing, the two is merely the coefficient. It would become ÷24 or in the case of multiplication 0.04 2dp.

The coefficient is not 2. Its 48/2. Like in 3*2x = 6x and has so the coefficient 6.

Lord, give me strength. The coefficient is 2, however it would be 48/2 if the equation was written as such (48/2)(9+3), however it isn't it's 48 ÷ 2(9+3) therefore the coefficient of (9+3) is 2.

Fine, if your interpretation of 2(x+y) is not the same as 2*(x+y) then you'r right, but the international standard is different. You see ÷2(9+3) as one function (apparently) while the standard is 48 op1 2 op2 (9 op3 3) meaning 3 functions, with multiplication and division beeing equal and to be read left to right.

But brackets are before both multiplication and division. And the coefficient of a bracket is part of the bracket. So you solve 2(9+3) or 2(12) first, which gives you 24. And 48/24 = 2

I can't believe how angry this is making me

 

[Keava]

48/2(12) =/= 48/2x12. The first one is dividing 48 by 2 x 12. The second one is multiplying 48/2 by 12. The first gives an answer of 2. The second gives an answer if 288.
However the question gave us brackets in the denominator - the answer is 2

Since when 48/2(12) is not equal to 48/2*12? What different mathematics they teach in your country? 2*2 is same as (2)(2).

Again. Let's try to make it simpler to understand the logic.

a=48 b=2 c=9+3

a:bc = a:b*c =/= abc)

Also, keep in mind that division is just multiplication by reverse. a:b = a(1/b) = a * (1/b)

so 48:2(9+3) = 48(1:2)(9+3) = 48*0.5*12 = 288

 

[ACman]

Okay, how about this.

A ÷ B * C

=A * 1/B * C
=AC/B

but here

A ÷ BC

= A * 1/BC
=A/BC

 

[JoshGod]

If there is no bracket around the 2(9+3) then how is that any different from writing 2*(9+3), moreover did you read my method, because when you rewrite ÷2 as *0.5 it doesn't matter how you do it as it becomes 288.
EDIT; i dont mean to sound like an ass, its just you didnt comment on my solution.

Sorry, I don't like being wrong and often get worked up when people keep telling me I'm wrong.

The ÷2 doesn't become *0.5 because it isn't the function itself. The function is ÷2(9+3) because it is all one thing, the two is merely the coefficient. It would become ÷24 or in the case of multiplication 0.04 2dp.

It is apparant to me that you think think 2(12) are grouped while I think that because there is no bracket around them and that you can rewrite 2(12) as 2*(12) that they must be considered seperately instead of a single entity. I doubt we will see eye to eye however i'm sure we can agree the question should be written as either (48÷2)(9+3) or 48÷(2(9+3)). lets just agree the question is stupid.

 

[bliebblob]

Probably been said 46 times by now but just have to get this out of my system.

It's 2 because step 1 of bedmas (or whatever it's called in english) is getting rid of brackets.
In a case like x(a+b) however you cant just calculate whatever is between the brackets and than remove them, because it is special situation.
( dunno what the term is in english, word for word translation from my language is "strange multiplication" )
The proper way to deal with this special case is:
x(a+b) = (x*a)+(x*b)
so in this situation you get rid of the brackets like this:
2(9+3) = (2*9)+(2*3) = 18+6=24
This is also correct:
2(9+3)=2(12)=24
Since getting rid of brackets is always step 1 you do this before you do anything else. So you get:
48÷24
wich is ofcourse 2

This is NOT correct:
2(9+3)=2(12)=2*12
Followed by
48÷2*12
wich is 288 (step 3 and 4 of bedmas: divisions, than multiplications, from left to right)
Why is this wrong? Because you can't just replace 2(12) with 2*12 and move on to the next steps of BEDMAS. If you do this you didn't fully get rid of the brackets yet.
Step one of BEDMAS is not complete.
Only solving what is between the brackets and than removing them is not the same as properly getting rid of them. Even though it usually gives the same result.
The reason many people think replacing 2(12) with 2*12 is ok here is because it usually gives the same result anyway.


It's very very easy to get confused though because of the way it is written, that's why it's normally written like this:
48
---------- = 2
2(9+3)

or

48
---- * (9+3)= 288
2

Final note: calculators (and probably a lot of computer programs) do not automatically do the "weird multiplication". You have to force them to do it by putting extra brackets like this: 48÷(2(9+3))

 

[Thomas Rembrandt]

[quote="Thomas Rembrandt"


You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

 

[InfiniteSingularity]

48/2(12) =/= 48/2x12. The first one is dividing 48 by 2 x 12. The second one is multiplying 48/2 by 12. The first gives an answer of 2. The second gives an answer if 288.
However the question gave us brackets in the denominator - the answer is 2

Since when 48/2(12) is not equal to 48/2*12? What different mathematics they teach in your country? 2*2 is same as (2)(2).

Again. Let's try to make it simpler to understand the logic.

a=48 b=2 c=9+3

a:bc = a:b*c =/= abc)

Also, keep in mind that division is just multiplication by reverse. a:b = a(1/b) = a * (1/b)

so 48:2(9+3) = 48(1:2)(9+3) = 48*0.5*12 = 288

Did you not read my post? I explained the logic. Let me give you another one of my many justifications as to why I am right:

BODMAS specifies brackets come before anything, right?

2(9+3) is one set of brackets. It is ONE TERM. You solve it ALL AT ONCE. And guess what? It equals 24.

I'm pretty sure we all agree on the simplification up to 48/2(12). Now tell me: Does 48/2(12) equal 48(12)/2? You are moving the 12 from the bottom to the top - you are, quite literally, changing the value of 1/12 into 12/1. You are saying 1/12 = 12. Does it? Because last time I checked it doesn't.

[EDITED typo]

 

[The Unworthy Gentleman]

Fine, if your interpretation of 2(x+y) is not the same as 2*(x+y) then you'r right, but the international standard is different. You see ÷2(9+3) as one function (apparently) while the standard is 48 op1 2 op2 (9 op3 3) meaning 3 functions, with multiplication and division beeing equal and to be read left to right.

You're right, my interpretation of 2(x+y) is not the same as my interpretation of 2*(x+y) and neither should yours, otherwise I doubt every other countries mathematics. 2(x+y) is all one number, unlike 2*(x+y) because that is two numbers separated by a function. While they produce the same result on their own, they produce wildly different numbers when applied. This is exactly why you never add functions to an equation willy nilly, like those who got 288 did.

The order of operations is right, but your application of functions is wrong. It should have went 48 op1 2(9 op2 3).

 

[InfiniteSingularity]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

EDIT: 2(x+y) is one term, is it not? Isn't 2 the coefficient of the bracket? And does it not equal 2x + 2y?

Now lets substitute x and y with, say, 9 and 3

2(9+3) = 2x9 + 2x3. This is 18 + 6 - which is 24.

That SINGLE TERMis the denominator - so quite clearly this is 48/24 which is 2

 

[The Unworthy Gentleman]

It is apparant to me that you think think 2(12) are grouped while I think that because there is no bracket around them and that you can rewrite 2(12) as 2*(12) that they must be considered seperately instead of a single entity. I doubt we will see eye to eye however i'm sure we can agree the question should be written as either (48÷2)(9+3) or 48÷(2(9+3)). lets just agree the question is stupid.

I'm afraid I can't do that Dave Josh. It is one number because the 2 is a coefficient and there is no operation between them, where x = 12 2x = 2(12)... c'mon, argue with me. Okay, I'll let you go, you were a worthy foe.

 

[Thomas Rembrandt]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

 

[InfiniteSingularity]

You are suggesting that 48/2(9+3) is the same as 48(9+3)/2.

Yes i do. 48*(9+3)/2 = 48 * (9+3)* 0.5 and equals 288 as well.

I don't know what you learnt, but i think you misunderstand what a coefficient is. Usually we have equations like 2x + 3y where it is clear what numbers are bound to which variables.

In the OP's equation we have to remember how the basic notations work. 3x/2 is just 3 * x * 0.5.

You are wrong, sorry.

48-----1---------48----(9+3)
---- x ----- =/= ------ x -----
2-----(9+3)------2------1

This is your fatal error, and i'm afraid it's pretty significant

I don't know what you mean. That's like telling me 2+2 is not 2-2. I never said your strange equation there. (i use the star * as multiplication, maybe you misinterpreted my equation).

I'm pretty sure 4 isn't 0. And I understood the star * as multiplication. You just don't understand that multiplying something by 1/12 is not the same as multiplying it by 12/1.

Also read my edit to that post

2(x+y) is one term, is it not? Isn't 2 the coefficient of the bracket? And does it not equal 2x + 2y?

Now lets substitute x and y with, say, 9 and 3

2(9+3) = 2x9 + 2x3. This is 18 + 6 - which is 24.

That SINGLE TERM is the denominator - so quite clearly this is 48/24 which is 2