48÷2(9+3)=?

[ACman]

Right so it can be read as 48/2*(9+3) which is 48/2*12 then with order of operations taking / as standard division symbol and not a fraction line it is 288. You are taking it as though it would be a fraction line so we have 48 over 2*12 which does give 2. So yes it is ambiguous. You can chop and change it whatever way you like but standard order does not favour you but algebra shows you as right. What we need is more brackets and stop this shit everytime someone rehashes this flamebaiting thread.

My issue is not with the division symbol at all. My issue is that people are dismissing coefficients altogether. The 2 is a coefficient of (9+3) and not as something to divide the 48 by.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

This is why the answer must be 2. If the coefficient is disregarded and a function is added in like dividing the 48 by 2 then the answer will be changed drastically.

Ohhh! Thankyou fellow voice of reason.

 

[Sylvine]

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

 

[Thomas Rembrandt]

Right so it can be read as 48/2*(9+3) which is 48/2*12 then with order of operations taking / as standard division symbol and not a fraction line it is 288. You are taking it as though it would be a fraction line so we have 48 over 2*12 which does give 2. So yes it is ambiguous. You can chop and change it whatever way you like but standard order does not favour you but algebra shows you as right. What we need is more brackets and stop this shit everytime someone rehashes this flamebaiting thread.

My issue is not with the division symbol at all. My issue is that people are dismissing coefficients altogether. The 2 is a coefficient of (9+3) and not as something to divide the 48 by.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

This is why the answer must be 2. If the coefficient is disregarded and a function is added in like dividing the 48 by 2 then the answer will be changed drastically.

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

 

[ACman]

48 ÷ (9+3)2

It makes no difference to the way the equation works in the second form, but makes drastic changes to the way the equation works in the first one.

There is something you are missunderstanding which is that the 2 and the (9+3) are not glued together, they do not have brackets around them, the problem is due to peoples misinterpretation with the divide, however if we rewrite the equation to change it all into multiplication it becomes clearer.
48÷2(9+3)
=48÷2*(9+3)
as ÷2 = *0.5
48÷2*(9+3)
=48*0.5*(9+3)
=48*0.5*12
=48*6
=288

No, they are glued together and that is very much fact. The 2 is the coefficient of the brackets and must be treated as a part of them, there is no getting around that. Your mistake is treating the 2 as if it weren't glued to the brackets and inserting a multiplication symbol into it. There is no problem with the divide at all. Again, lets look at a different equation to prove I'm right (although the last one didn't go well). Also, I will end up seeming really patronising, so I apologise in advance, I just want to jump through every single hoop.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

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.

It's very different. You're adding an operation that wasn't there in the first place.

 

[intheweeds]

well if it were a statement in java, the brackets resolve first, leaving you with:
48/2(12)
now you have division and multiplication left to resolve. Since they are equal in priority, they resolve left to right. So:

24*12 = 288

I would assume programming languages use the same math as math, but i haven't been in high school for a very long time, i wouldn't remember exactly.

48/2(12) is different to 48/2*12

Brackets first! Including coefficients of brackets!

this is how it would resolve - IF it were in Java. However, in java you would never write 2(12), brackets confuse the reader since the language uses brackets for other reasons. Honest i wouldn't even know if it would resolve like that. never tried. In Java the equation would be:

48/2 *(9+3)

you'll notice the brackets did resolve first. I never claimed to be a high school math expert. Go start tutoring if you're so smart.

 

[legendp]

I have never seen a thread this long over a maths equation. this is sorta ridiculous (and intriguing) . why do you need to know ?

 

[ACman]

Right so it can be read as 48/2*(9+3) which is 48/2*12 then with order of operations taking / as standard division symbol and not a fraction line it is 288. You are taking it as though it would be a fraction line so we have 48 over 2*12 which does give 2. So yes it is ambiguous. You can chop and change it whatever way you like but standard order does not favour you but algebra shows you as right. What we need is more brackets and stop this shit everytime someone rehashes this flamebaiting thread.

My issue is not with the division symbol at all. My issue is that people are dismissing coefficients altogether. The 2 is a coefficient of (9+3) and not as something to divide the 48 by.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

This is why the answer must be 2. If the coefficient is disregarded and a function is added in like dividing the 48 by 2 then the answer will be changed drastically.

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

Yeah but here its a division operation so you'd end up with the fraction 3 on 2x.

 

[Thomas Rembrandt]

48 ÷ (9+3)2

It makes no difference to the way the equation works in the second form, but makes drastic changes to the way the equation works in the first one.

There is something you are missunderstanding which is that the 2 and the (9+3) are not glued together, they do not have brackets around them, the problem is due to peoples misinterpretation with the divide, however if we rewrite the equation to change it all into multiplication it becomes clearer.
48÷2(9+3)
=48÷2*(9+3)
as ÷2 = *0.5
48÷2*(9+3)
=48*0.5*(9+3)
=48*0.5*12
=48*6
=288

No, they are glued together and that is very much fact. The 2 is the coefficient of the brackets and must be treated as a part of them, there is no getting around that. Your mistake is treating the 2 as if it weren't glued to the brackets and inserting a multiplication symbol into it. There is no problem with the divide at all. Again, lets look at a different equation to prove I'm right (although the last one didn't go well). Also, I will end up seeming really patronising, so I apologise in advance, I just want to jump through every single hoop.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

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.

It's very different. You're adding an operation that wasn't there in the first place.

Where is he adding an operation? The original has 4 (three are seen, but thats just convenient notation) and his formula has 4 as well.

 

[Keava]

You're adding a operation that wasn't originally there and changing the answer.

No. Because multiplication symbol can be omitted if followed by brackets or variable. It doesn't change anything. It's still just multiplication.

2x = 2 * x
x(2+3) = x * (2+3) = x * 5 = 5x

So 2(9+3) = 2 * (9+3)


Thing is people misunderstand the way mathematical problems are supposed to be written.

When you have a:b(c+d) it equals
a
-(c+d)
b

You are allowed to skip the brackets if they do not change the order of calculations.

If it was written as a:[b(c+d)] then, and only then you could write it as
a
-----
b(c+d)

 

[JoshGod]

48 ÷ (9+3)2

It makes no difference to the way the equation works in the second form, but makes drastic changes to the way the equation works in the first one.

There is something you are missunderstanding which is that the 2 and the (9+3) are not glued together, they do not have brackets around them, the problem is due to peoples misinterpretation with the divide, however if we rewrite the equation to change it all into multiplication it becomes clearer.
48÷2(9+3)
=48÷2*(9+3)
as ÷2 = *0.5
48÷2*(9+3)
=48*0.5*(9+3)
=48*0.5*12
=48*6
=288

No, they are glued together and that is very much fact. The 2 is the coefficient of the brackets and must be treated as a part of them, there is no getting around that. Your mistake is treating the 2 as if it weren't glued to the brackets and inserting a multiplication symbol into it. There is no problem with the divide at all. Again, lets look at a different equation to prove I'm right (although the last one didn't go well). Also, I will end up seeming really patronising, so I apologise in advance, I just want to jump through every single hoop.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

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.

It's very different. You're adding an operation that wasn't there in the first place.

I'm not adding anything i'm mearly rewriting the equation as dividing by two is multiplaying by a half, 12*0.5=6 and 12/2=6.

 

[ACman]

well if it were a statement in java, the brackets resolve first, leaving you with:
48/2(12)
now you have division and multiplication left to resolve. Since they are equal in priority, they resolve left to right. So:

24*12 = 288

I would assume programming languages use the same math as math, but i haven't been in high school for a very long time, i wouldn't remember exactly.

48/2(12) is different to 48/2*12

Brackets first! Including coefficients of brackets!

this is how it would resolve - IF it were in Java. However, in java you would never write 2(12), brackets confuse the reader since the language uses brackets for other reasons. Honest i wouldn't even know if it would resolve like that. never tried. In Java the equation would be:

48/2 *(9+3)

you'll notice the brackets did resolve first. I never claimed to be a high school math expert. Go start tutoring if you're so smart.

In java but in java and most other languages insist on operations between each number.

On paper

48/2(12) = 2

and

48/2*12 = 288

 

[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)

If that makes sense. So you would expand the brackets/evaluate the denominator like so:

48
-----
2(12)

Now, the denominator is one term, and the numerator is another. You wouldn't cross them over like you did. Why? Because fractions divide the top and bottom into different terms. If you divided the 48 by 2 straight away (like you did) it would cancel it into 24/1.

24
-----
1(12)

Now we still have the 12 - you are suggesting that we would now multiply by 12, so instead it would look like this:

24
---- x 12
1

which is 288. However, what are we forgetting? the 12 is on the bottom. Therefore, we multiply 24 not by 12, but by 1/12

24...1
-- x ---
1.....12

which is 24/12 which is 2.

How do we know this? Well, take it back to the original question - what are we asked?

48...........48 .....1.---------.......48
-------- = ---- x -----, and not ----- x (9+3)
2(9+3)....2.....(9+3)....-.-------.2

Simple fraction multiplication. The answer is 2.

 

[intheweeds]

I have never seen a thread this long over a maths equation. this is sorta ridiculous (and intriguing) . why do you need to know ?

i feel like this is just an excuse for the math nerds to flame. Next OP should start a thread entitled "What's Wrong With This Grammar?"

 

[Thomas Rembrandt]

Right so it can be read as 48/2*(9+3) which is 48/2*12 then with order of operations taking / as standard division symbol and not a fraction line it is 288. You are taking it as though it would be a fraction line so we have 48 over 2*12 which does give 2. So yes it is ambiguous. You can chop and change it whatever way you like but standard order does not favour you but algebra shows you as right. What we need is more brackets and stop this shit everytime someone rehashes this flamebaiting thread.

My issue is not with the division symbol at all. My issue is that people are dismissing coefficients altogether. The 2 is a coefficient of (9+3) and not as something to divide the 48 by.

2x
It's plain to see that the coefficient of x is 2, correct? And that 2x can be rewritten as 2(x)? Because 2*x is 2x. So:

20 ÷ 2x can be rewritten as 20 ÷ 2(x)
So, with the same principle you applied to before you could say that

20 ÷ 2x = (20 ÷ 2)(x)
If x = 4 then

20 ÷ 2(4) = (20 ÷ 2)(4)
2.5 =/= 40

So you can't separate the coefficient from it's partner because they are very much glued together.

This is why the answer must be 2. If the coefficient is disregarded and a function is added in like dividing the 48 by 2 then the answer will be changed drastically.

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

Yeah but here its a division operation so you'd end up with the fraction 3 on 2x.

Right. 3/2*x = 1.5x and not 3/(2x).

 

[intheweeds]

well if it were a statement in java, the brackets resolve first, leaving you with:
48/2(12)
now you have division and multiplication left to resolve. Since they are equal in priority, they resolve left to right. So:

24*12 = 288

I would assume programming languages use the same math as math, but i haven't been in high school for a very long time, i wouldn't remember exactly.

48/2(12) is different to 48/2*12

Brackets first! Including coefficients of brackets!

this is how it would resolve - IF it were in Java. However, in java you would never write 2(12), brackets confuse the reader since the language uses brackets for other reasons. Honest i wouldn't even know if it would resolve like that. never tried. In Java the equation would be:

48/2 *(9+3)

you'll notice the brackets did resolve first. I never claimed to be a high school math expert. Go start tutoring if you're so smart.

In java but in java and most other languages insist on operations between each number.

On paper

48/2(12) = 2

and

48/2*12 = 288

ok i'm going to ignore you now since you clearly didn't read my post fully. TWICE.
I have bolded the parts you didn't read for your convenience.

 

[ACman]

You're adding a operation that wasn't originally there and changing the answer.

No. Because multiplication symbol can be omitted if followed by brackets or variable. It doesn't change anything. It's still just multiplication.

2x = 2 * x
x(2+3) = x * (2+3) = x * 5 = 5x

So 2(9+3) = 2 * (9+3)


Thing is people misunderstand the way mathematical problems are supposed to be written.

When you have a:b(c+d) it equals
a
-(c+d)
b

You are allowed to skip the brackets if they do not change the order of calculations.

If it was written as a:[b(c+d)] then, and only then you could write it as
a
-----
b(c+d)

No.

a:b(c+d) equals

a
-
b(c+d)

a:b*(c+d) equals

a
-(c+d)
b

In this question the b is a coefficient to the brackets so its processed before the division symbol.

 

[dday4you]

I have never seen a thread this long over a maths equation. this is sorta ridiculous (and intriguing) . why do you need to know ?

figures

 

[Thomas Rembrandt]

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

 

[Ashcrexl]

seven pages of pure mathematical madness. because i don't like implied multiplication, i'll go with the 288.

 

[InfiniteSingularity]

You're adding a operation that wasn't originally there and changing the answer.

No. Because multiplication symbol can be omitted if followed by brackets or variable. It doesn't change anything. It's still just multiplication.

2x = 2 * x
x(2+3) = x * (2+3) = x * 5 = 5x

So 2(9+3) = 2 * (9+3)


Thing is people misunderstand the way mathematical problems are supposed to be written.

When you have a:b(c+d) it equals
a
-(c+d)
b

You are allowed to skip the brackets if they do not change the order of calculations.

If it was written as a:[b(c+d)] then, and only then you could write it as
a
-----
b(c+d)

Close

BODMAS specifies that brackets must be solved first. So when there are brackets present they must be solved as a priority. Agreed?

Now when you have 2(9+3) it is the same as 2 x (9+3), which is the same as 2(12). When you put it as a denominator, it is different.

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