I said it was a fraction, but you misunderstand me.
A fraction is the symbol for division, so 48/2 = 24. If you use a fraction to demonstrate the division in the equation then there is no room to misunderstand what you have to do to get the answer
Debate: 48 ÷ 2(9+3) = ?
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A fraction is the symbol for division, so 48/2 = 24. If you use a fraction to demonstrate the division in the equation then there is no room to misunderstand what you have to do to get the answer
I see what you mean now. Yes, that is correct, but shouldn't be necessary still.
Due to a clash of understandings of order of operations, it could be both answers. Personally, I would have calculate the answer as 2, for reasons given below.
If we have the equation 3/7x this implies that the 7x takes priority in the calculation, as it does when you solve most algebraic equations, and thus is calculated before dividing 3 by it.
If we extend the brackets, we get 48 / 2*12
I prefer to represent divisions as fractions, and thus 48 / 2*12 is the same as 48/2 multiplied by 1/12 (remember the rule for multiplying fractions).
Which equals 24 * 1/12
Which equals 2.
Depends on your method.
If we have the equation 3/7x this implies that the 7x takes priority in the calculation, as it does when you solve most algebraic equations, and thus is calculated before dividing 3 by it.
If we extend the brackets, we get 48 / 2*12
I prefer to represent divisions as fractions, and thus 48 / 2*12 is the same as 48/2 multiplied by 1/12 (remember the rule for multiplying fractions).
Which equals 24 * 1/12
Which equals 2.
Depends on your method.
So, 48/2(9+3).
The issue here stems from the fact that the (9+3) is not clear whether it is multiplied to the numerator or the denominator. If it was going to the numerator, a more "clear" formula might have been (48/2)(9+3) which ends up being ((48)(9+3))/2 = (48*12)/2 = 288.
However, I see the implied multiplication as the second option:
48/(2*(9+3)) = 48/(2*12) = 2. I believe this to be the correct translation because of the way higher level mathematics is written. Imagine this on paper, it would be a 48 over a horizontal line, then 2(9+3) on the bottom. Things are written this way in more (not extremely) complex division where you might factor out a constant or an x and have that on the outside. When writing these examples via computer, the standard (at least at my university) is to use the division symbol as sort of a "division" of the problem; everything before it is multiplied on the top, everything after it is multiplied on the bottom.
Of course, following simple PEMDAS (order of operations) the answer should actually be 288, because Multiplication and Division are ranked equally, but from left to right.
So, by order of operations:
48/2(9+3) - parenthesis first, (9+3) -> 12
48/2(12) - Multiplication/division from right to left:
48/2 = 24 -> 24 * 12 = 288.
Jayfeather21
The issue here stems from the fact that the (9+3) is not clear whether it is multiplied to the numerator or the denominator. If it was going to the numerator, a more "clear" formula might have been (48/2)(9+3) which ends up being ((48)(9+3))/2 = (48*12)/2 = 288.
However, I see the implied multiplication as the second option:
48/(2*(9+3)) = 48/(2*12) = 2. I believe this to be the correct translation because of the way higher level mathematics is written. Imagine this on paper, it would be a 48 over a horizontal line, then 2(9+3) on the bottom. Things are written this way in more (not extremely) complex division where you might factor out a constant or an x and have that on the outside. When writing these examples via computer, the standard (at least at my university) is to use the division symbol as sort of a "division" of the problem; everything before it is multiplied on the top, everything after it is multiplied on the bottom.
Of course, following simple PEMDAS (order of operations) the answer should actually be 288, because Multiplication and Division are ranked equally, but from left to right.
So, by order of operations:
48/2(9+3) - parenthesis first, (9+3) -> 12
48/2(12) - Multiplication/division from right to left:
48/2 = 24 -> 24 * 12 = 288.
Jayfeather21
So following that, I guess you need context.
If it's normal math you use PEMDAS = 288
If it's calculus 2 tier divide 48 by the entire equation = 2
edit:
The equation is not asking for 48 OVER 2(9+3) but actually 48 DIVIDED BY 2 (9+3) with 9 plus 3 separated. The first completely ignores the rules of PEMDAS in pursuit of higher level math, which I don't think is the point of the basic equation at all
If it's normal math you use PEMDAS = 288
If it's calculus 2 tier divide 48 by the entire equation = 2
edit:
The equation is not asking for 48 OVER 2(9+3) but actually 48 DIVIDED BY 2 (9+3) with 9 plus 3 separated. The first completely ignores the rules of PEMDAS in pursuit of higher level math, which I don't think is the point of the basic equation at all
If it's not meant to have 48 as the numerator and 2(9+3) as the denominator, then why on earth is there a division symbol between them and why is 2 attached to (9+3)? The equation is just vague as stated above.
The 2(9+3) part can be seen as 2*(9+3) it's just mathematicians being lazy.
And the (9+3) just adds more confusion, as it's just a 12 split into two numbers.
Sigh, the answer is 288
What people seen to be mixing up when they get 2 is BODMAS or BIDMAS or PEMDAS or whichever they were taught
depending on which you notice that the D and the M are swapped around in some of the orders. really you should look at them as if they have 4 steps, not 6.
1. B
2. I
3. (DM)
4. (AS)
1. P
2. E
3. (MD)
4. (AS)
if you have done all brackets and exponents, and there are both multiplication and divisions, instead of doing one then the other, you do step 3, and just work from left to right doing both the divisions and the multiplications as they come.
After that you move to step 4. and do the additions and subtractions from left to right.
Ta da!
What people seen to be mixing up when they get 2 is BODMAS or BIDMAS or PEMDAS or whichever they were taught
depending on which you notice that the D and the M are swapped around in some of the orders. really you should look at them as if they have 4 steps, not 6.
1. B
2. I
3. (DM)
4. (AS)
1. P
2. E
3. (MD)
4. (AS)
if you have done all brackets and exponents, and there are both multiplication and divisions, instead of doing one then the other, you do step 3, and just work from left to right doing both the divisions and the multiplications as they come.
After that you move to step 4. and do the additions and subtractions from left to right.
Ta da!
288 for reasons everyone else said basically. PEMDAS is ethically wrong, which is why you hardly ever use it in things like calculus and beyond.
Also, Pfft, you call that a math problem?
Try doing the Double Integral of a Uniformed Thin Disk! In order to calculate it's Area! Hmmph!
Also, Pfft, you call that a math problem?
Try doing the Double Integral of a Uniformed Thin Disk! In order to calculate it's Area! Hmmph!
D
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Well, the reason why I got 2 was not because of PEMDAS but rather because I interpreted the question slightly differently.
Note that I would be using / as the division operation sign, not the fraction sign.
Here's the proof that it's 2:
Lets say that
x=48, y=2, a=3, b=9
Then the equation would be
x/y(a+b)
=x/(ay+by)
Put the numbers back
=48/(3x2+9+2)
=48/24
=2
We get 2.
Someone argued that distribution cannot be used here, but since I replaced every number by a variable, they cannot be added to each other, allowing us to distribute.
No matter how you try to simplify, you'll always get an answer of 2.
Here's something else. Let's say I give you this equation:
2(2+2)/2(2+2)
You know that both sides of the division sign are the same, which obviously results in 1. Here's how.
2(2+2)/2(2+2)
=2(4)/2(4)
=8/8 (Paranthesis first)
=1
But let's say we do it the other way, how the others did to get 288 in the other equation. You'll get this:
2(2+2)/2(2+2)
=2(4)/2(4)
=2x4/2x4
=8/2x4
=4x4
=16
We get another answer.
Now, what causes this? If you look case enough, you'll spot the problem. Take a look at this equation:
a/bc
Are you supposed to do the division of Multiplication first? The question is too vague. That's exactly what 48/2(3+9) is. Too vague to be solved properly.
That's all I have to say. I don't think this problem needs arguing at all. There's no point. There's nothing wrong with our methods, but there's something wrong with the question.
Note that I would be using / as the division operation sign, not the fraction sign.
Here's the proof that it's 2:
Lets say that
x=48, y=2, a=3, b=9
Then the equation would be
x/y(a+b)
=x/(ay+by)
Put the numbers back
=48/(3x2+9+2)
=48/24
=2
We get 2.
Someone argued that distribution cannot be used here, but since I replaced every number by a variable, they cannot be added to each other, allowing us to distribute.
No matter how you try to simplify, you'll always get an answer of 2.
Here's something else. Let's say I give you this equation:
2(2+2)/2(2+2)
You know that both sides of the division sign are the same, which obviously results in 1. Here's how.
2(2+2)/2(2+2)
=2(4)/2(4)
=8/8 (Paranthesis first)
=1
But let's say we do it the other way, how the others did to get 288 in the other equation. You'll get this:
2(2+2)/2(2+2)
=2(4)/2(4)
=2x4/2x4
=8/2x4
=4x4
=16
We get another answer.
Now, what causes this? If you look case enough, you'll spot the problem. Take a look at this equation:
a/bc
Are you supposed to do the division of Multiplication first? The question is too vague. That's exactly what 48/2(3+9) is. Too vague to be solved properly.
That's all I have to say. I don't think this problem needs arguing at all. There's no point. There's nothing wrong with our methods, but there's something wrong with the question.