My first answer was 2 but I see how people get 288. This is the best way to explain it:
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
I have to go with 2 as well... As soon as I saw the 2(9+3), I had a flashback to school where we had a teacher that always expanded these to be (18+6)... In fact he used to deduct marks if you "didn't show your work" and actually expand the number through the brackets in your answers...
I believe that you have to treat the right side of the equation as a whole, meaning it is 48 / 24 = 2
After you deal with the 9+3 in the brackets, the multiplication and division operations occur in the order they appear, so your equation is incorrect, Yoda.
Once the brackets are dealt with you have the following:
48 divided by 2 multiplied by 12, or
24 multiplied by 12, or
288
I say 2 as well. Mr. Smith in grade 8 math said BODMAS (brackets, operations, division, multiplication, addition, subtraction). I still respect his advice and he still says hello to my Mom when he sees her, thus 2.
I say 2 as well. Mr. Smith in grade 8 math said BODMAS (brackets, operations, division, multiplication, addition, subtraction). I still respect his advice and he still says hello to my Mom when he sees her, thus 2.
The answer is still 288 when you use BODMAS.
The problem is that people are giving special meaning to the brackets that is not actually there. The B in BODMAS is to indicate to do what is INSIDE the brackets.
The fault in the logic of the person using the distributive property of multiplication is that that distributive property should be used after moving from left to right in the equation, thus:
48 / 2 (9 + 3)
= 24 (9 + 3)
= 24 * 9 + 24 + 3 (This is where the distributive property comes in)
= 216 + 72
= 288
Here's another way to look at it....
What if I changed the equation to (48)(1/2)(9+3)... What would you answer be then?
Well, that notation is exactly the same as saying 48 / 2 (9+3)
As Hobbes said, to get 2 you would need to make the equation 48 / (2 (9+3))
The big question here is whether we give more importance to the implied multiplication in 2(9+3) rather than explicit multiplication in 2*(9+3).
Not implied as in it's not there, but implied as in, there's no real multiplication SIGN.
If it was written as 48/2*(9+3), there would be no question we go left to right, and the answer would be 288. The question arises when we give importance, whether proper or not, to the lack of a *.
Clearing our minds of this example and starting fresh, let's look at 22/7x. Does this mean (22/7)x or 22/(7x)? There are 3 terms and one sign, but also the "implied multiplication" between the 7 and the a.
I don't believe there's a clear rule on this. In any real-world application, you would most likely be able to clarify, and wouldn't be looking at these problems on a single line like in a forum. If this question was posed on multiple lines, there is no question. It's either
22x
---
7
Are you guys serious? Quimby explained that perfectly. I've studied college math for the past 2,5 years as well as the highest level of highscool math for 3 years before that. I swear, some of you aren't even trying not to mess this up ^^'
In order to arrive at 288 you'd have to do something very wierd like:
The simple fact is the person who wrote the equation did not know how to write an equation without a clear understanding of equations. I think that is how Newton discovered gravity. Perhaps this is the begining of perpetual motion.
You guys clearly don't have enough to keep you busy. There is no single right answer to this. Depends on which rule you abide by and which way you were taught. lol @ those so adamant in their opinions...
Meh, there is exactly one right answer. Math is built on axioms and there is absolutely zero room for ambiguity. (1+1 will always equal 2 even if we're dealing with piles of sand or whatever)
Meh, there is exactly one right answer. Math is built on axioms and there is absolutely zero room for ambiguity. (1+1 will always equal 2 even if we're dealing with piles of sand or whatever)
Sorry Richard, the problem is this is not an axiom the way it is written that's why the ambiguity.... Both 288 or 2 can be construed as correct... Perhaps you mean a theorem?
You get 288 because that's what you perceive as the way you were taught and is correct but so is 2 because others were taught by different rules. As I said before it is similar to "local" poker rules.
I would however say that if majority ruled then 288 would be "most" correct. How's that for a politician?
Me thinks this was a trick question. The fact is, the Grown Up has stated
Both sides are probably right. It's just the way the question is presented and how you decide to solve it. :-\
Sorry Richard, the problem is this is not an axiom the way it is written that's why the ambiguity.... Both 288 or 2 can be construed as correct... Perhaps you mean a theorem?
You get 288 because that's what you perceive as the way you were taught and is correct but so is 2 because others were taught by different rules. As I said before it is similar to "local" poker rules.
I would however say that if majority ruled then 288 would be "most" correct. How's that for a politician?
appraently your math teacher wasn't of the same caliber as mine ^^'
He was an elite marine in Sweden for 30 years before becoming a teacher to help his daughter through the system. Once he convinced our entire math group that there was an error in our book just to be able to fail everyone on the next test and lecture us about thinking for ourselves. he was apperently picked on by some random teacher when he was in school and in his own words: "I graduated, grew bigger than him, came back 6 years later and punched him in the face. I had to pay quite a bit for that, but it was worth it, he never picked on me again" (story checked out ^^) Funny guy
Anyway, if you want to be a good politician you can call whichever solution gets the more votes the more correct one. However, you try that on onw od my high school math tests Göran is not gonna be like "this answer is mostly correct" he's gonna be like "you're 100% wrong, go study some more or I'll kick you from higher level math to standard level, and that teacher sucks" (he actually said that to)
appraently your math teacher wasn't of the same caliber as mine ^^'
He was an elite marine in Sweden for 30 years before becoming a teacher to help his daughter through the system. Once he convinced our entire math group that there was an error in our book just to be able to fail everyone on the next test and lecture us about thinking for ourselves. he was apperently picked on by some random teacher when he was in school and in his own words: "I graduated, grew bigger than him, came back 6 years later and punched him in the face. I had to pay quite a bit for that, but it was worth it, he never picked on me again" (story checked out ^^) Funny guy
Anyway, if you want to be a good politician you can call whichever solution gets the more votes the more correct one. However, you try that on onw od my high school math tests Göran is not gonna be like "this answer is mostly correct" he's gonna be like "you're 100% wrong, go study some more or I'll kick you from higher level math to standard level, and that teacher sucks" (he actually said that to)
While we can agree that, in math, there can only be one correct solution to an equation, I must maintain that your solution isn't it.
Please advise as to all future bridges you may be involved in building.
The simple fact is the person who wrote the equation did not know how to write an equation without a clear understanding of equations. I think that is how Newton discovered gravity. Perhaps this is the begining of perpetual motion.
yes the question is wrong (but me and rich are still right)
k i was just joking here.....prob won't get across....
um ya math profs all over have apperently argued this for years.....
Anyone who thinks this is an ambiguous question is wrong!
Anyone who thinks there are two correct answers is wrong!
Anyone who thinks the answer is 288 is wrong!
And I'm going to tell you why! Isn't that great?
Mathematics has its' very own language that uses symbols to represent mathematical operations like addition, subtraction, division, factorial, square roots, etc. We are all familiar with these symbols, and since we have seen and used them since the beginning of our education, some of us may become lazy in the way that we use or interpret this symbols, and the mathematical language in general.
For example, we all recognize the symbol " x " to mean multiplication.
6 x 4 = 24
Six times four equals twenty-four.
All is well.
Now consider the symbol " ∙ ". Also called the dot operator, middle dot, or something similar, many people consider it the same as a multiplication symbol, for it gives the same result!
6 ∙ 4 = 24
However it does not mean multiplication in the way many perceive it to. The above math statement is correctly interpreted as...
The product of six and four equals twenty-four.
A subtle difference that is important in this way. It specifically refers to the product of two (or more) factors. It refers to the product, a singular term, specifically 24 in this example. To add to the confusion, it is widely used in algebra, and is often omitted when used with variables. This is a widely standard practice!
" x ∙ y " becomes " xy "
" 4 ∙ b " becomes " 4b "
" 2 ∙ x ∙ y " becomes " 2xy "
The dot operator is implied anytime you see this convention. A multiplication symbol is not! This is an important difference that people forget, because 99.9% of the time it makes no difference!
"But there is no implied dot operator in the problem at hand!" you say.
"Correct!" agree I!
But there is another mathematical concept at work here. It is one of factors! Almost anything can be factored! Consider the following...
6a + 3b = 3(2a + b)
There's no simple english translation here, but the mouthful...
Six 'aye' plus three 'be' can be factored into three and two 'aye' plus 'be'.
What the hell does that mean? As someone previously mentioned, it means that the 3 has distributive properties across the other factor (2a + b). More importantly, what it doesn't mean is 3 x (2a + b) and it doesn't mean 3 ∙ (2 + b). When you see a term like 5(2m + n) it means 5 has been factored out of (10m + 5n) leaving the other factor (2m + n). A simpler example is 3(6) meaning 3 has been factored out of 18 leaving the other factor 6. And most importantly, it remains a single term. (more correctly, a single product)
This is very important, because almost anything can be factored! *Consider the following math statement...
48 ÷ 24 = 2
We can factor the 24 into...
48 ÷ 2(12) = 2
Even more we can expand the 12...
48 ÷ 2(9+3) = 2
The factored product is a single term and can not be treated as 2 x (9+3).
Comments
Excel only does what you tell it to do. answer is 2 as per my calculator that entered the equation as seen in OP.... that's my final answer!
Edit: when I put that equation into excel, it gives me an error, and forces the * between the 2 and the (
Your calculator behaves the way it was programmed to . . . no different than Excel does.
GIGO.
I will stand on 288.
The distributive property of multiplication CLEARLY states that the 2(9+3) is an entire term and CANNOT be broken up. 2(9+3) follows the distributive property which can be rewritten as (2*9+2*3). Let me repeat the 2 outside of the parenthesis follows the distributive property of multiplication and must be factored and simplified before performing any other operations on it.
So this can be rewritten as:
48 / (2*9 + 2*3)
Which leaves us with
48 / 24 = 2
2(9+3)
most of you lose.....
its 2
bedmas is correct but you read the question wrong.....
I believe that you have to treat the right side of the equation as a whole, meaning it is 48 / 24 = 2
48 divided by 2 multiplied by (9+3), which leads to
48 divided by 2 multiplied by 12, which leads to
24 multiplied by 12, which equals
288.
Mark
48 / 2(12)
Once the brackets are dealt with you have the following:
48 divided by 2 multiplied by 12, or
24 multiplied by 12, or
288
Good day.
The answer is still 288 when you use BODMAS.
The problem is that people are giving special meaning to the brackets that is not actually there. The B in BODMAS is to indicate to do what is INSIDE the brackets.
The fault in the logic of the person using the distributive property of multiplication is that that distributive property should be used after moving from left to right in the equation, thus:
48 / 2 (9 + 3)
= 24 (9 + 3)
= 24 * 9 + 24 + 3 (This is where the distributive property comes in)
= 216 + 72
= 288
Here's another way to look at it....
What if I changed the equation to (48)(1/2)(9+3)... What would you answer be then?
Well, that notation is exactly the same as saying 48 / 2 (9+3)
As Hobbes said, to get 2 you would need to make the equation 48 / (2 (9+3))
Not implied as in it's not there, but implied as in, there's no real multiplication SIGN.
If it was written as 48/2*(9+3), there would be no question we go left to right, and the answer would be 288. The question arises when we give importance, whether proper or not, to the lack of a *.
Clearing our minds of this example and starting fresh, let's look at 22/7x. Does this mean (22/7)x or 22/(7x)? There are 3 terms and one sign, but also the "implied multiplication" between the 7 and the a.
I don't believe there's a clear rule on this. In any real-world application, you would most likely be able to clarify, and wouldn't be looking at these problems on a single line like in a forum. If this question was posed on multiple lines, there is no question. It's either
22x
---
7
or
22
--
7x
In order to arrive at 288 you'd have to do something very wierd like:
48/2(9+3) =
48/2*1(9+3) =
24*(1*9+1*3) =
24*(12) =
288
And if you do that, you pretty much SUCK at expressions, please don't construct any bridges any time soon
=48/2(x+y)
= 48/(2x+2y)
= 48/(6+18)
= 48/24
=2
However, if we force the * sign between the 2 and the ( it changes the equation completely.
=48/2*(x+y)
=48/2*(3+9)
=48/2*(12)
=24*12
=288
Just throwin it out there....
I'm pretty positive the answer is 2 though....But I havent done any equations for a few years now...
the fact that this is a four page thread is absolutely mind numbing
48
--- = 2
2*(9+3)
Sorry Richard, the problem is this is not an axiom the way it is written that's why the ambiguity.... Both 288 or 2 can be construed as correct...
You get 288 because that's what you perceive as the way you were taught and is correct but so is 2 because others were taught by different rules. As I said before it is similar to "local" poker rules.
I would however say that if majority ruled then 288 would be "most" correct. How's that for a politician?
Me thinks this was a trick question. The fact is, the Grown Up has stated
Both sides are probably right. It's just the way the question is presented and how you decide to solve it. :-\
appraently your math teacher wasn't of the same caliber as mine ^^'
He was an elite marine in Sweden for 30 years before becoming a teacher to help his daughter through the system. Once he convinced our entire math group that there was an error in our book just to be able to fail everyone on the next test and lecture us about thinking for ourselves. he was apperently picked on by some random teacher when he was in school and in his own words: "I graduated, grew bigger than him, came back 6 years later and punched him in the face. I had to pay quite a bit for that, but it was worth it, he never picked on me again" (story checked out ^^) Funny guy
Anyway, if you want to be a good politician you can call whichever solution gets the more votes the more correct one. However, you try that on onw od my high school math tests Göran is not gonna be like "this answer is mostly correct" he's gonna be like "you're 100% wrong, go study some more or I'll kick you from higher level math to standard level, and that teacher sucks" (he actually said that to)
While we can agree that, in math, there can only be one correct solution to an equation, I must maintain that your solution isn't it.
Please advise as to all future bridges you may be involved in building.
k i was just joking here.....prob won't get across....
um ya math profs all over have apperently argued this for years.....
Anyone who thinks there are two correct answers is wrong!
Anyone who thinks the answer is 288 is wrong!
And I'm going to tell you why! Isn't that great?
Mathematics has its' very own language that uses symbols to represent mathematical operations like addition, subtraction, division, factorial, square roots, etc. We are all familiar with these symbols, and since we have seen and used them since the beginning of our education, some of us may become lazy in the way that we use or interpret this symbols, and the mathematical language in general.
For example, we all recognize the symbol " x " to mean multiplication.
6 x 4 = 24
Six times four equals twenty-four.
All is well.
Now consider the symbol " ∙ ". Also called the dot operator, middle dot, or something similar, many people consider it the same as a multiplication symbol, for it gives the same result!
6 ∙ 4 = 24
However it does not mean multiplication in the way many perceive it to. The above math statement is correctly interpreted as...
The product of six and four equals twenty-four.
A subtle difference that is important in this way. It specifically refers to the product of two (or more) factors. It refers to the product, a singular term, specifically 24 in this example. To add to the confusion, it is widely used in algebra, and is often omitted when used with variables. This is a widely standard practice!
" x ∙ y " becomes " xy "
" 4 ∙ b " becomes " 4b "
" 2 ∙ x ∙ y " becomes " 2xy "
The dot operator is implied anytime you see this convention. A multiplication symbol is not! This is an important difference that people forget, because 99.9% of the time it makes no difference!
"But there is no implied dot operator in the problem at hand!" you say.
"Correct!" agree I!
But there is another mathematical concept at work here. It is one of factors! Almost anything can be factored! Consider the following...
6a + 3b = 3(2a + b)
There's no simple english translation here, but the mouthful...
Six 'aye' plus three 'be' can be factored into three and two 'aye' plus 'be'.
What the hell does that mean? As someone previously mentioned, it means that the 3 has distributive properties across the other factor (2a + b). More importantly, what it doesn't mean is 3 x (2a + b) and it doesn't mean 3 ∙ (2 + b). When you see a term like 5(2m + n) it means 5 has been factored out of (10m + 5n) leaving the other factor (2m + n). A simpler example is 3(6) meaning 3 has been factored out of 18 leaving the other factor 6. And most importantly, it remains a single term. (more correctly, a single product)
This is very important, because almost anything can be factored! *Consider the following math statement...
48 ÷ 24 = 2
We can factor the 24 into...
48 ÷ 2(12) = 2
Even more we can expand the 12...
48 ÷ 2(9+3) = 2
The factored product is a single term and can not be treated as 2 x (9+3).
2 is the correct answer!
Have a nice day!