48÷2(9+3) = ?
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Originally Posted By: ARCOgraphite
What does the equation represent? Nothing. Its solution is moot and a near pointless exercise. If I wrote the equation, I would know the order of operation and would have written it in an unabiguous fashion not in a mixed algebra / elementary math form. All my colleagues queried solved the equation and get ans=2. The operation outside the parenthetical addition is performed BEFORE the linear division.
Which equation are you referring to? The mathematical "order of operations" is discrete and exact - the rules were made for this very reason - so there is only one correct answer to the equation. If followed, the correct answer will always be achieved regardless if the equation represents something or not. The answer for 48÷2(9+3) = 2 is incorrect ... follow the "rules of operations".
What does the equation represent? Nothing. Its solution is moot and a near pointless exercise. If I wrote the equation, I would know the order of operation and would have written it in an unabiguous fashion not in a mixed algebra / elementary math form. All my colleagues queried solved the equation and get ans=2. The operation outside the parenthetical addition is performed BEFORE the linear division.
Which equation are you referring to? The mathematical "order of operations" is discrete and exact - the rules were made for this very reason - so there is only one correct answer to the equation. If followed, the correct answer will always be achieved regardless if the equation represents something or not. The answer for 48÷2(9+3) = 2 is incorrect ... follow the "rules of operations".
The example equation itself is garbage. Again, It mixes basic math and algebraic operators and is idiotic. NO rules may apply on an improperly formed equation.
Reminds me somewhat of, "... I before E except after C" with the exception of about 30 very common use words ... the result of a [censored] language known as English.
Reminds me somewhat of, "... I before E except after C" with the exception of about 30 very common use words ... the result of a [censored] language known as English.
Last edited:
Originally Posted By: ARCOgraphite
The example equation itself is garbage. Again, It mixes basic math and algebraic operators and is idiotic. NO rules may apply on an improperly formed equation.
Math is exact and has exact rules. There really isn't any room for "interpretation". The rules for the mathematical "order of operations" was invented for a reason ... to curb the personal interpretation of the written equation.
The example equation itself is garbage. Again, It mixes basic math and algebraic operators and is idiotic. NO rules may apply on an improperly formed equation.
Math is exact and has exact rules. There really isn't any room for "interpretation". The rules for the mathematical "order of operations" was invented for a reason ... to curb the personal interpretation of the written equation.
Originally Posted By: Vikas
So are the computer languages! As is written, it will throw "syntax error" by the computer. If you put the missing "*", it will compile but the star is not there as written. We have rehashed this ample times.
For a computer to understand the mathematical "syntax" is a different subject matter - talk to Bill Gates about that.
Technically, in the equation 48÷2(9+3) = ? you don't need the * in the equation to represent multiplication.
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
If you want to test your "order of operations" skills, play with this website:
http://www.mathsisfun.com/algebra/operations-order-calculator.html
So are the computer languages! As is written, it will throw "syntax error" by the computer. If you put the missing "*", it will compile but the star is not there as written. We have rehashed this ample times.
For a computer to understand the mathematical "syntax" is a different subject matter - talk to Bill Gates about that.
Technically, in the equation 48÷2(9+3) = ? you don't need the * in the equation to represent multiplication.
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
If you want to test your "order of operations" skills, play with this website:
http://www.mathsisfun.com/algebra/operations-order-calculator.html
Originally Posted By: ZeeOSix
[
Technically, in the equation 48÷2(9+3) = ? you don't need the * in the equation to represent multiplication.
yes you do. you cannot borrow from one syntax and another at your whim.
Quote:
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
no they most certainly do not. see my previous post on context free grammar.
[
Technically, in the equation 48÷2(9+3) = ? you don't need the * in the equation to represent multiplication.
yes you do. you cannot borrow from one syntax and another at your whim.
Quote:
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
no they most certainly do not. see my previous post on context free grammar.
It is called the distributive property.
Just to make sure I remembered it correctly, I referenced a college algebra book I have on my bookshelf. According to page 9 of Algebra and Trigonometry 5th ed by Michael Sullivan:
(3 + 5)x = 3x + 5x
So 48/2(9+3) =
48/(2*9 + 2*3) =
48/(18+6) =
48/24 =
2
According to the Associative Property (page 8 of the same book):
2 * (3*4) = 2*12 = 24
So...
2*(9+3) = 2*12, which is not = to 2(9+3) which = (2*9)+(2*3)
So the pic of the Casio calculator earlier in the thread that had the answer of 2 withOUT the * sign between the 2 and ( and 288 with the * sign between the 2 and ( is correct.
Just to make sure I remembered it correctly, I referenced a college algebra book I have on my bookshelf. According to page 9 of Algebra and Trigonometry 5th ed by Michael Sullivan:
(3 + 5)x = 3x + 5x
So 48/2(9+3) =
48/(2*9 + 2*3) =
48/(18+6) =
48/24 =
2
According to the Associative Property (page 8 of the same book):
2 * (3*4) = 2*12 = 24
So...
2*(9+3) = 2*12, which is not = to 2(9+3) which = (2*9)+(2*3)
So the pic of the Casio calculator earlier in the thread that had the answer of 2 withOUT the * sign between the 2 and ( and 288 with the * sign between the 2 and ( is correct.
Originally Posted By: wallyuwl
It is called the distributive property.
Just to make sure I remembered it correctly, I referenced a college algebra book I have on my bookshelf. According to page 9 of Algebra and Trigonometry 5th ed by Michael Sullivan:
(3 + 5)x = 3x + 5x
So 48/2(9+3) =
48/(2*9 + 2*3) =
48/(18+6) =
48/24 =
2
According to the Associative Property (page 8 of the same book):
2 * (3*4) = 2*12 = 24
So...
2*(9+3) = 2*12, which is not = to 2(9+3) which = (2*9)+(2*3)
So the pic of the Casio calculator earlier in the thread that had the answer of 2 withOUT the * sign between the 2 and ( and 288 with the * sign between the 2 and ( is correct.
Ahhh, yes ... I see the difference now. Forgot about the X(Y+Z) = XY+XZ rule.
If you go look at the photo of the two Texas Instruments calculators on page 1 of this thread, both show the same exact equation 48÷2(9+3), but have two different answers. One equation does not have the * in it.
But if you use the rules of the "order of operations", it will come out as 288 because "Calculations in brackets (parenthesis) are done first". This is a good trick question for a math test.
1. Calculations must be done from left to right.
2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.
3. Exponents (or radicals) must be done next.
4. Multiply and divide in the order the operations occur.
5. Add and subtract in the order the operations occur.
It is called the distributive property.
Just to make sure I remembered it correctly, I referenced a college algebra book I have on my bookshelf. According to page 9 of Algebra and Trigonometry 5th ed by Michael Sullivan:
(3 + 5)x = 3x + 5x
So 48/2(9+3) =
48/(2*9 + 2*3) =
48/(18+6) =
48/24 =
2
According to the Associative Property (page 8 of the same book):
2 * (3*4) = 2*12 = 24
So...
2*(9+3) = 2*12, which is not = to 2(9+3) which = (2*9)+(2*3)
So the pic of the Casio calculator earlier in the thread that had the answer of 2 withOUT the * sign between the 2 and ( and 288 with the * sign between the 2 and ( is correct.
Ahhh, yes ... I see the difference now. Forgot about the X(Y+Z) = XY+XZ rule.
If you go look at the photo of the two Texas Instruments calculators on page 1 of this thread, both show the same exact equation 48÷2(9+3), but have two different answers. One equation does not have the * in it.
But if you use the rules of the "order of operations", it will come out as 288 because "Calculations in brackets (parenthesis) are done first". This is a good trick question for a math test.
1. Calculations must be done from left to right.
2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.
3. Exponents (or radicals) must be done next.
4. Multiply and divide in the order the operations occur.
5. Add and subtract in the order the operations occur.
Originally Posted By: QuadDriver
Originally Posted By: ZeeOSix
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
no they most certainly do not. see my previous post on context free grammar.
Sure they do:
2(9+3)=
18+6=24
2*(9+3)=
2*12=24
2x(9+3)=
2x12=24
Originally Posted By: ZeeOSix
2(9+3) and 2*(9+3) and 2x(9+3) all mean the same thing.
no they most certainly do not. see my previous post on context free grammar.
Sure they do:
2(9+3)=
18+6=24
2*(9+3)=
2*12=24
2x(9+3)=
2x12=24
To show that 288 is the correct answer.
If you put the equation =48/2*(9+3) in the equation line in Excel, it returns an answer of 288. Having the astrix (*) in the equation matters to Excel (so it can understand the equation), but it doesn't matter when it comes to the "order of operations". Obviously, Excel uses the correct order of operations (as does the TI-86 calculator on page 1 ... the TI-85 is mis-programmed), which is to add 9+3 first, then do division and multiplication from left to right.
48/2*(9+3) is mathematically the same as 48/2(9+3). 2*(9+3) means the same exact thing as 2(9+3). I highly doubt Excel is wrong.
48/2*(9+3) =
48/2*12 =
24*12 =
288
If you put the equation =48/2*(9+3) in the equation line in Excel, it returns an answer of 288. Having the astrix (*) in the equation matters to Excel (so it can understand the equation), but it doesn't matter when it comes to the "order of operations". Obviously, Excel uses the correct order of operations (as does the TI-86 calculator on page 1 ... the TI-85 is mis-programmed), which is to add 9+3 first, then do division and multiplication from left to right.
48/2*(9+3) is mathematically the same as 48/2(9+3). 2*(9+3) means the same exact thing as 2(9+3). I highly doubt Excel is wrong.
48/2*(9+3) =
48/2*12 =
24*12 =
288
Originally Posted By: ZeeOSix
Having the astrix (*) in the equation matters to Excel (so it can understand the equation),
Does no one listen anymore?
context free grammar.
50 years ago the arguments could be made. today, you cannot.
all longhand mathematical operations must be written in a way in that they can be interpreted. anything else, is wrong and if your prof is not enforcing it, get a new prof.
Having the astrix (*) in the equation matters to Excel (so it can understand the equation),
Does no one listen anymore?
context free grammar.
50 years ago the arguments could be made. today, you cannot.
all longhand mathematical operations must be written in a way in that they can be interpreted. anything else, is wrong and if your prof is not enforcing it, get a new prof.
Originally Posted By: QuadDriver
Originally Posted By: ZeeOSix
Having the astrix (*) in the equation matters to Excel (so it can understand the equation),
Does no one listen anymore?
context free grammar.
50 years ago the arguments could be made. today, you cannot.
all longhand mathematical operations must be written in a way in that they can be interpreted. anything else, is wrong and if your prof is not enforcing it, get a new prof.
You have better proof?
Like I've said, 2(9+3) means the same thing as 2x(9+3) or 2*(9+3) to someone looking at the equation. It may not not be "readable" by a computer or Excel in some of those forms, but they all mean exactly the same thing in mathematics.
I have 4 sources that all give the same answer of 288. You have 4 sources that give the wrong answer of 2?
Originally Posted By: ZeeOSix
Having the astrix (*) in the equation matters to Excel (so it can understand the equation),
Does no one listen anymore?
context free grammar.
50 years ago the arguments could be made. today, you cannot.
all longhand mathematical operations must be written in a way in that they can be interpreted. anything else, is wrong and if your prof is not enforcing it, get a new prof.
You have better proof?
Like I've said, 2(9+3) means the same thing as 2x(9+3) or 2*(9+3) to someone looking at the equation. It may not not be "readable" by a computer or Excel in some of those forms, but they all mean exactly the same thing in mathematics.
I have 4 sources that all give the same answer of 288. You have 4 sources that give the wrong answer of 2?
Geeze, people ask for proof (not from me since I hadn't responded in this thread previous to my post just a bit above) to support their answer and I quote from a college algebra book the exact properties, and what those properties mean in general and in the context of this exact problem, and people still are trying to incorrectly argue the asterisk being there or not being there doesn't matter. It does! Just because you get the same answer for an expression doesn't mean you get the same answer for an equation if that expression is part of the larger equation. A calculator is only as accurate as the programmer and the rules built into the program. What is so hard to get about that?
Threads like this are why China and India are eating out lunch.
Threads like this are why China and India are eating out lunch.
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations. They explain the properties of multiplication but not necesarily the order of operation. The fact that one brings up the distributive property is acknowledgment that the 2 in proximity of (9+3)implies multiplication, or 2*(9+12). Implied multiplication=explicit multiplication. The debate is whether implied multiplication by proximity takes precedence or not.
And China and India are not eating our lunch because of technical superiority, but because of trade policies.
And China and India are not eating our lunch because of technical superiority, but because of trade policies.
Originally Posted By: mechanicx
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations. They explain the properties of multiplication but not necesarily the order of operation. The fact that one brings up the distributive property is acknowledgment that the 2 in proximity of (9+3)implies multiplication, or 2*(a+b). The debate is whether implied multiplication takes precedence or not.
Exactly ... The order of operations says that the addition of (9+3) has to be done first, not the operation of 2(9+3) = 2x9 + 2x3 = 24.
Copy and paste =48/2(9+3) into the formula bar in Excel 2003 or newer and it will want to correct the equation to say =48/2*(9+3) because it doesn't recognize the lack of the multiplication character *. But Excel does know what the equation is meant to be, and therefore wants to add the astrix. Tell it to correct the formula (it then adds the astrix), and the answer comes out as 288.
Also, copy and paste 48/2(9+3) into this tool, and again the answer is 288.
http://www.mathsisfun.com/algebra/operations-order-calculator.html
Someone show me where tools reveal the answer as 2, beside that junk TI-85 calculator.
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations. They explain the properties of multiplication but not necesarily the order of operation. The fact that one brings up the distributive property is acknowledgment that the 2 in proximity of (9+3)implies multiplication, or 2*(a+b). The debate is whether implied multiplication takes precedence or not.
Exactly ... The order of operations says that the addition of (9+3) has to be done first, not the operation of 2(9+3) = 2x9 + 2x3 = 24.
Copy and paste =48/2(9+3) into the formula bar in Excel 2003 or newer and it will want to correct the equation to say =48/2*(9+3) because it doesn't recognize the lack of the multiplication character *. But Excel does know what the equation is meant to be, and therefore wants to add the astrix. Tell it to correct the formula (it then adds the astrix), and the answer comes out as 288.
Also, copy and paste 48/2(9+3) into this tool, and again the answer is 288.
http://www.mathsisfun.com/algebra/operations-order-calculator.html
Someone show me where tools reveal the answer as 2, beside that junk TI-85 calculator.
Originally Posted By: ZeeOSix
Exactly ... The order of operations says that the addition of (9+3) has to be done first, not the operation of 2(9+3) = 2x9 + 2x3 = 24.
Copy and paste =48/2(9+3) into the formula bar in Excel 2003 or newer and it will want to correct the equation to say =48/2*(9+3) because it doesn't recognize the lack of the multiplication character *. But Excel does know what the equation is meant to be, and therefore wants to add the astrix. Tell it to correct the formula (it then adds the astrix), and the answer comes out as 288.
Also, copy and paste 48/2(9+3) into this tool, and again the answer is 288.
http://www.mathsisfun.com/algebra/operations-order-calculator.html
Someone show me where tools reveal the answer as 2, beside that junk TI-85 calculator.
I have already told you how excel could successfully interpret 2(9+3). But that simply makes it wrong.
ever since, oh I dunno, roughly 1950 the 'mathematical community' (whatever that is) has decided that 2*(9+3) is an evaluatable equation, and 2(9+3) is a function, to be defined elsewhere.
This thread has ceased 31 pages ago to be a test on whether people understand order of operations and orders of precedence and instead became an exercise in demonstrating whether people can write an expression that is universally correct and understandable.
sure, someone can read the original and conclude "silly human, he really meant to insert the sign for multiplation in there" but that does not make it correct.
I am free to designate that 'smiley face' means left paren and 'frowny face' means right paren and those that know me will be able to deduce my intent, but that does not make it correct.
My first post on page 25 should have been all that anyone needed to know, learned and moved on.
In retrospect the correct answer, for the 'problem' as written is not 288 but rather unknown since we dont have a valid definition for the expression 2(x). Mebbe that was the intent of the OP. A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
fortunately the OP is not a rep from a planet of super smart aliens and this was a test to decide whether or not to zap the planet into unrecognizable form.
Exactly ... The order of operations says that the addition of (9+3) has to be done first, not the operation of 2(9+3) = 2x9 + 2x3 = 24.
Copy and paste =48/2(9+3) into the formula bar in Excel 2003 or newer and it will want to correct the equation to say =48/2*(9+3) because it doesn't recognize the lack of the multiplication character *. But Excel does know what the equation is meant to be, and therefore wants to add the astrix. Tell it to correct the formula (it then adds the astrix), and the answer comes out as 288.
Also, copy and paste 48/2(9+3) into this tool, and again the answer is 288.
http://www.mathsisfun.com/algebra/operations-order-calculator.html
Someone show me where tools reveal the answer as 2, beside that junk TI-85 calculator.
I have already told you how excel could successfully interpret 2(9+3). But that simply makes it wrong.
ever since, oh I dunno, roughly 1950 the 'mathematical community' (whatever that is) has decided that 2*(9+3) is an evaluatable equation, and 2(9+3) is a function, to be defined elsewhere.
This thread has ceased 31 pages ago to be a test on whether people understand order of operations and orders of precedence and instead became an exercise in demonstrating whether people can write an expression that is universally correct and understandable.
sure, someone can read the original and conclude "silly human, he really meant to insert the sign for multiplation in there" but that does not make it correct.
I am free to designate that 'smiley face' means left paren and 'frowny face' means right paren and those that know me will be able to deduce my intent, but that does not make it correct.
My first post on page 25 should have been all that anyone needed to know, learned and moved on.
In retrospect the correct answer, for the 'problem' as written is not 288 but rather unknown since we dont have a valid definition for the expression 2(x). Mebbe that was the intent of the OP. A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
fortunately the OP is not a rep from a planet of super smart aliens and this was a test to decide whether or not to zap the planet into unrecognizable form.
Originally Posted By: mechanicx
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations.
According to the college algebra book on my shelf, they do. As has said earlier in this thread, you need to get rid of the parentheses first before going on to multiplication/division. That is accomplished by using the distributive property.
Quote:
And China and India are not eating our lunch because of technical superiority, but because of trade policies.
I'll agree with that regarding China to a large extent, but not India. India has an education system designed to produce innovation.
But the distributive and associative property argument has already been brought up in this thread long ago and the consensus was these properties have no bearing on the order of operations.
According to the college algebra book on my shelf, they do. As has said earlier in this thread, you need to get rid of the parentheses first before going on to multiplication/division. That is accomplished by using the distributive property.
Quote:
And China and India are not eating our lunch because of technical superiority, but because of trade policies.
I'll agree with that regarding China to a large extent, but not India. India has an education system designed to produce innovation.
Originally Posted By: QuadDriver
ever since, oh I dunno, roughly 1950 the 'mathematical community' (whatever that is) has decided that 2*(9+3) is an evaluatable equation, and 2(9+3) is a function, to be defined elsewhere
A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
If they don't mean the same thing, then why do they give the same answer - I'm all ears ready to learn something new here. Any way you slice it, the answer is the same.
2(9+3) = 24
2*(9+3) = 24
2x(9+3) = 24
It doesn't matter what "symbol" is used to represent multiplication ... it's still multiplication.
Show me the rule where it says they mean a different operation and a different solution depending on the symbol used for multiplication. And just because a * wasn't used to represent multiplication doesn't defy or change the rules of the order of operations.
There are very similar equations in this link. See question #7 ... similar equation: 36 ÷ 4(5 - 2) + 6 = . What's your answer to it? Order of Operations still apply.
http://amby.com/educate/ord-op/pretest.html
Show me an order of operations tool that gives the answer of 2.
http://staff.argyll.epsb.ca/jreed/math7/strand1/1203.htm
ever since, oh I dunno, roughly 1950 the 'mathematical community' (whatever that is) has decided that 2*(9+3) is an evaluatable equation, and 2(9+3) is a function, to be defined elsewhere
A lot of people jumped to the conclusion that 2(9+3) = 2*(9+3) but wars have started for less.
If they don't mean the same thing, then why do they give the same answer - I'm all ears ready to learn something new here. Any way you slice it, the answer is the same.
2(9+3) = 24
2*(9+3) = 24
2x(9+3) = 24
It doesn't matter what "symbol" is used to represent multiplication ... it's still multiplication.
Show me the rule where it says they mean a different operation and a different solution depending on the symbol used for multiplication. And just because a * wasn't used to represent multiplication doesn't defy or change the rules of the order of operations.
There are very similar equations in this link. See question #7 ... similar equation: 36 ÷ 4(5 - 2) + 6 = . What's your answer to it? Order of Operations still apply.
http://amby.com/educate/ord-op/pretest.html
Show me an order of operations tool that gives the answer of 2.
http://staff.argyll.epsb.ca/jreed/math7/strand1/1203.htm
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