48÷2(9+3) = ?
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damn and all that time and effort that was wasted on deep thought, we only had to ask Gir633,
next to the = you have a - and also on the number keypad you have a - on top of the + sign
That is wrong
The correct answer is 288, you forgot division and multiplication is evaluated left to right
48/2(9+3) is actually
48/2*(9+3)
24*(9+3)
24*12
288
Lol. Funny how many stupid people are there are.
2(9+3) is one object.
This is basically year year 7 maths.
It's 48/(2)(9+3) = 48/24 = 2...
To get 288, it would have to be the question would have to be (48/2)(9+3)
Doesn't anybody have a calculator...? My goodness.
2(9+3) is one object.
This is basically year year 7 maths.
It's 48/(2)(9+3) = 48/24 = 2...
To get 288, it would have to be the question would have to be (48/2)(9+3)
Doesn't anybody have a calculator...? My goodness.
I agree with Example100000. Without a specified operator, it's treated as a function.
I ran it through my trusty ol' Casio fx-5000F, and it also concurs.
That's because 48÷2(9+3) = 48÷(2(9+3)) = 2 as shown in the scientific calculator.
And 48/2(9+3) = (48/2)(9+3) which is 288 as shown in the graphics calculator.
Is this completely clear yet? The answer's 2....
The problem with your calculator is similar to if you type -2^2 you will get -4 whereas if you type (-2)^2 you will get 4. That's what you're confused about.
When dealing with brackets, you must deal with the objects inside, then directly outside the brackets, making the first option correct.
The answer is ambiguous because no context is given. Every answer is assuming particular mathematical conventions. But different contexts (calculator, programming language, written mathematics) use different conventions and no particular convention is correct.
Precedence between division and multiplication varies. In some cases (most programming languages), multiplication and division have equal precedence. In some written mathematics a division written with the ÷ symbol takes precedence: the division is assumed to be multiplication by the reciprocal, i.e. 48 x (1/(2(9+3))). The reciprocal being part of the term so the brackets around the (1/...) are implied. However, some maths sources consider implied multiplication (the 2 written next to (9+3) without a multiplication sign) to be higher precedence than division. And other sources agree but only if there isn't a bracket involved (there is in this case). [See example below]. So in written maths the answer is 2 or 288 depending...
In programming languages, when multiplication and division precedence is equal, associativity comes into play: do we evaluate left or right term first? Again that is decided by convention dependent on context, although binary operators like these are usually left-associative.
In C++, C#, Java, JavaScript, Python, etc. etc. the expression must be written so: 48 / 2 * (9 + 3), there's no way to write implied multiplication without adding extra brackets (which would defeat the point of the question). Left-associativity will give the result 288 for all those languages and more.
All of that together means that there is no single correct answer to this question. The answer depends on where you wrote or typed or expected to use this. No particular convention is correct. And exactly because of that you are always be advised to write such an expression with brackets or a horizontal fractional line to remove the ambiguity.
Here's a specific example of discrepancy between calculator and maths text cited from Wikipedia: "Wolfram Alpha [prominent maths engine] considers that implied multiplication without parentheses precedes division, unlike explicit multiplication or implied multiplication with parentheses. 2*x/2*x and 2(x)/2(x) both yield x^2, but 2x/2x yields 1. The TI 89 calculator yields x^2 in all three cases."
Precedence between division and multiplication varies. In some cases (most programming languages), multiplication and division have equal precedence. In some written mathematics a division written with the ÷ symbol takes precedence: the division is assumed to be multiplication by the reciprocal, i.e. 48 x (1/(2(9+3))). The reciprocal being part of the term so the brackets around the (1/...) are implied. However, some maths sources consider implied multiplication (the 2 written next to (9+3) without a multiplication sign) to be higher precedence than division. And other sources agree but only if there isn't a bracket involved (there is in this case). [See example below]. So in written maths the answer is 2 or 288 depending...
In programming languages, when multiplication and division precedence is equal, associativity comes into play: do we evaluate left or right term first? Again that is decided by convention dependent on context, although binary operators like these are usually left-associative.
In C++, C#, Java, JavaScript, Python, etc. etc. the expression must be written so: 48 / 2 * (9 + 3), there's no way to write implied multiplication without adding extra brackets (which would defeat the point of the question). Left-associativity will give the result 288 for all those languages and more.
All of that together means that there is no single correct answer to this question. The answer depends on where you wrote or typed or expected to use this. No particular convention is correct. And exactly because of that you are always be advised to write such an expression with brackets or a horizontal fractional line to remove the ambiguity.
Here's a specific example of discrepancy between calculator and maths text cited from Wikipedia: "Wolfram Alpha [prominent maths engine] considers that implied multiplication without parentheses precedes division, unlike explicit multiplication or implied multiplication with parentheses. 2*x/2*x and 2(x)/2(x) both yield x^2, but 2x/2x yields 1. The TI 89 calculator yields x^2 in all three cases."
I can't comment on the mathematics aspect of contexts, as I don't have the knowledge base. However, I do know that conventions were introduced to handle this sort of dilemma.
In regard to programming languages, and calculators, my feeling is that omissions were made earlier in the creating of these elements, and the errors were propagated.
In much the same way as, for example, so many people think 'screen size' is 'resolution', and the continued creation of graphics at 72dpi, in a hardware environment set at 96dpi.
I didn't mean the word context in any technical sense. I'll try a simpler illustration:
Say A=4
What is 1/2A ?
Is it (1/2)A , so 2
Or is it 1/(2A), so 1/8
Most programming languages can't write 2A, they effectively write 1 / 2 x A. Does that change the answer?
So what about 1/2(A)? Looks more like (1/2)(A) doesn't it? Or not?
All these examples are simply the choice: "multiplication or division first?". Neither one is "correct", just a choice; left or right; red or blue. And the opinions of different people vary. I.e. there is no one set of arithmetic rules that seems "correct" to everyone. And so different parts of the mathosphere have settled on different rules (programming, maths texts, calculators).
The OP didn't specify division or multiplication first, so the answers have been judgements on that choice. But both choices are used in reality, so everyone is right and wrong.
Say A=4
What is 1/2A ?
Is it (1/2)A , so 2
Or is it 1/(2A), so 1/8
Most programming languages can't write 2A, they effectively write 1 / 2 x A. Does that change the answer?
So what about 1/2(A)? Looks more like (1/2)(A) doesn't it? Or not?
All these examples are simply the choice: "multiplication or division first?". Neither one is "correct", just a choice; left or right; red or blue. And the opinions of different people vary. I.e. there is no one set of arithmetic rules that seems "correct" to everyone. And so different parts of the mathosphere have settled on different rules (programming, maths texts, calculators).
The OP didn't specify division or multiplication first, so the answers have been judgements on that choice. But both choices are used in reality, so everyone is right and wrong.
I would see the answer being (1/2)A = 2
since the A is not implied to be included by the /
To be included, the question must be "What is 1/(2A)" or what is
Otherwise, the question "what is 1/2A" would mean "
That's why brackets are so important. I don't understand what's ambiguous about this.
Remember back in primary school, you were taught if there's only "X" and "÷" signs, you should do it from left to right.
However, if it's a "/" sign, you should do the "/" first.
"2*x/2*x and 2(x)/2(x) both yield x^2", makes perfect sense, "whereas 2x/2x yields 1." is incorrect since there is no difference between the 3.
Are you telling me that 2*x, 2(x) and 2x are different objects? Only (2x)/(2x) should yield 1...
Therefore, I agree with "The TI 89 calculator yields x^2 in all three cases."
I think many mathematicians would expect 1/2A to mean:
Code:
1
--
2ABut you think differently. You're not wrong, just a different choice. There's the ambiguity.
BTW. Wolfram Alpha gives 288 as the answer to the OP though because of the bracket positioning. I.e. It agrees with my assessment when there are no brackets 1/2A, but agrees with you when there are 1/2(A). If you doubt that site, go browse its sister site Wolfram Mathworld, to see that these guys know their math.