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48÷2(9+3) = ?

Discussion in 'Chatterbox' started by asiankid7, Sep 17, 2012.

  1. asiankid7

    asiankid7 New Member

    48÷2(9+3) = ?
    what answer did u get? curious to see how people would work this here!
  2. Gir633

    Gir633 Señor Member

    Everyone knows the answer is 42.

    Because that's the answer to everything.
  3. asiankid7

    asiankid7 New Member

    how on earth did you get 36??
  4. IdolFun

    IdolFun ★ ☆ I Am God ☆★ Super Moderator

    2 or 288
  5. SecretPal

    SecretPal Beyond Redemption

    Oh please..parenthese always first (12) * 2 = 24. Then use figure on otherside of the operand (48.) Answer is 2.

    Now anyone up for solving an econometric model using autoregressive conditional hetero skedacity??
  6. asiankid7

    asiankid7 New Member

    orders of operation rules : do whats IN the parentheses first, the 2 isn't in the parenthese hence it is a multiplication 2(12), it isn't (2*12)
  7. Wokkonno

    Wokkonno Wokkonno XP

    There are some simple equations that give erroneous results but they are implemented correctly.
    Apparently this is one of them. Lool.
  8. CoolKevin

    CoolKevin Nutcase on the loose Staff Member Super Moderator

    damn and all that time and effort that was wasted on deep thought, we only had to ask Gir633,
  9. porkar

    porkar New Member

    2(9+3)= 2(12) = 24

    48/24 = 2 (I don't have a division symbol on my keypad).
  10. CoolKevin

    CoolKevin Nutcase on the loose Staff Member Super Moderator

    next to the = you have a - and also on the number keypad you have a - on top of the + sign
  11. chupachups

    chupachups New Member

    That is wrong

    The correct answer is 288, you forgot division and multiplication is evaluated left to right

    48/2(9+3) is actually

  12. example100000

    example100000 Old Timer

    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.
  13. IdolFun

    IdolFun ★ ☆ I Am God ☆★ Super Moderator

    What calculator do you want to use?

  14. Kumi3

    Kumi3 Flaccid Member

    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.
  15. example100000

    example100000 Old Timer

    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.
  16. Vitreous

    Vitreous ° Former Staff

    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."
  17. Kumi3

    Kumi3 Flaccid Member

    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.
  18. Vitreous

    Vitreous ° Former Staff

    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.
  19. example100000

    example100000 Old Timer

    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 [​IMG]
    Otherwise, the question "what is 1/2A" would mean "[​IMG]" (ignore the capitalisation...)

    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."
  20. Vitreous

    Vitreous ° Former Staff

    I think many mathematicians would expect 1/2A to mean:
    With the A certainly included in the division. I would assume it meant that, and Wolfram Alpha, the computational engine of the largest math website does too. The implicit multiplication 2A is assumed to be done first. Sure brackets can be used to clarify, but they are not required and often omitted.
    But 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.