6 ms·

not quite, 48÷(2(9+3)) = 2, but 48÷2(9+3) = 288 to clarify: PEMDAS is the order of operations. so parenthesis first: 48÷2(9+3) = 48÷2(12) then multiplication a

by nlco 15y ago

not quite, 48÷(2(9+3)) = 2, but 48÷2(9+3) = 288 to clarify: PEMDAS is the order of operations. so parenthesis first: 48÷2(9+3) = 48÷2(12) then multiplication and division (they have the same precedence): 48÷2(12) = 24*12 = 288 for another reference: http://www.google.com/search?q=48%C3%B72(9%2B3) http://www.google.com/search?q=48%C3%B72(9%2B3)

dcosson 15y ago
multiplication and division have the same precedence, and division (like most operations) is left-associative. For example, exponentiation is right-associative, so 2^3^2 = 2^9 = 512, not 64.
- wging 15y ago
  While you're technically correct, of the standard four half (+, *) are both left- and right-associative. / and - are the ones that are only left-associative.
sga 15y ago
Best bet is to replace x÷y by x*(1/y) as division is not commutative while multiplication is commutative. Therefore 48÷2(9+3) => 48(1/(2(9+3)) => 2
- wging 15y ago
  You've still failed to correctly apply associativity, unfortunately. You're treating 2(9+3) as a single unit, but ÷ appears before the implicit multiplication between 2 and (9+3) and so should get evaluated first. The division should get simplified first with its immediate operands, 48 and 2. This yields (48÷2) * (9+3).
  - nostrademons 15y ago
    It's funny, the top Google result for [juxtaposition precedence] is exactly this question, posted on the PhysicsForum boards. 2 is actually leading 288 by a hair there. http://www.physicsforums.com/showthread.php?p=3235154 http://www.physicsforums.com/showthread.php?p=3235154 Anyway, the answer depends completely on whether you believe that multiplication by juxtaposition has the same precedence as multiplication by explicit symbol. There're good reasons to believe it doesn't, eg. the first post on that linked thread, but whatever the answer, it's entirely based on typographical convention. I don't work in the community that cares, so I don't really have an opinion, other than to point out it's not as cut-and-dried as virtually ever poster here believes. In the community that I do work, people who write parsers, things like this have to be explicitly specified. That's why I maintain that the correct answer is "syntax error".
    - parfe 15y ago
      the real answer is that thw juxtaposition rules are made up on the spit by people trying to rationilze their incorrect answer . there is not and never had been a n "implit mulitplication" rule in the irder if operations. sent frim my drunk phone
      - nostrademons 15y ago
        They did, however, cite sources (possibly made up almost on the spot), which is more than anyone on this thread has done.
- ddlatham 15y ago
  48÷2(9+3) => 48(1/2)(9+3) => 288

by nlco 15y ago

dcosson 15y ago

multiplication and division have the same precedence, and division (like most operations) is left-associative. For example, exponentiation is right-associative, so 2^3^2 = 2^9 = 512, not 64.

wging 15y ago
While you're technically correct, of the standard four half (+, *) are both left- and right-associative. / and - are the ones that are only left-associative.

sga 15y ago

Best bet is to replace x÷y by x*(1/y) as division is not commutative while multiplication is commutative. Therefore 48÷2(9+3) => 48(1/(2(9+3)) => 2

wging 15y ago
You've still failed to correctly apply associativity, unfortunately. You're treating 2(9+3) as a single unit, but ÷ appears before the implicit multiplication between 2 and (9+3) and so should get evaluated first. The division should get simplified first with its immediate operands, 48 and 2. This yields (48÷2) * (9+3).
- nostrademons 15y ago
  It's funny, the top Google result for [juxtaposition precedence] is exactly this question, posted on the PhysicsForum boards. 2 is actually leading 288 by a hair there. http://www.physicsforums.com/showthread.php?p=3235154 http://www.physicsforums.com/showthread.php?p=3235154 Anyway, the answer depends completely on whether you believe that multiplication by juxtaposition has the same precedence as multiplication by explicit symbol. There're good reasons to believe it doesn't, eg. the first post on that linked thread, but whatever the answer, it's entirely based on typographical convention. I don't work in the community that cares, so I don't really have an opinion, other than to point out it's not as cut-and-dried as virtually ever poster here believes. In the community that I do work, people who write parsers, things like this have to be explicitly specified. That's why I maintain that the correct answer is "syntax error".
  - parfe 15y ago
    the real answer is that thw juxtaposition rules are made up on the spit by people trying to rationilze their incorrect answer . there is not and never had been a n "implit mulitplication" rule in the irder if operations. sent frim my drunk phone
    - nostrademons 15y ago
      They did, however, cite sources (possibly made up almost on the spot), which is more than anyone on this thread has done.
ddlatham 15y ago
48÷2(9+3) => 48(1/2)(9+3) => 288