In last week's Free for All, Brian Bell, under the headline "Suit Yourself: The `New' Math," starts by saying that "mathematics is not my long suit," and he proceeds to prove it.
The question is: How much is two times two minus two divided by two plus two? The answer originally given by your bridge columnist, Frank Stewart [Style, Sept. 5], was "5," and the correspondent takes strong exception to this. He claims that the only correct answer is two, and while proving this he re-sequences the entries in the original question, which changes the answer!
Frank Stewart's statement of the rules of arithmetic is correct: Do multiplication and division first, then do addition and subtraction. However, even following these rules, the correct answer depends on how the terms in this question are grouped. I can identify five different possible answers, depending on how I do the grouping, and none of them is a value of two, and all of them follow the sequencing shown in the original question:
[(2 X 2) - 2] / 2 + 2 = 3
(Two times two equals four minus two equals two) divided by two equals one plus two equals three.
[(2 X 2) - 2] / (2 + 2) = 1/2
(Two times two equals four minus two equals two) divided by (two plus two equals four) equals one-half.
(2 X 2) - (2 / 2) + 2 = 5
(Two times two equals four) minus (two divided by two equals one) which equals three plus two equals five.
(2 X 2) - [(2 / (2 + 2)] = 3 1/2
(Two times two equals four) minus [two divided by (two plus two equals four) equals one-half] equals three and one-half.
[2 X (2 - 2)] / (2 + 2) = 0
[Two times (two minus two equals zero) equals zero] divided by (two plus two equals four) equals zero.
There may be other groupings that would give different final answers, but these are all that I could come up with.
-- Daniel R. Schimmel
Sorry, Brian Bell, you cannot reorder the equation. Math is even less forgiving than a cake recipe. Just do multiplication and division within the existing order; adding parentheses helps to make the arithmetic clear.
The original "two times two minus two divided by two plus two" can be rewritten as (2 x 2) - 2 / 2 + 2, or 4 - 1 + 2, which equals five, as Frank Stewart correctly wrote.
-- Gordon Burck
I would suggest that Brian Bell stick to bridge. I believe that if the question were put in the form of an equation, and the rules of mathematics were applied, the answer would be obvious. Recalling my elementary algebra, which I learned more than 60 years ago, the equation would be the following: X = (2 X 2) -- (2 / 2) + 2 =4 -1 + 2 = 5.
Any further questions?
-- Harvey Geller