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Lamrot Hakol (Despite Everything)

Musings and kvetchings and Torah thoughts from an unconventional Orthodox Jew.

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Sunday, April 10, 2011

48÷2(9+3) -- The Meme

Okay, it seems to me that the answer to this little arithmetic problem that's been working its way around the internet is 2, and not 288. A lot of people are going to argue with that, but hear me out.

According to Wikipedia, for those who aren't already aware, the standard order of operations in arithmetic is:

* terms inside brackets (or parentheses)

* exponents and roots

* multiplication and division

* addition and subtraction

So the very first thing we do is simplify this to 48÷2(12). And here's where things get problematic.

Are 2(12) and 2 × 12 the same? They're both notations for multiplication, but are they the same? I'd maintain that they are not, and I'll show you why.

Suppose our problem was 48 ÷ 2x. Is this the same as 48 ÷ 2 × x? If so, we'd go from left to right and say 48 ÷ 2 is 24, 24 × x is 24x. But if ÷ and / both signify division, then 48 ÷ 2x is 48/2x which I think anyone would correctly evaluate as 24/x.

See the problem?

So either the two notations for "divided by" are different in some way, or the two notations for "multiplied by" are different in some way. (Or both, obviously.) This whole problem could be avoided, of course, by the use of parentheses, like this:

(48 ÷ 2)(9 + 3)


48 ÷ (2(9 + 3)).

It's possible that the standard order of operations simply isn't clear enough. But I think the correct answer is that / and ÷ are the same, but × and positioning the two expressions right next to each other, while both signifying multiplication, are different.

The reason brackets or parentheses are evaluated first is that they are a means of grouping. I'd maintain that the positioning of two expressions right next to each other for the purpose of multiplication is an implicit method of grouping them, and that this kind of multiplication should be evaluated prior to division or any other multiplication.

Comments are welcome.


Blogger rightsaidfred said...

I agree with you.

The immediate placement of terms, such as 2(4), implies grouping, similar to a fraction.

3:34 PM  
Blogger Ben-Yehudah said...

You're right, of course.

The answer is 2.

Which operations come before other operations is like from pre-Algebra, if I remember correctly.

4:39 AM  

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