Why is 15 + 15 different from 15 * 2?

Question

(Apologies if the tag is incorrect. I can't find a "Multiplication" tag or similar)

I'm going to be adding a set of 5 numbers up and dividing them to get the average for a java game I am making.

However, there seems to be something wrong with it. I would have thought 15 + 15 / 2 would have been 15, however that seems incorrect.

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However, 15 * 2 / 2 yields the expected result.

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What is the difference here? Will doing counting up the variables and dividing them by the amount of variables work correctly in my game?

score 2 · Answer 1 · answered Jan 20 '15 at 16:05

2

Order of Operations: Division comes before addition. So when you input 15+15/2 you get 15+7.5. To get the answer you want input (15+15)/2.

answered Jan 20 '15 at 16:05

Tim Raczkowski

20,046

I think you mean "before addition" – Alex Silva Jan 20 '15 at 16:06
Yes. Quite right. – Tim Raczkowski Jan 20 '15 at 16:07

score 1 · Accepted Answer · answered Jan 20 '15 at 16:02

1

You should probably write $(15+15)/2$ with parentheses and this will yield $15$.

Note that $22.5$ is $15+(15/2)$. In fact Google shows you that this is what it is calculating (taking into account the conventional order of operations).

answered Jan 20 '15 at 16:02

Guest

4,158

Oh dammit. Of course it is. Because I use Java, I am not used to that sort of behaviour. – user2722083 Jan 20 '15 at 16:03
4

@user2722083 Java has exactly the same behaviour. – AlexR Jan 20 '15 at 16:04
@AlexR Java does things in the order you typed them. This means that if I did (15 + 15 / 2), it would do 15 + 15, then divide that by 2. In C++, if I did the same, then it would do the same as google has done. – user2722083 Jan 20 '15 at 16:05
@user2722083 Nope. Try it out and see. Every meaningful programming language respects this so-called "precedence" order. – AlexR Jan 20 '15 at 16:05
2

@user2722083 Certainly not, check the docs. Actually, I doubt that any programming language with arithmetic expressions exhibits this confusing behaviour. – Hagen von Eitzen Jan 20 '15 at 16:06
@HagenvonEitzen Wow. Looks like I've been living with that misconception for at least 3 years. – user2722083 Jan 20 '15 at 16:06
2

@user2722083 It's about time to revisti your last three years worth of code ;) – Hagen von Eitzen Jan 20 '15 at 16:08

score 1 · Answer 3 · answered Jan 20 '15 at 16:03

1

Well when you write 15+15/2, the interpretation is $15+\dfrac{15}{2}$. You need brackets to solve this ambiguity: $\dfrac{(15+15)}{2}$

answered Jan 20 '15 at 16:03

voldemort

13,182

Why is 15 + 15 different from 15 * 2?

3 Answers3