# What is half of two plus two?

1. Nov 21, 2011

### riaudo

When someone says "half of two plus two", what are they referring to?

A) Half of 2+2
= (Half of 2) + 2
= (1) + 2
= 3

B) Half of 2+2
= Half of (2+2)
= (.5)(4)
= 2

Which answer is the correct way to express "half of two plus two"?

2. Nov 21, 2011

### Number Nine

We don't know. This is why we have mathematical notation; language is ambiguous. Presumable they're referring to $\frac{(2 + 2)}{2}$, but we have no way to be sure.

3. Nov 21, 2011

### iMAGICIALoTV

I believe it's A, but Number Nine's right. We have no way to be sure...

4. Nov 21, 2011

### DaveC426913

Technically the correct answer is 3.

It is not ambiguous; there are no brackets or parentheses, only arithmetical operators.

The http://en.wikipedia.org/wiki/Order_of_operations#Easy_Remembering" rule tells us to apply multipliers first then adders.

The word "of" is english-speak for "multiply" (eg.: "1/2 of 10" is synonymous with "1/2 x 10" ).

Since the question is 1/2 x 2 + 2, the order of operations is:
1/2 x 2 = 1
+ 2 = 3

However, if I were a betting man, and this were a fair game (no tricks), and were asked to bet on which one the person meant when they said this (it was spoken after all) , I would bet on 4.

Last edited by a moderator: Apr 26, 2017
5. Nov 21, 2011

### cmb

I was taught, at an early age, ' DMAS ' was the rule.

In any 'unbracketed' function, it always goes division first, then multiplication, add, then subtract.

It is, therefore, 3.

With that rule, you can freely write, for example, A+B/2 and it unambiguously means [A]+[B/2], or 3-1+2=4.

6. Nov 21, 2011

### Number Nine

This isn't a issue of orders of operation, it's a language issue. The fact it, someone saying "half of two plus two" is ambiguous unless you have certain knowledge that they have considered the order of operations when formulating the sentence. Grammar and pragmatism are different things, and plenty of people would say "half of two plus two" to mean half of the sum of two and two.

7. Nov 21, 2011

### DaveC426913

Wiki says it is MDAS (PEMDAS). That's what I was taught. Multiply then divide.

For for this question, it is moot.

8. Nov 21, 2011

### Staff: Mentor

Please see this stickie thread at the top of this General Math forum:

That and the language issue discussed in this thread should help you understand.