# What is half of two plus two?

## Main Question or Discussion Point

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"?

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.

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

DaveC426913
Gold Member
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.

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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.

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.
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.

DaveC426913
Gold Member
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.
Wiki says it is MDAS (PEMDAS). That's what I was taught. Multiply then divide.

For for this question, it is moot.

berkeman
Mentor
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"?
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