Which verb is grammatically correct when used to describe addition?
- One and one are two.
- One and one is two.
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It would be grammatically correct to use "are" if the subjects were indeed "two" individually, but they are not.
By saying "One and one are two," that means that each "one" is two. The equivalent would be, "One is two, and one is two."
Saying "One and one is two" groups "one and one" to be the subject of the sentence. And "one and one" is two. ;)
In your post, you said "which question is grammatically correct?" You would ask, "Is one and one two?" Although, that can be confusing without something to separate the "one" and the "two" at the end. The preferred method would be "Does one plus one equal two?"
Logically, I think it should be "one and one are". By the normal rules of grammar, that is a compound subject. We wouldn't say "Bob and Charlie is ..."; we say "Bob and Charlie are ..." Etc.
@Snailplane's deleted answer—I don't know why it's deleted, it seems a valid answer to me—makes the interesting point that we sometimes use such compounds to refer to a single unit, like "Peanut butter and jelly is my favorite sandwich." I think the key there is that the words surrounding the "and" are a name or a title, like of course we would say, "Pride and Prejudice IS Sally's favorite book", not "... are Sally's favorite book", because we're talking about one book whose title happens to have the word "and" in it. It's not like Sally likes a book called Pride and she also likes a book called Prejudice. Do "one and one" in this sentence fall into that category? I don't think so.
Even when the point of a sentence is to say that two are more things are joined in some way, we still use "are". "Bob and Mary are a couple." "Smith, Jones, and Brown are a dangerous gang." "The four legs are what hold up the table." Etc.
So if you go by common usage, either is acceptable, but "is" is slightly preferred. If you go by conventional rules of grammar, I think "are" is correct. Obviously others answering on here disagree with me. Which, perhaps, is why we see the split in common usage.
I think you should feel free to use whichever you prefer. In day-to-day usage no one is likely to even notice. If you have a teacher or an editor who insists that one is wrong, I'd just do whatever they ask for rather than argue about it.
Either can be correct, but it depends on your context and meaning.
"One and one is two" is grammatically correct if you are using "and" to mean "plus" (addition). Adding the number one with the number one produces the number two, which is a singular thing, therefore "one and one" (one plus one) is singular.
A clearer (and thus arguably better) way to say this, however, would be "one plus one equals two".
On the other hand, "One and one are two" is grammatically correct if you are using "and" to mean "grouped with" or "put together". That is, "one (of these) and one (of those) are two (things put together)".
Fear and Loathing... is the truncated name of a book and movie; a bacon, lettuce, and tomato is a kind of sandwich and (well done) the pinnacle of human cuisine. Always. These days, the United States is a country. Almost always.
It's neither true that one and one is obviously and only plural nor that every side of an equation is obviously and only singular. It sits in that odd place in English grammar where 'favorite' questions are. You can speak pompously ("My favorite food is apple" or "the apple") or colloquially ("My favorite food is/are apples") but the real solution is usually just to completely rephrase ("I like apples").
You can't usually rephrase statements of addition. You aren't even trying to; it's more often an educational mantra or an expression of a truism. The normal thing to do with a compound subject is to use the plural, and that's what usually happens.
is almost exclusively the way people will express that idea.
When you take the objects out and start making it more purely math, it becomes a bit wonkier. It's more common to say
because we tend to say 'make' when talking about creating groups of objects but tend to say 'equal' when talking about equations, which have one group—all taken together as a unit—on either side.
Similarly, even though 'plus' is a preposition whose object (the second number) shouldn't change the grammatical number of the subject, what you actually see is
because of the pull of the idea of 'make' referring to actual objects, while the others are talking about math on its own. (That irregularity completely disappears when using 'one plus one...' since the first 'object' being added is singular as well.)
Side point: It doesn't help that people often wrongly consider 'plus' and 'and' to be exactly equivalent grammatically, instead of semantically.
The oddities happen because the addition can be considered as objects
One [apple] and one [apple] are two [apples].
One [apple] plus one [apple] is two [apples].
Two [apples] plus two [apples] are four [apples].
or as numbers combined together to form half of an equation
[The sum of] one and one is two.
[The sum of] one plus one is two.
[The sum of] two plus two is four.
or as noncount words in a grammatical construction.
One and one are two.
One plus one is two.
Two plus two is four.
The verb 'to make' pulls more people towards the first way of thinking; the verb 'to equal' pulls more people towards the second, especially because of the influence of similar sentences using 'plus'; and the verb 'to be' tends to (and should) follow the third, but with some bleed-over from the other ways. The grammatical sense also takes over in abstract cases with variables instead of numbers.
"One and two are numbers." "One and two is three."
As others have pointed out, it depends on whether "one and two" are taken separately or combined. I'd say the grammar points strongly to "one and two is three", because "one and two /are/ three" suggests that one is three and two is three -- which is false!
The short answer is that "is" would be more appropriate, despite the popular Len Barry lyric: "One and one are two". If you look up the word "and" in a dictionary, you'll see that it can be used to mean "plus", in addition to being used to mean what it more frequently does. Sentences that begin with two nouns joined by an "and" being used to mean "plus" typically are followed by a singular verb.
Consider the following examples of such sentences:
Two and two makes four.
One and five equals six.
In these examples, the singular verbs "makes" and "equals" are used, not the plural verbs "make" and "equal". It is no different for the verb "to be". Use "is" instead of "are".