Five and two make/makes seven.
Five times two is/are ten.
Five minus two leave/leaves three.
Which ones are correct? Could someone explain the logic behind them?
You will generally hear the singular verb. I doubt that language can be explained in terms of logic.
5 + 2 = 7 means that the two expressions denote the same number.
Now obviously, if we look at the left hand side of that equation in terms of the number of symbols used, we see three and, if we focus on the number of symbols, we shall say the numerals for five and two joined by a plus sign represent the same number as the numeral for seven. Note the plural verb.
If on the other hand we focus on what the symbols mean, we shall say the number formed by adding five and two is seven. Note the singular verb.
The language used tends to follow what we are trying to convey. If we are trying to convey the number of symbols used, we shall use the plural. If we are trying to convey the number represented, we shall use the singular.
In at least some cases, correctly spoken English sentences exist using both singular and plural verbs for the same mathematical statement.
For example, I would consider all of the following to be correct:
Five and two make seven.
Five and two are seven.
Five plus two equals seven.
All of these are ways of expressing the equation 5 + 2 = 7 in words.
The plural forms seem old-fashioned to me (possibly due to a public education in the United States, where we consistently would have said five plus two equals seven), but you can certainly find them in literature and song. For example, when Danny Kaye sings "Inchworm" in the film Hans Christian Andersen, the children in the background are singing:
Two and two are four.
Four and four are eight. ...
In everyday language, one and one are two, and two and two are four. The "and" here stands for addition, and grammatically causes the plural form "are". Two and two also make four if you understand this as an addition.
Mathematically, two plus two equals four. This is an mathematical statement and the "plus" is part of the first expression that is equal to four (which is the second expression). Similarly, two times three equals six, and three minus one equals five minus three.
When you use "is" instead of "equals", as in "one plus one is two", you will be understood, but it is somewhat informal because equality and "being" are different concepts (example: if A and B are two sides of a square, they are equal, but it would be incorrect to say "A is B").
For a longer discussion (and debates) on the role and usage of the verb "to be", see E prime.
English is pretty strict when it comes to number agreement, and the reasoning is pretty clear.
The two numbers 5 and 2, when summed, they make 7.
This is pretty standard sentence structure. 5 and 2 are the subject, being operated via verb, to produce a result. As already noted you can also use a non-idiomatic rearrangement, but most native English speakers will stick with the subject-verb-object order. Hence, you would reword to use the singular subject as:
7 is the sum of 5 and 2.
In English, the sum of numbers is considered plural, and multiplication is singular. The reasons are somewhat odd, but do have some logic. For addition (and subtraction), the two numbers are thought of as two separate entities (5 and 7), whereas multiplication (and division) there is one entity that is being scaled (5 by 2, or vice versa). If you were to look at a word problem using these functions, you are liking to see the following:
John has five apples, Susie gives him 2 more. How many apples does John have?
John has two bags of apples, and each bag has five apples in it. How many apples does John have?
In the first example, the number of apples are added together, creating a larger group of apples, in the second, the question is on the total number of apples, which is scaled up by the number of bags.
English is a little abnormal, but does use (sometimes roundabout) logic.