Mathematically correct expressions for basic operations

There are several similar questions out there, but there is no systematic approach to the problem. So I will try to put all four operations together:

c = a + b

c = a * b

c = a - b

c = a / b

What are mathematically (not everyday speaking) correct expressions for these four operations?

Now, the first two are more-or-less straightforward:

c is the sum of a and b

c is the product of a and b

Things become ambiguous for the third expression:

c is the difference of a and b

c is the difference between a and b

The fourth expression is even more ambiguous

c is the quotient of a and b

c is the ratio of a and b

c is the ratio between a and b

Which of those would be most appropriate for use in mathematics and physics?

Solution 1:

Regarding a - b

c is the difference of a and b (see wikipedia for an example)

c is the difference between a and b (see math is fun for an example)

Both are acceptable, and both mean a - b, but "difference between" is more common than "difference of".

As for a/b

c is the quotient of a and b

is correct.

According to lexico, a quotient is:

1 Mathematics

A result obtained by dividing one quantity by another.

whereas lexico also defines ratio as:

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Besides, a ratio is typically represented with ":" rather than "/". If you did have a:b, you would write

c is the ratio of a to b (see this post for example)

"ratio" should be used with "to".