# Multiplication: names of some mathematical symbols

As far as I know, in Italian mathematics books, the symbol for multiplication can take several forms:

1. B × 3

2. B · 3

3. B * 3 (rare)

I'm not sure of having ever seen case 3 in English books, perhaps because "*" is not used in the English mother tongue in this sense.

Also, in English mathematics books I sometimes see

1. B . 3

In reference to mathematical contexts, what are the names of the symbols I used in 2 and 4?

• The asterisk is too used for multiplication in English... – Martha Mar 17 '13 at 22:27
• Although B·3 is a dot product (as mentioned in answers) the · character itself is a centered dot. – James Waldby - jwpat7 Mar 18 '13 at 1:21
• As a mathematician, I have also seen 4 on very rare occasions. I could probably count its occurrences using my fingers, though, and I cannot recall precisely even a single one now. Maybe they did not come from native English speakers, but from someone from a different culture writing a math book in English. – Federico Poloni Mar 18 '13 at 8:25
• I have kept my eyes open for it, and I just noticed notation (4) used in a conference talk; the speaker was a Belgian/French student. So maybe it's a notation from the French tradition. – Federico Poloni Jun 7 '13 at 15:28
• To support this, I just found this on en.wikipedia.org/wiki/Multiplication_sign#Similar_notations: "In some languages (especially, French) the use of full stop as a multiplication symbol, such as a.b, is not uncommon." – Federico Poloni Jun 7 '13 at 15:30

The precise name of a symbol in mathematics sometimes depends on what you're using it for. For example, `×` is often referred to simply as the multiplication sign, but if you need to distinguish scalar from vector multiplication, you might refer to it more specifically as the cross multiplication sign, vector multiplication sign, or something similar.

In your second example, the `・` symbol is called dot. The product of two numbers multiplied using the dot operator is the dot product. In some contexts, you might call it the scalar multiplication sign.

Outside of programming, we usually only use `*` for multiplication when we can't type `×`. The `*` symbol is usually called the asterisk or star, though if you're using it as a multiplication sign, you might call it that, instead.

The last example appears to be using a period. Like `*`, I assume this is simply because they couldn't type `・`. I could call this a period, but more usefully, I could call it whatever it represented: in this case, I might call it dot, since it's standing in for `・`.

• But I would note that I've never seen a period used as a multiplication sign in any English math book and that the asterisk is probably the most common substitution; i.e., not rare – Jim Mar 17 '13 at 23:01
• I believe the * for multiplication became popular with programming languages. Some token was needed, and the designers of the languages wanted to use something readily available on the keyboard (that eliminates × and ・, and the letter x would not have been a good choice, either). I've always assumed that * looked more like a multiplication sign than #, &, @, etc., so that's what was chosen. – J.R. Mar 18 '13 at 1:24
• @J.R. Oh, sure. That makes sense. That's why I wrote "outside of programming", since I think that's the main use of `*` (apart from when you can't type `×`). – snailplane Mar 18 '13 at 1:28
• Actually, the interpunct/middle dot is used for normal multiplication in many European countries, as well as in the SI system. The dot product uses a thicker dot, something like `&bullet;` (as opposed to `&middot;`), as illustrated by this image: i.stack.imgur.com/h9lHJ.png – jocap Dec 3 '13 at 21:53
• Maybe "outside programming" is turning into "outside high-quality typesetting?" Because if I want Google to do my arithmetic homework for me, I use type `4*8` using the `*` key between the division symbol and the subtraction symbol on my 16-key number pad. (I.E. `*` is more and more being used as the default symbol. I see it in my daughter's homework sheets now that she has started using variables.) – Adam Oct 16 '15 at 22:14

It depends on context.

For scalar values (all "normal" numbers that we know and love are scalar), all of those operators are the same, and are called multiplication, and the operator is called the multiplication operator, or much less frequently as the times operator.

When reading the equation "3 x 2" out loud, natives would typically use the following forms:

Three times two (common usage)

Three multiplied by two (common usage, formal)

Three by two (in common use by people who do a lot of math, vernacular informal).

Three timesed by two (primarily British English in my experience. Less common than "times").

For non-scalar values, the operator × and · do different things, and so different vocabulary is needed to distinguish them.

For "A × B" (often miswritten as "A x B"), the following phrases might be used:

A cross B

A crossed with B

The cross-product of A and B

The operator is called the cross-multiplication operator.

For "A · B" (often miswritten as "A . B"), the following phrases might be used:

A dot B

A dotted with B

The dot product of A and B

The operator is called the dot product operator.

"A * B" is generally not used in mathematics or formal writing. It is used because typing middot and cross-multiply quickly on a keyboard is hard, and period and letter-X have alternative meanings in many computer programming languages (for example is "3.2" == 32/10 or is "3.2" == 6?). For this reason, asterisk (*) is commonly used as a "poor man's ×" to symbolize multiplication.

One other thing to bear in mind is that in English math textbooks, it's fairly rare to see multiplication ever explicitly denoted by an operator at all (particularly in education above about age 15); "A * B" is much more commonly written as just "AB"

I think 1. and 3. are generally used in math. 2. is likely to be handwritten or in books.
I have never seen 4.
When we speak the expression, we usually say

B times three

so if B = 5, then

B times three equals fifteen.

As already mentioned, the symbol itself is called the multiplication sign.