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10*7 means "ten times seven." We could use an x instead of a * to be the multiplication symbol, but that could get confusing if we used x as a variable (variables and constants are explained here). Generally, on a computer, the * symbol is used to mean "multiplied by." When writing, you could also use a dot. There are different symbols in different cultures, but these are the generally recognized symbols you'll most often come across.

When you multiply a number by a variable, it is customary to just place the number in front of the variable - you don't need a multiplication symbol.

That sounds like it might be confusing, but it doesn't have to be if you understand that math is meant to be a streamlined language. If I wanted to write eight times five, I'd have to use a symbol between the numbers, or else it would simply look like this: 85. That would mean the number 85, though, not eight times five. Therefore we use a symbol when we are multiplying numbers by numbers. But if you are multiplying a number by a variable, like a, n, x, or whatever, you could simply write the number and then the variable, as in 8a. You would never confuse that for a specific number. After all, there is no "eighty-a," is there? So we leave out the multiplication symbol to save space.

The same holds for multiplying variables. You can streamline it.  a*b can simply be written ab (think of E=mc².) You know that a is a variable, and b is a variable. They are seperate things, and wouldn't be confused as 85 could be for 8*5. ab is usually not a single variable. I say "usually" because it s conceivable that someone may decide to use ab to represent something like "arctic bear" for some reason. Like 4ab = l (where ab = arctic bears and l = legs of arctic bears). In this case, 4ab = l would mean "four times the amount of artic bears equals the amount of artic bears' legs."

Of course I am being silly here (because I can!) You could have an example like that, but it would be a bit confusing. It'd be simpler to say 4a = b (where a = arctic bears and b = legs).

It would be still simpler to not make up goofy examples like this.

Just remember that:

• number times number needs a symbol. Example: 4*5.
• variable times variable generally doesn't need a symbol. Example: ab.
• number times variable generally doesn't need a symbol. Example: 10a.

What about constants that are represented as symbols, like π (pi)?

They have the same rules as variables when multiplied. (Think of the formula for finding the area of a circle, which is A = π r²). Also, the constant comes before the variable. It is easy to remember that if you consider that a number is a constant, and as we have learned above, numbers come before the variable.

For a thorough (and amazingly boring) discussion of mathematical typography, head out to this page.

There are, of course, exceptions, and much more that can be said of numbers, constants, variables, symbols and multiplication.

But not here. It's time for a nap.