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Multiplication is often described as a sort of shorthand for repeated addition. For example,

Although multiplication isn’t as warm and fuzzy as addition, it’s a great timesaver. For example, suppose you coach a Little League baseball team, and you’ve just won a game against the toughest team in the league. As a reward, you promised to buy three hot dogs for each of the nine players on the team. To find out how many hot dogs you need, you can add 3 together 9 times. Or you can save time by multiplying 3 times 9, which gives you 27. Therefore, you need 27 hot dogs (plus a whole lot of mustard and sauerkraut).

When you multiply two numbers, the two numbers that you’re multiplying are called factors, and the result is the product.

When you’re first introduced to multiplication, you use the times sign (×). As you move onward and upward on your math journey, you need to be aware of the conventions I discuss in the following sections.

The symbol · is sometimes used to replace the symbol ×. For example,

In Units 1 through 4 of this book, I stick to the tried-and-true symbol × for multiplication. Just be aware that the symbol · exists so that you won’t be stumped if your teacher or textbook uses it.

In math beyond arithmetic, using parentheses without another operator stands for multiplication. The parentheses can enclose the first number, the second number, or both numbers. For example,

This switch makes sense when you stop to consider that the letter x, which is often used in algebra, looks a lot like the multiplication sign ×. So in this book, when I start using x to discuss algebra topics in Unit 7, I also stop using × and begin using parentheses without another sign to indicate multiplication.