Technical Mathematics, Sixth Edition

1.3. Multiplication

Addition and subtraction were easy enough. Let's move on to multiplication.

1.3.1. Symbols and Definitions

Multiplication can be indicated in several ways: by the usual × symbol; by a dot; or by parentheses, brackets, or braces. Thus the product of b and d could be written

b · d b × d b(d) (b)d (b)(d)

Most common of all is to use no symbol at all. The product of b and d would usually be written bd. When doing algebra avoid using the × symbol because it could get confused with the letter x.

We get a product when we multiply two or more factors.

(factor) (factor) (factor) = product

1.3.2. Multiplying by Calculator

Many calculators use the key for multiplication and use an asterisk or star (*) on the screen to represent a multiplication dot.

This TI-83/84 screen shows the multiplication of the factors 13 and 27.

1.3.3. Multiplying Signed Numbers

To get our rules of signs for multiplication, we use the idea of multiplication as repeated addition. For example, to multiply 3 by 4 means to add four 3's (or three 4's)

3 × 4 = 3 + 3 + 3 + 3

or

3 × 4 = 4 + 4 + 4

Let us return to our shoebox example. Recall that it contains uncashed checks and unpaid bills. Let's first add 5 checks (+5), each worth $100 (+100), to the box. The value of the contents of the box then increases ...