Algebra Know-It-ALL

In this chapter we’ll explore the mechanics of multiplication and division. Multiplication is a

shortcut for repeated addition. Division is something like “undoing” multiplication. These two

operations, like addition and subtraction, obey certain rules as long as they aren’t “stretched”

too far!

Moving Out and In

Think of the number line again, where the integers are points above and below a “number

reflector” plane that goes through 0. As you move upward, the numerical value increases; as

you go downward, it decreases. As you get farther in either direction from the “number reflec-

tor,” the absolute value increases.

To multiply, move out

When you add an integer to itself, you multiply it by 2. When you add an integer to itself twice,

you multiply it by 3. When you add an integer to itself 3 times, you multiply it by 4. You can keep

going with this. Here’s an example of what happens when the integer is positive:

5 + 5 = 5 × 2

5 + 5 + 5 = 5 × 3

5 + 5 + 5 + 5 = 5 × 4

Here’s what happens when the integer is negative:

− 5 + (−5)=− 5 × 2

− 5 + (−5)+ (−5)=− 5 × 3

− 5 + (−5)+ (−5)+ (−5)=− 5 × 4

65

CHAPTER

5 Multiplication and Division

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