Chapter 6: Multiplying Signed Numbers

6.1 The Logic of Direction

Multiplication is just repeated addition. For example, 3 times 5 means "add 5 three times." But what happens when we multiply by a negative number? In Algebra, a negative sign often acts as an "opposite" command.

Think of it this way:

A positive number keeps the direction the same.
A negative number flips the direction to the opposite.

6.2 The Sign Rules

When multiplying two numbers, the signs follow a very specific pattern. It doesn't matter which number is larger; only the signs matter.

Same Signs = Positive Result

Different Signs = Negative Result

The Four Scenarios:

( + ) × ( + ) = ( + ) (Example: 4 × 2 = 8)
( - ) × ( - ) = ( + ) (Example: -4 × -2 = 8)
( + ) × ( - ) = ( - ) (Example: 4 × -2 = -8)
( - ) × ( + ) = ( - ) (Example: -4 × 2 = -8)

6.3 Why does a "Negative × Negative" equal a Positive?

This is the question every student asks. A good way to think about it is using video.

Imagine a video of a person walking forward (Positive). If you play it in reverse (Negative), they look like they are walking backward. But if you take a video of someone walking backward (Negative) and play it in reverse (Negative), they appear to be moving forward (Positive)!

Modern Context: Business Debt
If a company removes 5 debts (Negative) of $100 each (Negative), the company's value actually goes up by $500.
Math: -5 × -100 = 500

6.4 Division Rules

Good news! The rules for division are exactly the same as the rules for multiplication.

10 / 2 = 5
-10 / -2 = 5
-10 / 2 = -5
10 / -2 = -5

Disclosure: This page contains affiliate links; we may earn a commission from qualifying purchases.

Doctor's Recommendation: Never Lose a Sign

In Chapter 6, the rules for multiplying negatives can get dizzying. To help keep your work consistent while these rules become second nature, the Doctor suggests a high-visibility reference tool like the Sproutbrite Integer Rules Poster.

Unlike a small bookmark, this large, clear poster can be placed directly in your study area. It provides a constant visual reinforcement of the "Same Signs = Positive" and "Different Signs = Negative" rules, helping you internalize the patterns of signed multiplication as you work through your exercises.

View Integer Rules Poster on Amazon