Lesson 1.11

Integer Operations

Adding, subtracting, multiplying, and dividing negative numbers is where most students first stumble. Master the sign rules now and the rest of algebra flows smoothly.

Introduction

When you first learned subtraction, every answer was positive. Now we need to handle results like . The key is understanding the sign rules for each operation.

Past Knowledge

You can classify and order integers on a number line and take absolute values.

Today's Goal

Add, subtract, multiply, and divide positive and negative integers.

Future Success

Every equation you solve involves combining terms with mixed signs.

Key Concepts

1. Adding Integers

Same Signs → Add & Keep the Sign

Different Signs → Subtract & Take the Larger Absolute Value's Sign

(because )

2. Subtracting Integers

Change subtraction to adding the opposite, then use the addition rules.

3. Multiplying & Dividing Integers

SignsResultExample
+
+
or −

Same signs → positive. Different signs → negative.

Worked Examples

Example 1: Adding Two Negatives

Basic

Evaluate .

1

Same Signs → Add Absolute Values

2

Keep the Common Sign

Example 2: Subtracting a Negative

Intermediate

Evaluate .

1

Change to Addition

2

Add

Example 3: Mixed Operations

Advanced

Evaluate .

1

Exponent

2

Multiply

3

Divide

4

Add

Common Pitfalls

Double Negative = Negative

does not equal . Two negatives make a positive: .

Negative × Negative = Negative

, not . Same signs always produce a positive product.

Real-Life Applications

Bank accounts use integer operations every day. A withdrawal is subtraction, an overdraft fee is adding a negative. If you owe (balance = ) and deposit , your balance is — still overdrawn!

Practice Quiz

Loading...