Adding and Subtracting Integers Lesson

Lesson Overview

• What Are Integers?
• The Number Line and Integer Direction
• Rules for Adding Integers
• Rules for Subtracting Integers
• Rule: Change Subtraction to Addition
• Absolute Value and Integer Comparison
• Practice: Adding Integers Step by Step
• Practice: Subtracting Integers Step by Step
• Adding and Subtracting Multiple Integers
• Subtracting a Negative Number

In math, numbers can go in two directions-positive and negative. Positive numbers go above zero, and negative numbers go below zero. These are called integers. When you add and subtract integers, you need to pay close attention to signs (+ or -) and direction.

Adding and subtracting integers is important in everyday situations-like tracking temperature changes, managing money, or calculating gains and losses. In this lesson, you'll learn how to add and subtract integers, how to visualize them on a number line, and how to avoid common mistakes.

What Are Integers?

Integers are a group of numbers that include:

• All positive whole numbers
  
• All negative whole numbers
  
• Zero
  

Examples:

• -5, -2, 0, 3, 12, 100
  

Integers do not include fractions or decimals. They are used when working with gains and losses, temperature changes, elevation, and many math problems that involve direction or movement.

The most important thing to remember about integers is their sign:

• A positive number has no sign or a "+" sign.
  
• A negative number always has a "–" sign.
  

The Number Line and Integer Direction

A number line helps you visualize positive and negative integers.

... -5 -4 -3 -2 -1  0  1  2  3  4  5 ...

• Numbers to the right of 0 are positive.
  
• Numbers to the left of 0 are negative.
  

Using the number line, you can:

• Add by moving to the right
  
• Subtract by moving to the left
  

Understanding this movement will help when adding or subtracting both positive and negative integers.

Take This Quiz:

Adding And Subtracting Integers Quiz

Rules for Adding Integers

When adding integers, the sign of the numbers matters. Here are the basic rules:

Rule 1: Adding Two Positive Integers

• Simply add the values.
  
• The result is positive.
  

Example: 5 + 3 = 8

Rule 2: Adding Two Negative Integers

• Add the values.
  
• Keep the negative sign.
  

Example: -4 + (-6) = -10

Rule 3: Adding a Positive and a Negative Integer

• Subtract the smaller absolute value from the larger absolute value.
  
• Keep the sign of the number with the greater absolute value.
  

Example 1: -3 + 7
→ 7 - 3 = 4
→ Keep the sign of 7 → Answer: 4

Example 2: 5 + (-9)
→ 9 - 5 = 4
→ Keep the sign of 9 (which is negative) → Answer: -4

Always use absolute value when deciding which number is larger. The absolute value is how far a number is from 0, without the sign.

Take This Quiz:

Adding and Subtracting Integers Test

Rules for Subtracting Integers

Subtracting integers may look tricky, but there's a helpful shortcut:

Rule: Change Subtraction to Addition

To subtract integers:

• Change the subtraction sign to addition
  
• Change the sign of the second number to its opposite
  

Example 1: 7 - 3 = 7 + (-3) = 4
(Same answer as normal subtraction, but now we think of it using integers.)

Example 2: 6 - (-2) = 6 + 2 = 8
(Remember: subtracting a negative = adding a positive.)

Example 3: -5 - 4 = -5 + (-4) = -9

By following this method, subtraction problems become easier to manage using the same rules as addition.

Absolute Value and Integer Comparison

Absolute value means how far a number is from 0 on a number line.

You use absolute values when:

• Comparing integers
  
• Adding or subtracting integers with different signs
  

In a problem like: -7 + 4, compare:

• |−7| = 7
  
• |4| = 4
  

Subtract: 7 − 4 = 3
Keep the sign of the larger absolute value → Answer: -3

Take This Quiz:

Addition and Subtraction of Integers

Practice: Adding Integers Step by Step

Let's walk through several examples.

Example 1: -2 + (-6)
Same signs → Add the numbers
2 + 6 = 8
Keep the negative sign → Answer: -8

Example 2: 9 + (-5)
Different signs → Subtract absolute values
9 − 5 = 4
9 is positive → Answer: 4

Example 3: -10 + 3
Different signs → 10 − 3 = 7
10 is negative → Answer: -7

Take This Quiz:

Trivia quiz about Adding And Subtracting Integers

Practice: Subtracting Integers Step by Step

We'll now change subtraction problems into addition and solve.

Example 1: 5 - 7
Change: 5 + (-7)
→ Different signs: 7 − 5 = 2
7 is bigger and negative → Answer: -2

Example 2: -6 - (-4)
Change: -6 + 4
→ Different signs: 6 − 4 = 2
6 is negative → Answer: -2

Example 3: -8 - 3
Change: -8 + (-3)
→ Same signs: Add and keep negative
8 + 3 = 11 → Answer: -11

Adding and Subtracting Multiple Integers

Sometimes you have more than two integers to work with.

Example 1: -2 + 5 + (-3)
Step 1: -2 + 5 = 3
Step 2: 3 + (-3) = 0
Answer: 0

Example 2: -7 + (-2) + 4
Step 1: -7 + (-2) = -9
Step 2: -9 + 4 = -5
Answer: -5

Break the problem into two parts at a time and apply the rules.

Subtracting a Negative Number

Subtracting a negative number is one of the most common mistakes students make.

Rule:
Subtracting a negative number becomes adding a positive number

Example 1: 6 - (-2)
Change: 6 + 2 = 8

Example 2: -3 - (-4)
Change: -3 + 4 = 1

This shortcut helps avoid sign errors and keeps your work accurate.

Take This Quiz:

Subtracting Integers Quiz: Trivia Test!