Understanding Integers Addition

Integers are a set of numbers that include all whole numbers (0, 1, 2, 3…) and their negative counterparts (-1, -2, -3…). Adding them follows specific rules based on their signs.

1. Key Concept: Absolute Value

Before adding integers, it is important to understand Absolute Value. The absolute value of a number is its distance from zero on a number line, regardless of direction. It is always positive.

• The absolute value of |+5| is 5.

• The absolute value of |-8| is 8

2. Rule 1: Adding Integers with the Same Sign

When both numbers have the same sign (both positive or both negative):

1. Add their absolute values.

2. Keep the common sign for the result.

Examples:

• (+5) + (+3) = +8

• (-4) + (-6) = -10

3. Rule 2: Adding Integers with Different Signs

When the numbers have different signs (one positive and one negative):

1. Subtract the smaller absolute value from the larger absolute value.

2. Take the sign of the number with the larger absolute value.

Examples:

• (+10) + (-3) \rightarrow 10 – 3 = 7. Since 10 is larger than 3, the result is +7.

• (+2) + (-9 ) rightarrow    9    2 = 7. Since 9 is larger than 2, the result is -7

4. Visualizing on a Number Line

Think of addition as movement on a number line:

• Positive numbers mean move to the Right.

• Negative numbers mean move to the Left.

Example: (-2) + (+5)

1. Start at -2.

2. Move 5 units to the right.

3. You land on +3