The Number Line

A number line is a straight line where numbers are placed at equal intervals.

Basic Structure

$\leftarrow -5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \rightarrow$

• Numbers increase to the right
• Numbers decrease to the left
• Zero is in the middle

Positive and Negative Numbers

• Positive numbers: Right of zero (+1, +2, +3...)
• Negative numbers: Left of zero (-1, -2, -3...)
• Zero: Neither positive nor negative

Using the Number Line

Comparing Numbers

Numbers to the right are always greater. $-2 > -5$ (because -2 is to the right of -5)

Adding on the Number Line

• Adding a positive: Move right
• Adding a negative: Move left

Example: $3 + (-5)$ Start at 3, move 5 units left → Land on -2

Finding Distance

The distance between two numbers is called the absolute value of their difference.

Distance between 3 and -2: $|3 - (-2)| = |3 + 2| = |5| = 5$

Absolute Value

The absolute value of a number is its distance from zero.

$|5| = 5$ $|-5| = 5$

Absolute value is always positive (or zero).