Lesson 1: Negative Numbers and Absolute Value

Property

The number line consists of a straight line extending indefinitely in two directions from a central point, denoted as $0$ (zero), and a line segment starting at $0$, denoted as the unit distance.
For each counting number $n$, a tick mark is made on the straight line that is $n$ units distance from $0$ (the origin).
The marks on the right side of $0$ are denoted by the positive integers $1, 2, 3, 4, \ldots$, and the marks on the left side are denoted by the negative integers $-1, -2, -3, -4, \ldots$, called the opposites of the positive integers.

Examples

Property

On a vertical number line, integers positioned higher are greater than integers positioned lower.
If integer $a$ is above integer $b$ on a vertical number line, then $a > b$.
If integer $a$ is below integer $b$ on a vertical number line, then $a < b$.

Examples

Property

Negative numbers appear in real-world measurements that are two-sided, with a value of zero acting as a reference point.
Examples include temperature (degrees below freezing), elevation (below sea level), and finance (debits or debt).

Examples

• The temperature rose from a low of $-8^\circ$F to a high of $15^\circ$F. The total temperature spread is the distance from $-8$ to $0$ plus the distance from $0$ to $15$, so $8+15=23^\circ$F.

• A submarine at $-300$ feet ascends to $-120$ feet. The submarine traveled a vertical distance of $|-300 - (-120)| = |-180| = 180$ feet.