Lesson 1: Interpreting Negative Numbers

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.

Property

Negative numbers are numbers less than 0.
The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.
The notation $-a$ is read as “the opposite of $a$.”
The whole numbers and their opposites are called the integers.
The integers are the numbers $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$.

Examples

• The opposite of $15$ is $-15$, as both are 15 units from zero.
• The opposite of $-9$ is $9$. This can be written as $-(-9) = 9$.
• If $y = -25$, then $-y$ means the opposite of $-25$, which is $-(-25) = 25$.

Explanation

Integers expand our number system to include negative values, which are like mirror images of positive numbers across zero. The 'opposite' of a number is simply its reflection on the other side of the number line.