Lesson 14: The Number Line: Negative Numbers

New Concept

A negative number is a real number that is less than zero, representing the opposite of a positive number.

The points to the left of zero represent negative numbers.

What’s next

Soon, we'll use the number line for a visual breakdown of comparing, ordering, and subtracting with negative numbers in worked examples.

Property

Negative numbers are represented by writing a minus sign before a number: $-5$. The number $-5$ is read 'negative five.'

Examples

• The number $-15$ is read aloud as 'negative fifteen'.
• To write 'negative one hundred,' you would write $-100$.
• When a calculator displays $-50$, it means 'negative fifty'.

Explanation

That little dash isn't just for subtraction; when it's attached to the front of a number, it's a 'negative' sign! It tells you that the number lives on the left side of zero, in the cool, shady part of the number line. Reading it correctly makes you sound like a math pro!

Property

The points to the right of zero on a number line represent positive numbers. The points to the left of zero represent negative numbers. Zero is neither positive nor negative.

Examples

• A temperature of twenty degrees below zero is written as $-20^\circ\text{F}$.
• An elevation of 300 feet below sea level is shown as 'elev. $-300$ ft.'
• A drop in a stock's price by 2.50 dollars can be shown as $-2.50$.

Explanation

Think of zero as the ground floor. Positive numbers are floors going up in a skyscraper, and negative numbers are the secret basement levels going down! They help us talk about things like freezing temperatures, being below sea level, or when the price of a cool gadget drops in value.

Property

Numbers like $5$ and $-5$ are the same distance from zero but are on opposite sides of zero. We say that $5$ and $-5$ are opposites.

Examples

• The opposite of $12$ is $-12$.
• The opposite of $-25$ is $25$.
• On a number line, $7$ and $-7$ are both 7 steps away from $0$.

Explanation

Imagine you and your mirror image standing on opposite sides of a puddle (that's zero). You're both the same distance from it! That's how opposites work in math. Every positive number has a negative twin, and they perfectly balance each other out across zero on the number line.