Adapted from Wentworth's Elementary Algebra for MathDoctor.net
In Arithmetic, 0 usually means "nothing." But in Algebra, 0 is often just a starting point. Numbers can go in two opposite directions from zero.
Think of it like a thermometer or a bank account. A temperature of -10° isn't "nothing"—it's a specific amount of cold. A bank balance of -$50 means you owe money.
The Absolute Value of a number is simply its distance from zero, regardless of direction. We use vertical bars to show this.
The absolute value of both 5 and -5 is 5.
|5| = 5 |-5| = 5
When adding numbers with different signs, think of it as a battle between "Teams."
1. Same Signs: Add the numbers together and keep the sign.
5 + 3 = 8
-5 + (-3) = -8
2. Different Signs: Subtract the smaller number from the larger one. The "Team" with more points wins the sign.
10 + (-4) = 6 (Positive team had more points)
-10 + 4 = -6 (Negative team had more points)
Negative numbers appear everywhere in modern life. Here is how we translate them into Algebra:
Example 1: Finance
You have $20 in your Venmo account. You spend $25 on lunch.
Math: 20 - 25 = -5
Meaning: You are overdrawn by $5.
Example 2: Altitudes
A drone is flying at 100 feet above sea level. It drops 150 feet into a canyon.
Math: 100 - 150 = -50
Meaning: The drone is now 50 feet below sea level.
Practice these "directional" math problems:
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