Problem 26 - Prealgebra and Introductory Algebra

Question

Add. $$-11+11$$

Step-by-Step Solution

Answer

The answer is 0.

Step 1: Understand the Numbers

Notice that you have two numbers: -11 and +11. One is negative and the other is positive, but they are the same odd number.

Step 2: Carry Out the Addition

Since one is negative and the other is positive, their sum will be 0. This happens because you are basically negating the quantity of one with the other. So, -11 + 11 equals 0.

Key Concepts

Negative Numbers

Negative numbers are numbers which are less than zero. They are found on the left side of the number line. It's like walking in a direction opposite to positive numbers, towards zero and beyond.

• Negative numbers are represented with a minus sign (-).
• Common examples include -1, -5, -11, etc.
• They are used to express various real-world situations like temperatures below zero or debts.

When you add a negative number to a positive number, it's like moving left on the number line.
Imagine if a character moves 11 steps left when adding -11 to a neutral starting point. This helps understand how operations with negatives shift positions on the number line.

Positive Numbers

Positive numbers are numbers greater than zero. You find them on the right side of the number line. They tell you that you're moving forward or gaining something.

• They don't need a sign in front of them but can be shown with a plus (+).
• Examples include 1, 7, 11, etc.
• They represent assets like heights above sea level or income.

When you add a positive number to another number, you move to the right on the number line.
So, adding 11 means moving 11 steps to the right from a point, reaching a higher number.

Zero Sum Property

The zero sum property in mathematics is a fascinating concept where when you combine a number with its opposite, the sum is zero.

• For example, with numbers like -11 and +11, they are exact opposites.
• Add them together, and they balance each other out to zero, like a perfect balance scale.
• This property shows how systems can reach equilibrium or cancellation.

Consider it like this: if you have a debt of 11 dollars (-11) and then get paid 11 dollars (+11), you're back to zero.
This balance is key in many areas, from accounting to physics, demonstrating how opposites can negate each effect.