Problem 80 - Algebra 2

Question

PREREQUISITE SKILL Identify the additive inverse for each number or expression. 25

Step-by-Step Solution

Answer

The additive inverse of 25 is -25.

Step 1: Understand the Concept of Additive Inverse

The additive inverse of a number is what you add to that number to get zero. In other words, it's the negative of the original number.

Step 2: Determine Additive Inverse of 25

To find the additive inverse of 25, we need to find a number that, when added to 25, results in zero. This number is simply -25.

Step 3: Verify the Solution

Add 25 and its additive inverse -25 together: \(25 + (-25) = 0\). Since they sum to zero, -25 is indeed the additive inverse of 25.

Key Concepts

Addition

Addition is a fundamental mathematical operation where two or more numbers are combined to make a sum. It's a straightforward concept, yet essential in math and daily life.
In the operation of addition, each number involved is called an "addend." When you add these numbers together, you get the "sum." For example, in the equation \(3 + 5 = 8\), both 3 and 5 are addends, and their total, 8, is the sum.
An important property of addition is its commutative nature, meaning the order of the addends doesn't affect the sum. Whether you calculate \(3 + 5\) or \(5 + 3\), the result is always 8. Addition also helps in understanding concepts like subtraction and solving complex equations.

Negative Numbers

Negative numbers are numbers with a value less than zero. They are located to the left of zero on the number line. These numbers are often used to represent situations involving deficiency or debt.
Negative numbers are denoted with a minus sign (-). For instance, -10 is a negative number that indicates 10 units less than zero. Negative numbers are crucial when performing tasks such as calculating temperatures below freezing or managing loss in financial contexts.
When you add two numbers where one is negative, you are essentially balancing the equation between positive and negative values. For example, if you have \(-3 + 3 = 0\), these two numbers cancel each other out to zero, perfectly illustrating the concept of additive inverses.

Zero Sum Property

The zero sum property is at the heart of understanding additive inverses. This property states that when a number is added to its additive inverse, the result is zero.
Consider the example of the number 25 with its additive inverse, -25. Adding these two, we find \(25 + (-25) = 0\). This equation confirms that when you add a number to its opposite, or negative, the sum is zero.
This property is especially useful in algebra and helps to simplify equations. Recognizing how additive inverses interact in a sum can assist in solving for unknown variables or checking equation balance. Knowing this can enhance mathematical problem-solving skills and is a critical part of a math student's toolkit.