Problem 21 - Elementary and Intermediate Algebra

Question

Find the opposite, or additive inverse. $$ -3.14 $$

Step-by-Step Solution

Answer

The additive inverse of -3.14 is 3.14.

Step 1 - Understand the Concept of Additive Inverse

The additive inverse of a number is what you add to the number to get zero. For any number, the additive inverse is its negative if it is positive, and positive if it is negative.

Step 2 - Identify the Number

Here, the given number is -3.14, which is a negative number.

Step 3 - Find the Opposite

To find the opposite (additive inverse) of -3.14, one needs to change its sign. Therefore, the opposite of -3.14 is 3.14.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero and are usually represented with a minus sign (e.g., -1, -3.14, -10). Understanding negative numbers is crucial in mathematics because they are widely used to represent loss, debt, decreases, and temperature below zero. For example:

• If you owe someone $5, you can say you have -5 dollars.
• If the temperature is 10 degrees below zero, it's -10 degrees.

Negative numbers are found on the left side of the number line. The further left you go, the smaller the value. For instance, -10 is smaller than -5. Knowing how to handle negative numbers helps in many areas like arithmetic, algebra, and even real-life financial calculations.

Positive Numbers

Positive numbers are numbers greater than zero, represented without any sign or with a plus sign (e.g., 1, +2, 3.14). They signify quantities like gains, heights, and distances. Consider these examples:

• If you have 5 apples, you have +5 or simply 5 apples.
• If a building is 30 feet tall, it is +30 feet high.

Positive numbers lie on the right side of the number line. Similar to negative numbers, the further right you go, the larger the value. Mastering positive numbers is foundational in basic arithmetic operations like addition, subtraction, multiplication, and division, which are essential in both academic studies and everyday life tasks.

Finding Opposites

Finding opposites, or additive inverses, is a key concept in mathematics. The opposite of a number is what you add to it to get zero. Here are some quick tips to find opposites:

• If the number is positive, its opposite will be negative. For example, the opposite of +5 is -5.
• If the number is negative, its opposite will be positive. For instance, the opposite of -3.14 is 3.14.

Let's use an example to make it clear: If you have the number -3.14, you need to change its sign to find its opposite. That gives you 3.14. Knowing how to find opposites is important for solving equations and understanding more complex topics like vectors and functions in advanced mathematics. It's a simple yet powerful tool for various math problems.