Problem 10 - Elementary Algebra

Question

Find the opposite of each real number. $$ -15 $$

Step-by-Step Solution

Answer

Answer: The opposite of the real number -15 is +15.

Step 1: Identify the given real number

The given real number is -15.

Step 2: Determine the opposite of the number

Since the given number is negative, we will change its sign to positive. Therefore, the opposite of -15 is +15.

Step 3: Display the result

The opposite of the real number -15 is +15.

Key Concepts

Opposite Numbers

Opposite numbers are pairs of numbers that are the same distance away from zero on the number line but in different directions. Think of them as mirror images of each other, where the mirror is placed at zero. For example, if you have a number like -15, its opposite would be +15.

Opposite numbers have the following properties:

• They always sum up to zero. For instance, -15 + 15 equals zero.
• If one number is negative, its opposite will be positive, and vice versa.
• Opposites help us easily solve equations and understand the relationship between numbers on the number line.

Understanding opposite numbers is beneficial in various mathematical operations, especially when dealing with addition and subtraction.

Negative Numbers

Negative numbers are numbers less than zero. They appear on the left side of the zero on a number line. Negative numbers are important because they allow us to represent values below a baseline, like when dealing with temperatures below freezing or debts in finances.

Key features of negative numbers:

• They are identified with a minus sign (-) in front. Examples include -3, -7, and -15.
• Negative numbers are less than any positive numbers. For example, -15 is less than +3.
• Adding two negative numbers gives a more significant negative number. For example, -10 + (-5) = -15.

By grasping the concept of negative numbers, you can efficiently tackle problems that involve decreases or deficits.

Positive Numbers

Positive numbers are numbers greater than zero and are located to the right of zero on the number line. These numbers are used to represent values above a baseline like income, elevation above sea level, or anything else that has a more-than-zero value.

Characteristics of positive numbers include:

• They do not need a sign to indicate positivity, but sometimes a plus (+) sign is used for clarity. For example, 5 and +5 are the same.
• Positive numbers are greater than any negative numbers. So, +15 is greater than -15.
• Adding two positive numbers always results in a larger positive number, such as 5 + 10 = 15.

Understanding positive numbers is crucial for problems involving increases, profits, or any growth.