Problem 34 - Elementary and Intermediate Algebra

Question

Change the sign. (Find the opposite.) $$ -7 $$

Step-by-Step Solution

Answer

7

Step 1: Understanding Opposite Numbers

An opposite number is the number with the same numerical value but the opposite sign. For example, the opposite of 5 is -5, and the opposite of -3 is 3.

Step 2: Identify the Given Number

The given number in the exercise is -7.

Step 3: Change the Sign

Change the sign of the given number. Since the number is -7, its opposite will be 7.

Key Concepts

Number Properties

Number properties are rules and characteristics that numbers follow. One important property is the idea of opposites. Opposite numbers have the same absolute value but different signs. This means that if you have a number like 7, its opposite is -7. Similarly, the opposite of -7 is 7. Understanding this property can help you solve various math problems easily.

Negative Numbers

Negative numbers are numbers less than zero. They are written with a minus sign (-) before them. For example, -7 is a negative number. Negative numbers are found to the left of zero on a number line. They are used in various real-life contexts like temperatures below freezing, debts, or elevations below sea level.

Dealing with negative numbers often involves changing signs and using basic arithmetic operations like addition, subtraction, multiplication, and division. It is important to remember the rules for these operations to solve problems accurately. For example, when you add a negative number, you are essentially subtracting its absolute value.

Sign Change

Changing the sign of a number means finding its opposite. If the number is positive, its opposite or the result of changing its sign, will be negative. For example, changing the sign of 7 results in -7.

Conversely, if the number is negative, changing the sign makes it positive. The opposite of -7 is 7. This process is essential because it helps in solving equations and understanding the relationships between numbers.

To change the sign in a step-by-step manner:

• Identify the given number.
• Observe its sign (negative or positive).
• Write the same number with the opposite sign.

Utilizing this approach can make complex calculations simpler and error-free.