Problem 81 - Elementary Algebra

Question

Simplify. $$ -(10) $$

Step-by-Step Solution

Answer

-10

Step 1: Identify the Expression

The expression given is \(- (10)\).This means the negative of the number 10.

Step 2: Apply the Negative Sign

To simplify, apply the negative sign to the number 10. Multiply by \(-1\) which gives:\(-1 imes 10 = -10\).

Step 3: Simplified Result

The simplified form of \(- (10)\) is \(-10\).

Key Concepts

Negative Numbers

Negative numbers are an essential concept in mathematics. They are numbers that are less than zero and usually have a minus (-) sign in front of them. In the number line, negative numbers are placed to the left of zero.

Understanding negative numbers is crucial because they are widely used in various fields such as finance, science, and engineering. For instance, they represent losses, temperatures below freezing, or directions below a reference point. Here are some important points to know:

• Negative numbers are opposite to positive numbers.
• Combining negative and positive numbers requires careful attention to their signs.
• If you subtract a positive number, you move left on the number line, just like when you add a negative number.

Grasping this concept is the first step in solving operations involving negative numbers, like the one shown in the original exercise.

Multiplication by Negative

In mathematics, multiplying by a negative number can be a bit tricky, especially if you are doing it for the first time. Let's take a deeper look into how this works.

When you multiply a positive number by a negative number, the result is always a negative number. Conversely, if you multiply two negative numbers, the result is positive. This rule is crucial:

• Positive × Negative = Negative
• Negative × Negative = Positive

In the original exercise, you see: - Multiply 10 by -1, which results in -10, since a negative times a positive gives a negative.

Remember: this change of signs during multiplication underpins algebraic simplifications and is foundational in many mathematical operations.

Algebraic Expressions

Algebraic expressions are a key component of algebra and include numbers, variables (like x or y), and operations (such as adding and multiplying). They are the building blocks for algebraic equations and inequalities.

Let's break it down:

• Expressions can be simplified by performing the operations involved, like addition or multiplication.
• Negative numbers can be part of algebraic expressions, requiring careful application of their rules.

For example, an expression like - (10) is simplified to -10 by understanding the multiplication by negative numbers. In more complex expressions, similar steps can be applied to ensure all operations respect the correct sign shifts.

Understanding the roles of numbers and variables in expressions can help solve more complex problems efficiently. By grasping algebraic expressions, students can solve equations that model real-world phenomena more easily.