Problem 31 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ -(-5) $$

Step-by-Step Solution

Answer

Question: Simplify the expression -(-5) and provide the final answer. Answer: The simplified form of the expression is 5.

Step 1: Understand the expression

Here, we have a double negative operation. The expression is simplified by understanding that a negative times a negative results in positive.

Step 2: Simplify the double negative

Since a negative times a negative is positive, we can simplify the expression as follows: $$ -(-5) = 5 $$

Step 3: Write the final answer

The simplified form of the expression is: $$ 5 $$

Key Concepts

Double Negative

Understanding the concept of a double negative is very important, especially in math expressions involving negative numbers. A double negative consists of two negative signs placed in sequence. For example, in the expression \(-(-5)\), the two negatives act together. This might seem tricky at first, but don't worry, it’s actually quite simple once you get the hang of it!

When you encounter two negative signs next to each other, they combine to make a positive. You can think of it as two negatives canceling each other out, resulting in a positive. This rule comes from the multiplication property of integers, where a negative times a negative equals a positive. For instance, \(-1 \times -5\) becomes \(5\).

• A double negative results in a positive.
• \(-(-x) = x\), where \(x\) is any number or variable.
• This is because multiplying two negative numbers results in a positive.

Simplifying Expressions

Simplifying expressions is all about making math problems easier to handle. When faced with complex expressions, it's important to identify all components and apply mathematical rules to simplify them. With expressions involving negative numbers, using the correct rules can significantly reduce the complexity.

In the original exercise \(-(-5)\), we simplify it by removing the double negative. We can rewrite this simply as \(5\) because the \(-\) signs cancel each other out. Remember, the key to simplifying is looking for these opportunities to reduce what's in front of you.

• Identify any double negatives.
• Use the rule that two negatives make a positive.
• Simplify the expression to make calculations easier.

Integer Operations

Integer operations are fundamental in math, and they involve basic arithmetic using whole numbers. Mastery of these operations, including addition, subtraction, multiplication, and division, is crucial, especially when working with negative numbers. Let's look at the essential points to remember:

• Adding a positive number increases the value, while adding a negative number decreases it.
• Subtracting a positive number decreases the value, whereas subtracting a negative number increases it.
• For multiplication: a positive times a positive is positive, and a negative times a negative is also positive.
• Division follows similar rules: a positive divided by a positive or a negative divided by a negative gives a positive result.

In operations like \(-(-5)\), you use multiplication rules of integers: two negatives make a positive. This understanding eases the simplification of expressions.