Problem 64 - Prealgebra

Question

Simplify each of the following. $$-(-5)$$

Step-by-Step Solution

Answer

-(-5) simplifies to 5.

Step 1: Understand Negation

When you see a minus sign in front of a number or an expression, it indicates the opposite or negation of that number or expression. If a number is negative, its negation is positive.

Step 2: Apply Double Negation

The expression given is -(-5). The negative sign in front of another negative sign turns the entire expression into a positive. So, -(-5) is the same as +(5) . This is because negating a negative number results in a positive number.

Step 3: Final Simplification

After applying the double negation, you simplify the expression to 5. This means -(-5) simplifies to 5.

Key Concepts

Double Negation Rule

The double negation rule is a key concept in math that turns two negatives into a positive. This rule states that when you negate a negative number, you end up with a positive number. For instance, in the expression \(-(-5)\), the first negative sign negates the negative sign of 5. You can think of this as removing the negative aspect of that number, which effectively makes it positive. So, \(-(-5)\) becomes 5.

• Double negatives cancel each other out.
• This rule is helpful in simplifying mathematical expressions.
• Using this rule can help avoid confusion when dealing with complex calculations.

Apply this rule whenever you encounter a double negative, especially in expressions like \(-(-x)\), to easily convert them into a positive value.

Integer Simplification

Integer simplification involves the process of making an expression as concise as possible without changing its value. When simplifying integers, especially with negations, it's essential to follow the standard rules of arithmetic.

• Remove double negatives using the double negation rule.
• Convert complicated expressions into simpler ones step by step.
• Aim for expressions that are easier to compute or understand.

For example, using the double negation rule simplifies \(-(-5)\) to 5. By recognizing double negatives and converting them to positives, you can streamline any calculations and minimize mistakes.

Negative Numbers in Math

Negative numbers are numbers less than zero and are marked by a minus sign before the number. They represent a deficiency, or something below a reference point. Understanding how to handle negative numbers is crucial in math.

• Negative numbers are used in various applications, like temperatures or financial debts.
• Adding a negative number results in subtraction.
• Subtracting a negative number equates to addition due to the double negation rule.

In the expression \(-(-5)\), the first negative indicates we are taking the opposite of the second negative, hence turning \(-5\) into 5. This ability to transform and simplify expressions with negatives is essential for solving more complex math problems correctly.