Problem 67 - Prealgebra

Question

Simplify each of the following. $$-|-2|$$

Step-by-Step Solution

Answer

The simplified expression is \(-2\).

Step 1: Understand the Absolute Value

The absolute value of a number is the distance of that number from zero on the number line without considering which direction from zero the number lies. The absolute value of negative numbers is the number itself without the negative sign. Therefore, for \(-2\), we have \(|-2| = 2\).

Step 2: Apply the Negative Sign Outside the Absolute Value

Once you have calculated the absolute value inside the expression, apply any operations outside of it. The problem is \(-|-2|\), so now it becomes \(-2\).

Step 3: Conclusion

With the calculated absolute value and the applied operation, the final simplified expression is \(-2\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are represented with a minus sign "-" before the number. Common negative numbers include -1, -2, -3, etc. Negative numbers are useful in various real-world contexts, such as indicating temperatures below zero or depths below sea level.

• In mathematical expressions, negative numbers have a profound impact when combined with other numbers through operations.
• The absolute value of a negative number is its distance from zero, which always results in a positive number.

In the given exercise, \(-2\) becomes 2 when considering its absolute value.

Number Line

A number line is a straight, horizontal line that visually represents numbers. At the center stands zero, with positive numbers extending to the right and negative numbers extending to the left.

• The number line provides a simple, visual way to understand the magnitude and relationships of numbers, including their absolute values.
• When considering the absolute value, we measure the distance a number is from zero, regardless of its direction on the number line.

In our exercise, \(-2\) is two units away from zero on the number line, thus its absolute value is 2.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. It's a fundamental skill in mathematics that makes expressions easier to work with.

• Begin by solving operations inside parentheses or absolute value bars first.
• Then, perform any operations outside these structures.

In the problem \(-|-2|\), first, solve \(|-2|\) to get 2. Next, apply the negative sign in front, simplifying it to \(-2\).
This systematic approach ensures that expressions are correctly and efficiently reduced.

Mathematical Operations

Mathematical operations include addition, subtraction, multiplication, and division. Understanding these operations is key for solving expressions.

• Absolute value bars act like parentheses, which means you solve within them first.
• The order of operations, sometimes known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is critical.

In the given exercise, after finding the absolute value, apply the negative sign: \(-|-2| = -2\). This demonstrates using operations correctly to simplify expressions.