Problem 57 - College Algebra

Question

Rewrite expression without absolute value bars. \(\frac{-3}{|-3|}\)

Step-by-Step Solution

Answer

The expression simplifies to -1.

Step 1: Evaluate the Absolute Value

The number inside the absolute value bars is -3. The absolute value of -3, denoted by |-3|, is its numerical value without its negative sign, which is 3.

Step 2: Substitute the Absolute Value in the Expression

Replace the absolute value |-3| in the expression with the value obtained in step 1. The simplified expression becomes: \(\frac{-3}{3}\).

Step 3: Simplify the Expression

Divide -3 by 3. This gives -1.

Key Concepts

Numerical Expression

A numerical expression refers to a combination of numbers and operations such as addition, subtraction, multiplication, and division. In the exercise, we start with a numerical expression that includes an absolute value: \(\frac{-3}{|-3|}\). This particular expression involves:

• Numerator: \(-3\) , which is a negative integer.
• Denominator: Absolute value \(|-3|\).

Absolute values are special components in numerical expressions. They represent the distance of a number from zero on the number line, effectively removing the sign of the number. Therefore, \(|-3|\) becomes just \(3\).
At the core, when you deal with numerical expressions, especially those with absolute values, you're tasked with simplifying them to their basic form or solving them to find a numerical value.

Simplification

Simplification is the process of making a mathematical expression easier to understand or solve. In this situation, simplifying involves evaluating and reducing the expression \(\frac{-3}{|-3|}\) to its simplest form. First, you need to address any operations like absolute value, which requires converting \(|-3|\) into \(3\). This is achieved because the absolute value removes the negative sign. Once you substitute |-3| with 3, the expression transforms to \(\frac{-3}{3}\).
The next phase of simplification involves fraction division, specifically dividing \(-3\) by \(3\). Performing this operation gives the result of \(-1\). Simplification generally aims to make expressions cleaner or more manageable, ensuring that you don't miss the fundamental input values or relationships.

Fraction Division

Fraction division takes place when you divide one number by another, which is a core operation in many numerical expressions. In our example, once the absolute value has been substituted (\(\frac{-3}{3}\)), we proceed to divide.

• Numerator: \(-3\)
• Denominator: \(3\)

To divide \(-3\) by \(3\), you follow the division rule: simply divide the numerical values. Here, \(-3 \div 3\) results in \(-1\). This division operation simplifies the entire exercise because it reduces the expression to a single integer.In fraction division, understanding the roles of numerators and denominators is crucial. Properly handling negations is key to reaching the correct solution without errors. This concept shows how operations can turn seemingly complex expressions into straightforward solutions.