Problem 49 - Algebra A Combined Function

Question

Simplify. See Sections 1.5 and \(1.6 .\) \(\frac{0-6}{5-0}\)

Step-by-Step Solution

Answer

The simplified form is \(\frac{-6}{5}\).

Step 1: Simplify the Numerator

The numerator of the fraction is \(0 - 6\). Simplify this expression: \(0 - 6 = -6\).

Step 2: Simplify the Denominator

The denominator of the fraction is \(5 - 0\). Simplify this expression: \(5 - 0 = 5\).

Step 3: Form the Fraction

Place the results from Steps 1 and 2 into the fraction form: \(\frac{-6}{5}\).

Step 4: Simplify the Fraction

The fraction \(\frac{-6}{5}\) is already in its simplest form, as there are no common factors between the numerator and the denominator besides 1.

Key Concepts

Understanding Numerator and Denominator

When dealing with fractions, it's essential to know what the terms numerator and denominator mean. The numerator is the top part of a fraction. It shows how many parts of the whole are being considered. In our example, the numerator is represented by the expression \(0 - 6\). After simplifying, the numerator becomes \(-6\).

• Numerator: The top number in a fraction.
• Denominator: The bottom number in a fraction.

On the other hand, the denominator is the bottom part which indicates the total number of equal parts the whole is divided into. In the exercise, the denominator was \(5 - 0\), which simplifies to 5. Together, they form the fraction \(\frac{-6}{5}\). Knowing these terms helps in understanding and working with fractions more effectively.

Simplifying Expressions Made Easy

Simplifying expressions is all about making them as straightforward as possible. This involves reducing expressions to their most basic form without changing their value. Let's look at our exercise example. The expression \(0 - 6\) was simplified directly to \(-6\).

• Direct subtraction: Simplify \(0 - 6\) to get \(-6\).
• Another example: Simplify \(a - b\) by substituting values if known.

Simplification often involves:

• Performing basic arithmetic operations such as addition, subtraction, multiplication, and division.
• Removing any unnecessary terms or common factors that don’t change the overall expression.

Mastering simplification is key to making complex problems more manageable and is a fundamental skill in algebra.

Basic Algebra Steps for Simplifying Fractions

Simplifying fractions involves using basic algebra steps to break down the problem. Initially, this can seem difficult, but with practice, it becomes a clear process. Let's revise the steps we applied in this exercise:

• Simplify the numerator: First, we tackled \(0 - 6\), turning it into \(-6\).
• Simplify the denominator: Next, the expression \(5 - 0\) was calculated to be 5.
• Form the fraction: Place the simplified numerator and denominator into fraction form, \(\frac{-6}{5}\).
• Check for further simplification: In the example of \(\frac{-6}{5}\), there are no common factors apart from 1, suggesting it’s in simplest form.

These steps show how amateur and experienced students alike can approach fraction problems. Following a systematic approach ensures fewer mistakes and provides a sound basis for more complex algebraic tasks. Remember, practice is vital and reviewing these steps regularly can reinforce your understanding.