Problem 42 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ \frac{-24}{-4} $$

Step-by-Step Solution

Answer

6

Step 1: Understand the Problem

The problem requires evaluating the fraction \(\frac{-24}{-4}\). This means dividing -24 by -4.

Step 2: Simplify the Signs

A negative divided by a negative results in a positive. Therefore, \(\frac{-24}{-4} = \frac{24}{4}\).

Step 3: Perform the Division

Divide 24 by 4. The result of \(\frac{24}{4}\) is 6.

Step 4: Write the Final Answer

Combine the results from previous steps. The final answer is 6.

Key Concepts

fraction evaluation

To understand and solve fraction problems, it's crucial to grasp the concept of fraction evaluation. It involves simplifying and resolving fractions to get a final value. A fraction consists of a numerator (top number) and a denominator (bottom number).
For instance, in the fraction \(\frac{-24}{-4}\), -24 is the numerator, and -4 is the denominator.

* Follow these steps for fraction evaluation:

• Identify the numerator and denominator.
• Simplify the signs if needed (negative or positive).
• Perform the actual division involved.

In the given exercise, \(\frac{-24}{-4}\) requires first understanding the negative signs before performing the division.

negative division rules

Negative division rules are essential for properly solving problems with negative numbers. Let's summarize these:
When you divide:

• A positive number by a positive number, the result is positive.
• A negative number by a positive number, the result is negative.
• A negative number by a negative number, the result is positive.

Using these rules for the given problem, \(\frac{-24}{-4}\):
Both the numerator (-24) and the denominator (-4) are negative. According to the rules, dividing two negatives results in a positive value. Thus, \(\frac{-24}{-4} = \frac{24}{4} \).

basic arithmetic division

Basic arithmetic division is fundamental and simply involves dividing one number by another to find out how many times the second number fits into the first.
For painless division, follow these steps:

• Determine what you are dividing (numerator) and by what you are dividing it (denominator).
• If needed, first simplify the fraction based on sign rules.
• Perform the division by determining how many times the denominator fits into the numerator.

In our case, after simplifying \(\frac{ -24 }{ -4 } \) to \(\frac{ 24 }{ 4 }\), we then divide 24 by 4 to get 6. The final answer to \(\frac{-24}{-4}\) is 6.