Problem 40 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

-6

Step 1: Identify the Numerator and Denominator

The fraction given is \(\frac{-24}{4}\). The numerator is -24 and the denominator is 4.

Step 2: Perform Division

Divide the numerator by the denominator: \(\frac{-24}{4} = -6\).

Key Concepts

Numerator and Denominator

In every fraction, you will find two main components: the numerator and the denominator. The numerator is the top number. It shows how many parts we have. The denominator is the bottom number. It shows into how many parts the whole is divided. For instance, in the fraction \(\frac{-24}{4}\), the numerator is -24, and the denominator is 4.
Understanding these two parts is crucial. To simplify or perform operations with fractions, you always need to deal with the numerator and the denominator correctly.
The numerator can be a positive or a negative number. Likewise, the denominator can be positive or negative. Sign plays an essential role in determining the final value of the fraction.
Let's move to how we can perform basic operations with fractions.

Basic Division

Division is one of the core operations you will encounter frequently in mathematics. When dividing fractions, your job is to divide the numerator by the denominator. In the given problem, you need to divide -24 by 4.
To understand this better, let’s imagine sharing -24 apples among 4 friends. Each friend would get an equal number of apples. If you do the division, each friend would get:\[\ \frac{-24}{4} = -6\].
Here are some steps to help you perform the division easily:

• Check the signs of the numbers (numerator and denominator).
• If both numbers have different signs, the result will be negative.
• If both numbers have the same sign, the result will be positive.
• Divide the absolute values of the numerator by the denominator.
• Finally, apply the sign to your result.

From this, you see that \(\frac{-24}{4} = -6\).

Negative Numbers in Fractions

When dealing with negative numbers in fractions, things can seem a bit tricky. However, it’s not too complicated. Just remember: If either the numerator or the denominator is negative, the fraction itself will be negative. Here are some quick tips to help you:

• If both numerator and denominator are positive, the fraction is positive.
• If one (numerator or denominator) is negative, the fraction is negative.
• If both are negative, the fraction is positive (since two negatives cancel each other out).

In our given problem, the numerator is -24, and the denominator is 4, making the fraction negative.
Applying these rules, the fraction \(\frac{-24}{4}\) evaluates to -6, as mentioned earlier. This means our final answer after performing the division remains -6.