Question

Evaluate each expression. $$ \frac{2-4}{5-3} $$

Short answer

-1

Step-by-step solution

Simplify the Numerator

First, simplify the numerator of the fraction. The numerator is given by the expression \( 2 - 4 \) Simplify this by subtracting 4 from 2, which results in \( 2 - 4 = -2 \).

Simplify the Denominator

Next, simplify the denominator of the fraction. The denominator is given by the expression \( 5 - 3 \) Simplify this by subtracting 3 from 5, which results in \( 5 - 3 = 2 \).

Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator: \( \frac{-2}{2} \). Simplify the fraction by dividing the numerator by the denominator: \( -2 \, \div \, 2 = -1 \).

Key concepts

Understanding the Numerator

The numerator is the top part of a fraction. It tells us how many parts of the whole we have. In the exercise, the numerator is given by the expression \( 2 - 4 \). To simplify the numerator, we perform basic arithmetic by subtracting 4 from 2. This gives us \(-2\). When dealing with numerators, remember that the value can be positive or negative, which will influence the final value of the fraction.

Grasping the Denominator

The denominator is the bottom part of a fraction. It tells us the total number of equal parts the whole is divided into. In the exercise, the denominator is given by the expression \( 5 - 3 \). We need to simplify this expression by subtracting 3 from 5, resulting in \( 2 \). A denominator can never be zero because division by zero is undefined.

Basic Arithmetic in Fraction Simplification

Basic arithmetic involves operations like addition, subtraction, multiplication, and division. In the given exercise, we performed subtraction in both the numerator and the denominator. For the numerator, we calculated \( 2 - 4 = -2 \), and for the denominator, we calculated \( 5 - 3 = 2 \). These simplified values allow us to write the fraction as \( \frac{-2}{2} \). Mastering basic arithmetic is essential for fraction simplification, as it forms the foundation of more complex calculations.

Dividing Fractions

To complete the fraction simplification process, we divide the simplified numerator by the simplified denominator. In the exercise, we divide \( -2 \) by \( 2 \), which gives us \( -1 \). So, \( \frac{-2}{2} = -1 \). This step requires a good grasp of division and understanding that dividing a negative number by a positive number results in a negative value. Simplifying fractions through division is a technique that helps make complex expressions more manageable.