Question

Evaluate each expression. $$ \frac{4+8}{5-3} $$

Short answer

6

Step-by-step solution

Evaluate the Numerator

First, add the numbers in the numerator. Here we have: \[ 4 + 8 = 12 \]

Evaluate the Denominator

Next, subtract the numbers in the denominator. Here we have: \[ 5 - 3 = 2 \]

Divide the Numerator by the Denominator

Now, divide the results from Step 1 and Step 2: \[ \frac{12}{2} = 6 \]

Key concepts

Understanding the Numerator

In a fraction, the numerator is the top number. It represents how many parts of the whole we are considering. For example, in the fraction \(\frac{4+8}{5-3}\), the numerator is \(4 + 8\). To evaluate the numerator, you need to add these numbers together. So, \(4 + 8 = 12\). The numerator plays a crucial role because it defines the number of parts we have.

Comprehending the Denominator

The denominator is the bottom number in a fraction. It denotes the total number of equal parts the whole is divided into. For instance, in the fraction \(\frac{4+8}{5-3}\), the denominator is \(5 - 3\). To evaluate this, you subtract the second number from the first one: \(5 - 3 = 2\). The denominator is essential because it tells us how many pieces make up the whole.

Applying Basic Arithmetic

Basic arithmetic includes operations like addition, subtraction, multiplication, and division. In the given problem, you need to use addition first to evaluate the numerator and then subtraction to calculate the denominator. After that, you divide the evaluated numerator by the denominator. So, starting with \(4 + 8 = 12\) and \(5 - 3 = 2\), you then divide: \(\frac{12}{2} = 6\). Understanding these basic operations is important for simplifying and solving fractions effectively.