Problem 85 - Elementary Algebra

Question

\(\frac{14-2}{6-3}\)

Step-by-Step Solution

Answer

4

Step 1 - Evaluate the Numerator

First, simplify the numerator of the fraction. The numerator is given by the expression \(14 - 2\). Subtract 2 from 14 to get 12.

Step 2 - Evaluate the Denominator

Next, simplify the denominator of the fraction. The denominator is given by the expression \(6 - 3\). Subtract 3 from 6 to get 3.

Step 3 - Divide the Results

Now, divide the simplified numerator by the simplified denominator. This means computing \(\frac{12}{3}\). When you divide 12 by 3, you get 4.

Key Concepts

Numerator

The numerator is the top part of a fraction. It tells you how many parts you have. Let's take our exercise as an example: the numerator is represented by the expression \(14 - 2\).
First, we need to simplify this part to understand the fraction better.
Subtract 2 from 14, which gives us 12.
So, the numerator is 12.
In other words:

• Numerator = 12

Denominator

The denominator is the bottom part of a fraction. It indicates how many parts make up a whole. In our exercise, the denominator is represented by the expression \(6 - 3\).
We need to simplify this to understand the entire fraction properly.
Subtracting 3 from 6 gives us 3.
Now, we've found our denominator:

• Denominator = 3

Division

To simplify a fraction, the last step involves dividing the numerator by the denominator. This is the essence of fraction simplification.
Let's apply this to our exercise. We've determined:

• Numerator = 12
• Denominator = 3

Now, we divide the numerator by the denominator: \( \frac{12}{3}\).
When you divide 12 by 3, you get 4.