Problem 86 - Elementary Algebra

Question

\(\frac{15-3}{2+4}\)

Step-by-Step Solution

Answer

The answer is 2.

Step 1: Simplify the Numerator

Start by simplifying the numerator of the fraction. Subtract 3 from 15: \[ 15 - 3 = 12 \]

Step 2: Simplify the Denominator

Next, simplify the denominator by adding 2 and 4: \[ 2 + 4 = 6 \]

Step 3: Divide the Numerator by the Denominator

Finally, divide the simplified numerator by the simplified denominator: \[ \frac{12}{6} = 2 \]

Key Concepts

Numerator

Understand that the numerator is the top part of a fraction. It represents how many parts of the whole you have.
In the given example, the numerator is the expression \(15 - 3\).
By simplifying the numerator, you perform the basic arithmetic operation, which in this case is subtraction:
\[ 15 - 3 = 12 \]
Once simplified, the numerator becomes 12, making it easier to work with the fraction.

Denominator

The denominator is the bottom part of a fraction. It shows into how many equal parts the whole is divided.
In the example, the denominator is the expression \(2 + 4\).
To simplify the denominator, you carry out the arithmetic operation of addition:
\[ 2 + 4 = 6 \]
After simplification, the denominator becomes 6. This helps in further reducing the fraction.

Basic Arithmetic Operations

Understanding basic arithmetic operations is crucial for fraction simplification.
In our example, we used two primary operations: subtraction and addition.
Here’s a quick refresher:

• Subtraction (\(-\)): This operation finds the difference between two numbers. For instance, \(15 - 3 = 12\).
• Addition (\(+\)): This operation combines numbers to get a sum, like \(2 + 4 = 6\).

After performing these operations separately on the numerator and the denominator:
1. The simplified numerator is 12.
2. The simplified denominator is 6.
You then divide the numerator by the denominator:
\[ \frac{12}{6} = 2 \]
Remember, mastering these basic operations makes fraction simplification straightforward and accessible.