Problem 88 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

The answer is 1.

Step 1: Simplify the expression inside the numerator

Evaluate the square in the numerator first. Calculate \(3^2\), which is 9. So, the expression becomes: \(15 - 9\).

Step 2: Perform the subtraction in the numerator

Subtract 9 from 15 in the numerator: \(15 - 9 = 6\).

Step 3: Perform the addition in the denominator

Calculate the denominator by adding 2 and 4: \(2 + 4 = 6\).

Step 4: Divide the simplified numerator by the simplified denominator

Now, simplify the fraction: \( \frac{6}{6} = 1\).

Key Concepts

numerator simplification

To begin with fraction simplification, we often need to simplify the numerator. The goal is to break down any expressions or perform any necessary arithmetic operations present in the numerator to obtain a simpler value.

In our exercise, we start by looking at the numerator: \(15 - 3^{2}\). Since there is an exponent, we perform the exponentiation first. Calculating \(3^2\), we get 9.

Now, the numerator becomes \(15 - 9\). The next step is to simplify further by performing the subtraction: \(15 - 9 = 6\).

Through these steps, we simplified the numerator of the fraction from a complex expression to a single number.

denominator simplification

Just like we simplify the numerator, we do the same for the denominator. The denominator is the bottom part of the fraction and it's equally important in the simplification process.

In the given exercise, our denominator starts as \(2 + 4\). To simplify, we need to carry out the addition. Thus, we calculate: \(2 + 4\), which equals 6.

This turns our denominator into a simpler form, making the entire fraction easier to handle.

Simplifying the denominator ensures that we can achieve a more refined and manageable fraction.

basic arithmetic operations

At the core of fraction simplification are the basic arithmetic operations: addition, subtraction, multiplication, and division. These operations are fundamental in breaking down complex fractions into simple ones.

Let's look at how these operations were used in our exercise:

• **Exponentiation**: We calculated the square of 3 (which is \(3^2 = 9\)) in the numerator.
• **Subtraction**: We then subtracted this result from 15 (\(15 - 9 = 6\)), also in the numerator.
• **Addition**: Lastly, in the denominator, we added 2 and 4 to get 6 (\(2 + 4 = 6\)).

After performing all basic operations, we ended up with a simplified fraction: \(\frac{6}{6}\). This fraction can be further reduced to its simplest form, which is 1. Utilizing these operations efficiently can significantly help in simplifying fractions accurately.