Problem 11 - Elementary Algebra

Question

For the following problems, simplify the expressions. $$ \frac{29+11}{6-1} $$

Step-by-Step Solution

Answer

Answer: The simplified expression is 8.

Step 1: Add the numbers in the numerator

To simplify the expression, we will first add the numbers in the numerator: \(29 + 11 = 40\).

Step 2: Subtract the numbers in the denominator

Next, we will subtract the numbers in the denominator: \(6 - 1 = 5\).

Step 3: Divide the simplified numerator by the simplified denominator

Lastly, we will divide the simplified numerator by the simplified denominator to get our final answer: \(\frac{40}{5} = 8\). So, the simplified expression is 8.

Key Concepts

Understanding the Numerator

The numerator is the top part of a fraction. It represents the number of parts we have. In the fraction \( \frac{a}{b} \), the number \( a \) is the numerator. In mathematical operations, the numerator is the number we are working with in the context of division. For example, in our given expression \( \frac{29+11}{6-1} \), the numerator is "\( 29+11 \)." This means we first need to add these numbers together.

Adding terms in the numerator is like counting how many items you have in total. In this case, adding 29 and 11 gives us 40, so our numerator becomes 40. This simplified numerator is going to be divided by the denominator to complete the expression simplification.

Exploring the Denominator

The denominator is the bottom part of a fraction. It tells you the total number of equal parts into which something is divided. In the simple fraction \( \frac{a}{b} \), the \( b \) is the denominator. The denominator acts as the divisor in a division operation. In our expression \( \frac{29+11}{6-1} \), the portion "\( 6-1 \)" is the denominator.

To simplify the denominator, we need to perform the subtraction \( 6 - 1 \), which results in 5. After simplifying the denominator, the simplified expression allows us to focus on the relationship between the numerator and the denominator. This gives us a clearer path to complete the operation by dividing the simplified numerator 40 by the simplified denominator 5.

Performing Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These are foundational skills used in simplifying expressions. In our exercise, we used these operations as follows:

• Addition: First, we combined the numbers in the numerator: \( 29 + 11 = 40 \). This step consolidated the terms into one easy-to-use figure for division.
• Subtraction: Then, in the denominator, we found the difference between the terms: \( 6 - 1 = 5 \). This step made the denominator simple to work with.
• Division: Finally, we divided the simplified numerator by the simplified denominator: \( \frac{40}{5} = 8 \). This division produced the final simplified answer of the expression.

Understanding these basic arithmetic operations is crucial not just for this problem, but for many others in mathematics where simplification is needed.