Problem 3 - Algebra A Combined Function

Question

Simplify by dividing the numerator by the denominator. See Examples 1 through \(6 .\) $$ \frac{20}{2} $$

Step-by-Step Solution

Answer

The simplified form of \( \frac{20}{2} \) is 10.

Step 1: Understand the Problem

The problem asks us to simplify the fraction \( \frac{20}{2} \), which means dividing the numerator (20) by the denominator (2).

Step 2: Divide the Numbers

Perform the division by calculating \( 20 \div 2 \).

Step 3: Calculate the Result

\( 20 \div 2 = 10 \). The quotient is 10, so the simplified form of the fraction is 10.

Key Concepts

Numerator and Denominator

In every fraction, two parts work together harmoniously: the numerator and the denominator. The numerator is the top number, representing the parts we have. For example, in the fraction \( \frac{20}{2} \), 20 is the numerator, signifying the total parts under consideration. The denominator, on the other hand, is the bottom number that tells us into how many equal parts the whole is divided. In this instance, 2 is the denominator. It indicates that our whole is divided into two equal parts. Understanding these components helps us see fractions as division expressions, where the numerator is divided by the denominator. A correct comprehension of these terms is crucial for handling fractions effectively.

Division in Fractions

Dividing in fractions involves a straightforward process. The fraction \( \frac{20}{2} \) essentially represents the division of 20 by 2. Each fraction can be seen as a division problem, where the numerator is divided by the denominator. Here’s how it works:

• Identify the numerator and the denominator.
• Perform the division operation \( 20 \div 2 \).
• The result is the simplified value of the fraction.

In simple terms, consider a fraction as two numbers set for division. This method provides a straightforward path to simplifying fractions, purely by viewing them through the lens of division.

Simplification Process

The simplification process is a key skill in working with fractions. In our exercise, simplifying \( \frac{20}{2} \) is accomplished by dividing 20 (the numerator) by 2 (the denominator).

• Start by identifying that 20 is the numerator and 2 is the denominator.
• Next, execute the division: \( 20 \div 2 \). This computes to 10.
• The result, 10, is the simplest form of the fraction \( \frac{20}{2} \).

The process doesn’t change regardless of the numbers involved. Here, we efficiently reduce the fraction by eliminating the common factor (2, in this case) between the numerator and the denominator, leading directly to a simplified, single number. This makes working with fractions much easier and more intuitive in both everyday math and advanced calculations.