Problem 49 - Prealgebra

Question

Simplify by dividing the numerator by the denominator. $$\frac{6}{3}$$

Step-by-Step Solution

Answer

The simplified form of \( \frac{6}{3} \) is 2.

Step 1: Identify Numerator and Denominator

In the fraction \( \frac{6}{3} \), the numerator is 6 and the denominator is 3. Your goal in simplifying is to divide the numerator by the denominator.

Step 2: Perform the Division

Divide 6 by 3: \[ 6 \div 3 = 2 \] This means that when the numerator divided by the denominator, the result is 2.

Step 3: Write the Simplified Form

Since the result of dividing the numerator by the denominator is 2, the simplified form of the fraction \( \frac{6}{3} \) is 2.

Key Concepts

Understanding Numerators and Denominators

In any fraction, we encounter two main components: the numerator and the denominator. To easily spot these parts in a fraction like \( \frac{6}{3} \):

• The **numerator** is the top number, in this case, 6. It represents the number of parts we are considering.
• The **denominator** is the bottom number, which is 3 for this fraction. It tells you into how many equal parts the whole is divided.

These parts of the fraction are crucial for understanding how fractions work and knowing how to simplify them, like we are doing with \( \frac{6}{3} \).
You start by figuring out what these numbers mean, which will guide the next steps to simplify the fraction.

Performing Division in Fractions

Division is the key operation used to simplify fractions. This means converting a fraction like \( \frac{6}{3} \) into its simplest form by dividing the numerator by the denominator.Here’s how it works with our example:

• Take the numerator 6 and divide it by the denominator 3.
• Mathematically, it looks like \( 6 \div 3 = 2 \).

What this division tells us is how many times the denominator fits into the numerator.
When the division results in a whole number, the fraction can often be simplified to that whole number.

Achieving the Simplified Form

Simplifying fractions means reducing them to their simplest form.For the fraction \( \frac{6}{3} \), after performing the division, you get 2.This 2 is considered the **simplified form** of the original fraction. Here's why:

• There are no common factors in the numerator and denominator other than 1 that could simplify it further.
• The result is a whole number, which is the simplest representation of a fraction that originally had a denominator of 1 (since \( \frac{2}{1} = 2 \)).

Simplifying fractions into whole numbers, like turning \( \frac{6}{3} \) into 2, makes calculations easier and results clearer. Always aim for the simplest form when working with fractions to ensure they are easy to understand and use.