Simplify Fractions Calculator: Reduce Fractions to Their Simplest Form

What is Simplifying Fractions?

Simplifying fractions means making a fraction as simple as possible by using the smallest numbers possible. It's like giving a fraction a haircut - we're trimming it down to its neatest form!

How to Simplify Fractions

To simplify a fraction, we divide both the top number (numerator) and bottom number (denominator) by their greatest common factor (GCF). This makes the fraction smaller without changing its value.

Formula

The formula for simplifying a fraction is:

\[ \frac{a}{b} = \frac{a \div \text{GCF}}{b \div \text{GCF}} \]

Where:

• \(a\) is the numerator (top number)
• \(b\) is the denominator (bottom number)
• GCF is the Greatest Common Factor of \(a\) and \(b\)

Calculation Steps

1. Find the factors of both the numerator and denominator
2. Identify the greatest common factor (GCF)
3. Divide both the numerator and denominator by the GCF
4. Write the new fraction with the results of step 3

Example and Visual Representation

Let's simplify the fraction 18/24

Step 1: Find factors of 18 and 24

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 8, 12, 24

Step 2: The greatest common factor is 6

Step 3: Divide both numbers by 6

18 ÷ 6 = 3, 24 ÷ 6 = 4

Step 4: Our simplified fraction is 3/4

Let's show this with a picture:

In this picture, we start with 18/24 at the top. The dashed line represents dividing by 6 (our GCF). The result at the bottom is our simplified fraction, 3/4.