Fraction to Ratio Calculator

How to Convert Fractions to Ratios

Converting fractions to ratios is a fundamental skill in mathematics. It involves expressing a fraction as a comparison between two numbers.

Formula for Converting Fractions to Ratios

The process to convert a fraction to a ratio is:

\[\frac{a}{b} \rightarrow a:b\]

Where:

• \(a\) is the numerator of the fraction
• \(b\) is the denominator of the fraction

Note: If the fraction can be simplified, we should do so before expressing it as a ratio.

Calculation Steps

1. Identify the numerator and denominator of the fraction.
2. Find the Greatest Common Divisor (GCD) of the numerator and denominator.
3. Divide both the numerator and denominator by the GCD to simplify the fraction.
4. Express the simplified fraction as a ratio by replacing the fraction bar with a colon.

Example Calculation

Let's convert the fraction \(\frac{12}{18}\) to a ratio:

1. Identify: numerator = 12, denominator = 18
2. Find the GCD: GCD(12, 18) = 6
3. Simplify: \(\frac{12 \div 6}{18 \div 6} = \frac{2}{3}\)
4. Express as ratio: \(\frac{2}{3} \rightarrow 2:3\)

Therefore, the fraction \(\frac{12}{18}\) as a ratio is 2:3

Visual Representation

These visualizations show how the fraction 12/18 converts to the ratio 2:3. The pie chart shows the original fraction, while the bar chart represents the simplified ratio. The conversion process shows how we simplify by dividing both numbers by their greatest common divisor (6).