Ratio to Fraction Calculator

Ratio to Fraction Converter

Ratio Part 1 (e.g., 3):

Ratio Part 2 (e.g., 4):

Results:

function gcd(a, b) { if (b === 0) { return a; } return gcd(b, a % b); } function calculateRatioToFraction() { var ratioPart1Input = document.getElementById("ratioPart1").value; var ratioPart2Input = document.getElementById("ratioPart2").value; var part1 = parseFloat(ratioPart1Input); var part2 = parseFloat(ratioPart2Input); var resultDiv = document.getElementById("result"); var simplifiedRatioElem = document.getElementById("simplifiedRatio"); var fractionPart1Elem = document.getElementById("fractionPart1"); var fractionPart2Elem = document.getElementById("fractionPart2"); var simplifiedFractionPart1Elem = document.getElementById("simplifiedFractionPart1"); var simplifiedFractionPart2Elem = document.getElementById("simplifiedFractionPart2"); if (isNaN(part1) || isNaN(part2) || part1 <= 0 || part2 <= 0) { resultDiv.innerHTML = "

Error:

Please enter valid positive numbers for both ratio parts."; return; } // Calculate GCD for simplifying the ratio var commonDivisorRatio = gcd(part1, part2); var simplifiedA = part1 / commonDivisorRatio; var simplifiedB = part2 / commonDivisorRatio; var totalParts = part1 + part2; // Fraction for Part 1 var fraction1Numerator = part1; var fraction1Denominator = totalParts; var commonDivisorF1 = gcd(fraction1Numerator, fraction1Denominator); var simplifiedF1Num = fraction1Numerator / commonDivisorF1; var simplifiedF1Den = fraction1Denominator / commonDivisorF1; // Fraction for Part 2 var fraction2Numerator = part2; var fraction2Denominator = totalParts; var commonDivisorF2 = gcd(fraction2Numerator, fraction2Denominator); var simplifiedF2Num = fraction2Numerator / commonDivisorF2; var simplifiedF2Den = fraction2Denominator / commonDivisorF2; simplifiedRatioElem.innerHTML = "Original Ratio: " + part1 + ":" + part2 + "Simplified Ratio: " + simplifiedA + ":" + simplifiedB; fractionPart1Elem.innerHTML = "Fraction of Part 1: " + fraction1Numerator + "/" + fraction1Denominator; fractionPart2Elem.innerHTML = "Fraction of Part 2: " + fraction2Numerator + "/" + fraction2Denominator; simplifiedFractionPart1Elem.innerHTML = "Simplified Fraction of Part 1: " + simplifiedF1Num + "/" + simplifiedF1Den; simplifiedFractionPart2Elem.innerHTML = "Simplified Fraction of Part 2: " + simplifiedF2Num + "/" + simplifiedF2Den; } // Initial calculation on page load with default values document.addEventListener('DOMContentLoaded', function() { calculateRatioToFraction(); });

Understanding Ratios and Fractions

Ratios and fractions are fundamental mathematical concepts used to express relationships between quantities. While they are closely related, they represent slightly different ideas. This calculator helps you seamlessly convert a given ratio into its equivalent fractional forms, both original and simplified.

What is a Ratio?

A ratio compares two or more quantities. It shows how much of one quantity there is compared to another. Ratios are typically written with a colon (e.g., 3:4), or sometimes using the word "to" (e.g., 3 to 4). For instance, if you have 3 red apples and 4 green apples, the ratio of red apples to green apples is 3:4.

It's important to note that a ratio compares parts to parts. In the 3:4 example, 3 is one part, and 4 is another distinct part.

What is a Fraction?

A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator indicates how many parts are being considered, and the denominator indicates the total number of equal parts that make up the whole. For example, 3/7 means 3 parts out of a total of 7 parts.

How to Convert a Ratio to a Fraction

Converting a ratio (e.g., A:B) into a fraction involves understanding that the total number of parts is the sum of the individual parts in the ratio (A + B). Once you have the total, you can express each part as a fraction of that total.

Fraction of Part A: A / (A + B)
Fraction of Part B: B / (A + B)

Let's use an example:

If the ratio of boys to girls in a class is 2:3:

Find the total parts: 2 (boys) + 3 (girls) = 5 total parts.
Fraction of boys: 2 / 5 (2 out of 5 students are boys).
Fraction of girls: 3 / 5 (3 out of 5 students are girls).

Simplifying Ratios and Fractions

Both ratios and fractions can often be simplified to their lowest terms. This makes them easier to understand and compare. To simplify, you divide both parts of the ratio or both the numerator and denominator of the fraction by their Greatest Common Divisor (GCD).

Example of Simplifying a Ratio:

Consider the ratio 6:8.

The GCD of 6 and 8 is 2.
Divide both parts by 2: 6 ÷ 2 = 3 and 8 ÷ 2 = 4.
The simplified ratio is 3:4.

Example of Simplifying a Fraction:

Using the simplified ratio 3:4, the total parts are 3 + 4 = 7.

The fraction for the first part is 3/7. This fraction is already in its simplest form because the GCD of 3 and 7 is 1.

If we had a fraction like 6/10:

The GCD of 6 and 10 is 2.
Divide both numerator and denominator by 2: 6 ÷ 2 = 3 and 10 ÷ 2 = 5.
The simplified fraction is 3/5.

Using the Calculator

Our Ratio to Fraction Converter simplifies this process for you. Simply enter the two parts of your ratio into the designated fields. The calculator will instantly provide:

The original ratio and its simplified form.
The fraction for each part based on the original ratio.
The simplified fraction for each part.

This tool is perfect for students, educators, or anyone needing quick and accurate conversions between ratios and fractions for various mathematical, scientific, or everyday applications.