Input three fractions to perform addition, subtraction, multiplication, or division.
+
–
*
/
Result
Understanding and Using the Fraction Calculator of 3
Fractions are a fundamental concept in mathematics, representing a part of a whole.
They are expressed as a ratio of two integers, a numerator (the top number)
and a denominator (the bottom number), written as $\frac{\text{numerator}}{\text{denominator}}$.
For example, $\frac{1}{2}$ represents one part out of two equal parts.
This "Fraction Calculator of 3" is designed to simplify operations involving three fractions.
Whether you need to add, subtract, multiply, or divide three fractional values, this tool provides
a quick and accurate solution. This is particularly useful in various academic and practical scenarios,
from solving complex equations in algebra to measuring ingredients in recipes or calculating proportions
in design and engineering.
How it Works: The Math Behind the Calculator
The calculator performs the selected operation (addition, subtraction, multiplication, or division)
sequentially. For instance, if you choose addition, it calculates (Fraction 1 + Fraction 2) + Fraction 3.
The core mathematical principles applied are:
Addition/Subtraction: To add or subtract fractions, they must share a common denominator.
The formula for two fractions $\frac{a}{b}$ and $\frac{c}{d}$ is $\frac{ad \pm bc}{bd}$. This process is repeated
for the third fraction. For three fractions $\frac{a}{b}, \frac{c}{d}, \frac{e}{f}$, the operation might look like
$\frac{a}{b} \text{ op } \frac{c}{d} \text{ op } \frac{e}{f}$. The calculator finds a common denominator for all three
and then performs the operation on the numerators.
Multiplication: Multiplying fractions is straightforward: multiply the numerators together
and multiply the denominators together. For $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$. For three fractions,
$\frac{a}{b} \times \frac{c}{d} \times \frac{e}{f} = \frac{a \times c \times e}{b \times d \times f}$.
Division: Dividing by a fraction is the same as multiplying by its reciprocal. To divide
$\frac{a}{b}$ by $\frac{c}{d}$, you calculate $\frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$. For three fractions,
$\frac{a}{b} / \frac{c}{d} / \frac{e}{f}$ is typically calculated as $(\frac{a}{b} / \frac{c}{d}) / \frac{e}{f}$.
The calculator also simplifies the resulting fraction to its lowest terms using the Greatest Common Divisor (GCD)
algorithm.
Practical Use Cases
Academic: Solving homework problems in mathematics, pre-algebra, and algebra.
Culinary Arts: Adjusting ingredient quantities in recipes that call for fractional measurements.
Engineering & Design: Calculating precise measurements and proportions for projects.
Finance: Understanding and calculating fractional changes or shares.
Using this calculator eliminates the potential for manual calculation errors and saves valuable time,
allowing you to focus on the application of the results.
// Helper function to find the Greatest Common Divisor (GCD)
function gcd(a, b) {
var absA = Math.abs(a);
var absB = Math.abs(b);
while (absB) {
var temp = absB;
absB = absA % absB;
absA = temp;
}
return absA;
}
// Helper function to simplify a fraction
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { num: NaN, den: NaN }; // Indicate error
}
if (numerator === 0) {
return { num: 0, den: 1 };
}
var commonDivisor = gcd(numerator, denominator);
var simplifiedNum = numerator / commonDivisor;
var simplifiedDen = denominator / commonDivisor;
// Ensure the denominator is positive
if (simplifiedDen < 0) {
simplifiedNum = -simplifiedNum;
simplifiedDen = -simplifiedDen;
}
return { num: simplifiedNum, den: simplifiedDen };
}
function calculateFractionSum() {
// Get input values
var num1 = parseFloat(document.getElementById("numerator1").value);
var den1 = parseFloat(document.getElementById("denominator1").value);
var num2 = parseFloat(document.getElementById("numerator2").value);
var den2 = parseFloat(document.getElementById("denominator2").value);
var num3 = parseFloat(document.getElementById("numerator3").value);
var den3 = parseFloat(document.getElementById("denominator3").value);
var operation = document.getElementById("operation").value;
var resultElement = document.getElementById("result");
var resultValueElement = document.getElementById("resultValue");
// Validate inputs
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2) || isNaN(num3) || isNaN(den3)) {
resultValueElement.innerText = "Error: Please enter valid numbers for all inputs.";
resultElement.style.backgroundColor = "#dc3545"; // Red for error
resultElement.style.display = "block";
return;
}
if (den1 === 0 || den2 === 0 || den3 === 0) {
resultValueElement.innerText = "Error: Denominator cannot be zero.";
resultElement.style.backgroundColor = "#dc3545"; // Red for error
resultElement.style.display = "block";
return;
}
// Perform calculations sequentially
var currentNum, currentDen;
// Step 1: Calculate between the first two fractions
if (operation === "add") {
currentNum = num1 * den2 + num2 * den1;
currentDen = den1 * den2;
} else if (operation === "subtract") {
currentNum = num1 * den2 – num2 * den1;
currentDen = den1 * den2;
} else if (operation === "multiply") {
currentNum = num1 * num2;
currentDen = den1 * den2;
} else if (operation === "divide") {
// Dividing by zero check for the second fraction
if (num2 === 0) {
resultValueElement.innerText = "Error: Division by zero in intermediate step.";
resultElement.style.backgroundColor = "#dc3545"; // Red for error
resultElement.style.display = "block";
return;
}
currentNum = num1 * den2;
currentDen = den1 * num2;
}
// Step 2: Calculate with the third fraction
if (operation === "add") {
currentNum = currentNum * den3 + num3 * currentDen;
currentDen = currentDen * den3;
} else if (operation === "subtract") {
currentNum = currentNum * den3 – num3 * currentDen;
currentDen = currentDen * den3;
} else if (operation === "multiply") {
currentNum = currentNum * num3;
currentDen = currentDen * den3;
} else if (operation === "divide") {
// Dividing by zero check for the third fraction
if (num3 === 0) {
resultValueElement.innerText = "Error: Division by zero in final step.";
resultElement.style.backgroundColor = "#dc3545"; // Red for error
resultElement.style.display = "block";
return;
}
currentNum = currentNum * den3;
currentDen = currentDen * num3;
}
// Simplify the final result
var simplifiedResult = simplifyFraction(currentNum, currentDen);
if (isNaN(simplifiedResult.num) || isNaN(simplifiedResult.den)) {
resultValueElement.innerText = "Calculation Error";
resultElement.style.backgroundColor = "#dc3545"; // Red for error
} else if (simplifiedResult.den === 1) {
resultValueElement.innerText = simplifiedResult.num.toString();
} else {
resultValueElement.innerText = simplifiedResult.num + " / " + simplifiedResult.den;
}
resultElement.style.backgroundColor = "#28a745"; // Green for success
resultElement.style.display = "block";
}