This calculator is designed to perform arithmetic operations on three fractions. Fractions represent a part of a whole and are fundamental in mathematics. They consist of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. This tool allows you to add, subtract, multiply, or divide two fractions, and then perform the same operation with the result and a third fraction.
How it Works: The Math Behind the Calculator
The calculator follows standard arithmetic rules for fractions.
Addition and Subtraction: To add or subtract fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators, convert each fraction to an equivalent fraction with the LCM as its denominator, and then add or subtract the numerators.
For a/b + c/d = (ad + bc) / bd For a/b - c/d = (ad - bc) / bd
Multiplication: To multiply fractions, you multiply the numerators together and the denominators together.
For a/b × c/d = ac / bd
Division: To divide fractions, you multiply the first fraction by the reciprocal (inverse) of the second fraction.
For a/b ÷ c/d = a/b × d/c = ad / bc
The calculator performs the operation between Fraction 1 and Fraction 2 first, then takes that intermediate result and performs the same operation with Fraction 3.
Simplifying Fractions
While this calculator provides the direct result, it's often important to simplify fractions to their lowest terms. This is done by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. For example, 2/4 simplifies to 1/2.
Use Cases
This type of calculator is useful in various scenarios:
Mathematics Education: Helping students understand and verify fraction arithmetic.
Cooking and Recipes: Adjusting ingredient quantities, which often involve fractional measurements.
Engineering and Construction: Calculating precise measurements and proportions.
Finance: Understanding ratios and proportions, although typically handled with decimals.
Everyday Problem Solving: Dividing resources or calculating parts of a whole.
By inputting your fractions and selecting the desired operation, you can quickly obtain accurate results for complex fractional calculations.
// Helper function to find the Greatest Common Divisor (GCD)
var gcd = function(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while(b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
// Helper function to simplify a fraction
var simplifyFraction = function(num, den) {
if (den === 0) {
return { num: num, den: den, error: "Denominator cannot be zero." };
}
if (num === 0) {
return { num: 0, den: 1, error: null };
}
var commonDivisor = gcd(num, den);
var simplifiedNum = num / commonDivisor;
var simplifiedDen = den / commonDivisor;
// Ensure denominator is positive
if (simplifiedDen < 0) {
simplifiedNum = -simplifiedNum;
simplifiedDen = -simplifiedDen;
}
return { num: simplifiedNum, den: simplifiedDen, error: null };
}
var calculateFractions = function() {
var num1a = parseInt(document.getElementById("num1a").value);
var den1a = parseInt(document.getElementById("den1a").value);
var num1b = parseInt(document.getElementById("num1b").value);
var den1b = parseInt(document.getElementById("den1b").value);
var num2 = parseInt(document.getElementById("num2").value);
var den2 = parseInt(document.getElementById("den2").value);
var operation1 = document.getElementById("operation1").value;
var resultDisplay = document.getElementById("result");
// Validate inputs
if (isNaN(num1a) || isNaN(den1a) || isNaN(num1b) || isNaN(den1b) || isNaN(num2) || isNaN(den2)) {
resultDisplay.textContent = "Error: Please enter valid numbers.";
return;
}
if (den1a === 0 || den1b === 0 || den2 === 0) {
resultDisplay.textContent = "Error: Denominator cannot be zero.";
return;
}
// — First Operation: Fraction 1 and Fraction 2 —
var intermediateNum, intermediateDen;
var operation2 = document.getElementById("operation1").value; // Using the same operation for the second step
// First fraction simplification
var simplifiedFrac1a = simplifyFraction(num1a, den1a);
if (simplifiedFrac1a.error) {
resultDisplay.textContent = "Error: " + simplifiedFrac1a.error;
return;
}
num1a = simplifiedFrac1a.num;
den1a = simplifiedFrac1a.den;
// Second fraction simplification
var simplifiedFrac1b = simplifyFraction(num1b, den1b);
if (simplifiedFrac1b.error) {
resultDisplay.textContent = "Error: " + simplifiedFrac1b.error;
return;
}
num1b = simplifiedFrac1b.num;
den1b = simplifiedFrac1b.den;
if (operation1 === '+') {
intermediateNum = num1a * den1b + num1b * den1a;
intermediateDen = den1a * den1b;
} else if (operation1 === '-') {
intermediateNum = num1a * den1b – num1b * den1a;
intermediateDen = den1a * den1b;
} else if (operation1 === '*') {
intermediateNum = num1a * num1b;
intermediateDen = den1a * den1b;
} else if (operation1 === '/') {
if (num1b === 0) {
resultDisplay.textContent = "Error: Cannot divide by zero.";
return;
}
intermediateNum = num1a * den1b;
intermediateDen = den1a * num1b;
}
// — Second Operation: Intermediate Result and Fraction 3 —
var finalNum, finalDen;
var simplifiedIntermediate = simplifyFraction(intermediateNum, intermediateDen);
if (simplifiedIntermediate.error) {
resultDisplay.textContent = "Error: " + simplifiedIntermediate.error;
return;
}
intermediateNum = simplifiedIntermediate.num;
intermediateDen = simplifiedIntermediate.den;
// Third fraction simplification
var simplifiedFrac2 = simplifyFraction(num2, den2);
if (simplifiedFrac2.error) {
resultDisplay.textContent = "Error: " + simplifiedFrac2.error;
return;
}
num2 = simplifiedFrac2.num;
den2 = simplifiedFrac2.den;
if (operation2 === '+') {
finalNum = intermediateNum * den2 + num2 * intermediateDen;
finalDen = intermediateDen * den2;
} else if (operation2 === '-') {
finalNum = intermediateNum * den2 – num2 * intermediateDen;
finalDen = intermediateDen * den2;
} else if (operation2 === '*') {
finalNum = intermediateNum * num2;
finalDen = intermediateDen * den2;
} else if (operation2 === '/') {
if (num2 === 0) {
resultDisplay.textContent = "Error: Cannot divide by zero.";
return;
}
finalNum = intermediateNum * den2;
finalDen = intermediateDen * num2;
}
// Simplify the final result
var finalResult = simplifyFraction(finalNum, finalDen);
if (finalResult.error) {
resultDisplay.textContent = "Error: " + finalResult.error;
} else {
if (finalResult.den === 1) {
resultDisplay.textContent = finalResult.num;
} else {
resultDisplay.textContent = finalResult.num + " / " + finalResult.den;
}
}
}
var clearInputs = function() {
document.getElementById("num1a").value = "";
document.getElementById("den1a").value = "";
document.getElementById("num1b").value = "";
document.getElementById("den1b").value = "";
document.getElementById("num2").value = "";
document.getElementById("den2").value = "";
document.getElementById("result").textContent = "–";
}