Fractions are a fundamental concept in mathematics, representing a part of a whole. They are expressed as two numbers, a numerator (the top number) and a denominator (the bottom number), separated by a line or a slash. The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.
For example, the fraction 1/2 means a whole is divided into 2 equal parts, and we are considering 1 of those parts. The fraction 3/4 means a whole is divided into 4 equal parts, and we are considering 3 of them.
Core Operations with Fractions
This calculator assists in performing the four basic arithmetic operations on fractions:
Addition ( + ): To add fractions with the same denominator, simply add their numerators and keep the denominator the same. If the denominators are different, find a common denominator first. For example, 1/2 + 1/4. The common denominator is 4. So, 1/2 becomes 2/4. Then, 2/4 + 1/4 = 3/4.
Subtraction ( – ): Similar to addition, subtract the numerators if the denominators are the same. If they are different, find a common denominator first. For example, 3/4 - 1/2. Convert 1/2 to 2/4. Then, 3/4 - 2/4 = 1/4.
Multiplication ( * ): To multiply fractions, multiply the numerators together and multiply the denominators together. Simplification can be done before or after multiplication. For example, 1/2 * 3/4 = (1*3) / (2*4) = 3/8.
Division ( / ): To divide fractions, invert the second fraction (the divisor) and multiply it by the first fraction. For example, 1/2 รท 3/4 is the same as 1/2 * 4/3 = (1*4) / (2*3) = 4/6. This fraction can then be simplified to 2/3.
Simplifying Fractions
The calculator automatically simplifies the resulting fraction to its lowest terms. This means dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, 4/6 simplifies to 2/3 because the GCD of 4 and 6 is 2.
Use Cases
Fraction calculations are essential in various fields:
Cooking and Baking: Scaling recipes often involves fractions (e.g., doubling a recipe that calls for 1/2 cup of flour).
Construction and DIY: Measuring and cutting materials (e.g., wood, fabric) frequently uses fractional units like inches (1/4, 1/2, 3/4).
Mathematics and Science: Integral for algebra, geometry, calculus, and many scientific disciplines.
Finance: While decimals are more common, understanding fractional shares or proportions can be relevant.
Sharing and Proportions: Dividing items or resources among groups.
This calculator provides a quick and accurate way to perform these operations, helping to avoid manual errors and speed up calculations.
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;
}
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { num: numerator, den: denominator, error: "Denominator cannot be zero." };
}
if (numerator === 0) {
return { num: 0, den: 1, error: null };
}
var commonDivisor = gcd(numerator, denominator);
var simplifiedNumerator = numerator / commonDivisor;
var simplifiedDenominator = denominator / commonDivisor;
// Ensure the denominator is positive
if (simplifiedDenominator < 0) {
simplifiedNumerator = -simplifiedNumerator;
simplifiedDenominator = -simplifiedDenominator;
}
return { num: simplifiedNumerator, den: simplifiedDenominator, error: null };
}
function calculateFraction() {
var num1 = parseInt(document.getElementById("numerator1").value);
var den1 = parseInt(document.getElementById("denominator1").value);
var num2 = parseInt(document.getElementById("numerator2").value);
var den2 = parseInt(document.getElementById("denominator2").value);
var operation = document.getElementById("operation").value;
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDiv.innerHTML = "Error: Please enter valid numbers for all fields.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = "Error: Denominator cannot be zero.";
return;
}
var resultNum, resultDen;
if (operation === "add") {
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
} else if (operation === "subtract") {
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
} else if (operation === "multiply") {
resultNum = num1 * num2;
resultDen = den1 * den2;
} else if (operation === "divide") {
if (num2 === 0) {
resultDiv.innerHTML = "Error: Cannot divide by zero.";
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
}
var simplified = simplifyFraction(resultNum, resultDen);
if (simplified.error) {
resultDiv.innerHTML = "Error: " + simplified.error;
} else {
if (simplified.den === 1) {
resultDiv.innerHTML = "Result: " + simplified.num;
} else {
resultDiv.innerHTML = "Result: " + simplified.num + " / " + simplified.den;
}
}
}