Multi-Fraction Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calc-container {
max-width: 700px;
margin: 30px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.input-section, .result-section, .article-section {
margin-bottom: 30px;
padding: 20px;
border: 1px solid #e0e0e0;
border-radius: 6px;
background-color: #ffffff;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #004a99;
}
.input-group input[type="text"] {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
font-size: 1rem;
}
.fraction-input {
display: flex;
align-items: center;
gap: 5px;
width: 100%;
}
.fraction-input input {
width: 45%; /* Adjust width for numerator and denominator */
text-align: center;
}
.fraction-bar {
font-size: 1.5em;
font-weight: bold;
color: #333;
margin: 0 5px;
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #004a99;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1.1rem;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
background-color: #e7f3ff;
color: #004a99;
padding: 20px;
border-radius: 6px;
text-align: center;
font-size: 1.8em;
font-weight: bold;
margin-top: 20px;
border: 1px solid #004a99;
}
.article-section h2 {
text-align: left;
color: #004a99;
}
.article-section p {
margin-bottom: 15px;
}
.article-section ul {
margin-left: 20px;
margin-bottom: 15px;
}
.error-message {
color: #dc3545;
font-weight: bold;
text-align: center;
margin-top: 15px;
}
/* Responsive adjustments */
@media (max-width: 600px) {
.calc-container {
padding: 20px;
}
.fraction-input {
flex-wrap: wrap;
justify-content: center;
}
.fraction-input input {
width: 40%;
}
.fraction-bar {
width: 100%;
text-align: center;
margin: 5px 0;
}
#result {
font-size: 1.5em;
}
}
Multi-Fraction Calculator
Understanding Fraction Operations
Fractions represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. Understanding how to perform arithmetic operations on fractions is fundamental in mathematics and has numerous practical applications.
Core Operations:
- Addition & 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 and convert each fraction to an equivalent fraction with that LCM as its new denominator. Then, you add or subtract the numerators while keeping the common denominator.
- Multiplication: To multiply fractions, you simply multiply the numerators together and multiply the denominators together. Simplification can be done before or after multiplication.
- Division: To divide one fraction by another, you invert the second fraction (its reciprocal) and then multiply the first fraction by this inverted second fraction.
The Multi-Fraction Calculator:
This calculator simplifies the process of performing a single operation (+, -, *, /) between three fractions. You enter the numerators and denominators for each of the three fractions, select the desired operation, and the calculator will display the simplified result. This is useful for complex calculations where you need to combine multiple fractional values efficiently.
Example Calculation (Addition):
Let's calculate 1/2 + 1/3 + 1/4.
- Find a Common Denominator: The least common multiple (LCM) of 2, 3, and 4 is 12.
- Convert Fractions:
- 1/2 becomes (1 * 6) / (2 * 6) = 6/12
- 1/3 becomes (1 * 4) / (3 * 4) = 4/12
- 1/4 becomes (1 * 3) / (4 * 3) = 3/12
- Add Numerators: 6 + 4 + 3 = 13
- Result: The sum is 13/12.
The calculator handles these steps automatically to provide the simplified answer.
// Helper function to find the Greatest Common Divisor (GCD)
function gcd(a, b) {
var a = Math.abs(a);
var b = Math.abs(b);
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
// Helper function to simplify a fraction
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
throw new Error("Denominator cannot be zero.");
}
if (numerator === 0) {
return { num: 0, den: 1 };
}
var commonDivisor = gcd(numerator, denominator);
var num = numerator / commonDivisor;
var den = denominator / commonDivisor;
// Ensure denominator is positive
if (den < 0) {
num = -num;
den = -den;
}
return { num: num, den: den };
}
// Function to parse fraction input into numerator and denominator
function parseFraction(numId, denId) {
var numStr = document.getElementById(numId).value.trim();
var denStr = document.getElementById(denId).value.trim();
var num = parseFloat(numStr);
var den = parseFloat(denStr);
if (isNaN(num) || isNaN(den)) {
throw new Error("Numerator and denominator must be valid numbers.");
}
if (den === 0) {
throw new Error("Denominator cannot be zero.");
}
return simplifyFraction(num, den);
}
// Main calculation function
function calculateFractions() {
var resultDiv = document.getElementById("result");
var errorMessageDiv = document.getElementById("errorMessage");
resultDiv.innerText = "Result: "; // Reset result
errorMessageDiv.innerText = ""; // Clear previous errors
try {
var operation = document.getElementById("operation").value;
var frac1 = parseFraction("num1", "den1");
var frac2 = parseFraction("num2", "den2");
var frac3 = parseFraction("num3", "den3");
var resultNum, resultDen;
// Combine first two fractions
var tempNum, tempDen;
if (operation === "add" || operation === "subtract") {
tempDen = frac1.den * frac2.den;
tempNum = (frac1.num * frac2.den) + (operation === "add" ? frac2.num * frac1.den : -(frac2.num * frac1.den));
} else if (operation === "multiply") {
tempNum = frac1.num * frac2.num;
tempDen = frac1.den * frac2.den;
} else if (operation === "divide") {
tempNum = frac1.num * frac2.den;
tempDen = frac1.den * frac2.num;
}
var tempFrac = simplifyFraction(tempNum, tempDen);
// Combine temp fraction with the third fraction
if (operation === "add" || operation === "subtract") {
resultDen = tempFrac.den * frac3.den;
resultNum = (tempFrac.num * frac3.den) + (operation === "add" ? frac3.num * tempFrac.den : -(frac3.num * tempFrac.den));
} else if (operation === "multiply") {
resultNum = tempFrac.num * frac3.num;
resultDen = tempFrac.den * frac3.den;
} else if (operation === "divide") {
resultNum = tempFrac.num * frac3.den;
resultDen = tempFrac.den * frac3.num;
}
var finalResult = simplifyFraction(resultNum, resultDen);
if (finalResult.den === 1) {
resultDiv.innerText = "Result: " + finalResult.num;
} else {
resultDiv.innerText = "Result: " + finalResult.num + " / " + finalResult.den;
}
} catch (error) {
errorMessageDiv.innerText = "Error: " + error.message;
resultDiv.innerText = "Result: ";
}
}