.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
max-width: 600px;
margin: 20px auto;
border: 1px solid #ddd;
}
.calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.calculator-container p {
color: #555;
text-align: center;
margin-bottom: 25px;
}
.calc-input-group {
margin-bottom: 15px;
}
.calc-input-group label {
display: block;
margin-bottom: 5px;
color: #333;
font-weight: bold;
}
.calc-input-group input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
}
.calc-button-group {
display: flex;
justify-content: space-around;
margin-top: 20px;
flex-wrap: wrap;
gap: 10px;
}
.calc-button-group button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
flex: 1 1 auto; /* Allow buttons to grow and shrink */
min-width: 120px; /* Minimum width for buttons */
}
.calc-button-group button:hover {
background-color: #0056b3;
}
.calc-result {
margin-top: 30px;
padding: 15px;
background-color: #e9ecef;
border: 1px solid #ced4da;
border-radius: 5px;
font-size: 1.1em;
color: #333;
text-align: center;
min-height: 50px;
display: flex;
align-items: center;
justify-content: center;
font-weight: bold;
}
@media (max-width: 480px) {
.calc-button-group button {
width: 100%;
margin-bottom: 10px;
}
}
// Function to find the greatest common divisor (GCD) using Euclidean algorithm
function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
// Function to simplify a fraction
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { num: numerator, den: denominator }; // Error case, handle outside
}
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 performOperation(operation) {
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 resultDiv = document.getElementById('result');
resultDiv.innerHTML = ''; // Clear previous result
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDiv.innerHTML = 'Please enter valid numbers for all fields.';
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = 'Denominator cannot be zero.';
return;
}
var resultNum, resultDen;
switch (operation) {
case 'add':
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
break;
case 'subtract':
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
break;
case 'multiply':
resultNum = num1 * num2;
resultDen = den1 * den2;
break;
case 'divide':
if (num2 === 0) {
resultDiv.innerHTML = 'Cannot divide by zero.';
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDiv.innerHTML = 'Invalid operation.';
return;
}
var simplifiedResult = simplifyFraction(resultNum, resultDen);
if (simplifiedResult.den === 1) {
resultDiv.innerHTML = 'Result: ' + simplifiedResult.num;
} else {
resultDiv.innerHTML = 'Result: ' + simplifiedResult.num + ' / ' + simplifiedResult.den;
}
}
Understanding Rational Numbers and Their Operations
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Examples include 1/2, 3/4, -5/7, and even integers like 3 (which can be written as 3/1).
Why are Rational Numbers Important?
Rational numbers are fundamental in mathematics and everyday life. They allow us to represent parts of a whole, ratios, and rates. From dividing a pizza to calculating probabilities, rational numbers provide a precise way to express quantities that aren't whole numbers.
How to Perform Operations on Rational Numbers
1. Addition and Subtraction
To add or subtract rational numbers, 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 common denominator. Then, you add or subtract the numerators and keep the common denominator.
Formula:
- Addition:
(a/b) + (c/d) = (ad + bc) / bd
- Subtraction:
(a/b) - (c/d) = (ad - bc) / bd
Example: 1/2 + 1/3
Common denominator is 6. (1*3)/(2*3) + (1*2)/(3*2) = 3/6 + 2/6 = 5/6
2. Multiplication
Multiplying rational numbers is straightforward: multiply the numerators together and multiply the denominators together. The result is a new fraction.
Formula: (a/b) * (c/d) = (ac) / (bd)
Example: 2/3 * 3/4
(2*3) / (3*4) = 6/12. This simplifies to 1/2.
3. Division
To divide one rational number by another, you multiply the first rational number by the reciprocal of the second rational number. The reciprocal of a fraction c/d is d/c.
Formula: (a/b) / (c/d) = (a/b) * (d/c) = (ad) / (bc)
Example: 1/2 / 1/4
1/2 * 4/1 = (1*4) / (2*1) = 4/2. This simplifies to 2/1 or 2.
Simplifying Rational Numbers
After performing an operation, the resulting fraction should always be simplified to its lowest terms. This means dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, 6/12 simplifies to 1/2 because the GCD of 6 and 12 is 6.
Using the Rational Number Calculator
Our Rational Number Calculator simplifies these operations for you. Simply input the numerator and denominator for your two rational numbers. Then, select the desired operation (addition, subtraction, multiplication, or division). The calculator will instantly display the result in its simplest fractional form, or as a whole number if applicable.
This tool is perfect for students learning about fractions, or anyone needing to quickly perform calculations with rational numbers without manual simplification.