Use this calculator to perform basic arithmetic operations (addition, subtraction, multiplication, and division) on two rational numbers (fractions). Enter the numerator and denominator for each fraction, then select the desired operation.
.rational-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
max-width: 700px;
margin: 20px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
color: #333;
}
.rational-calculator-container h2 {
text-align: center;
color: #2c3e50;
margin-bottom: 20px;
font-size: 1.8em;
}
.rational-calculator-container h3 {
color: #34495e;
margin-top: 15px;
margin-bottom: 10px;
font-size: 1.3em;
}
.rational-calculator-container p {
text-align: center;
margin-bottom: 25px;
line-height: 1.6;
color: #555;
}
.calculator-inputs {
display: flex;
justify-content: space-around;
gap: 20px;
margin-bottom: 25px;
flex-wrap: wrap;
}
.fraction-input {
background-color: #ffffff;
border: 1px solid #e0e0e0;
border-radius: 6px;
padding: 15px 20px;
flex: 1;
min-width: 250px;
box-shadow: 0 2px 5px rgba(0, 0, 0, 0.05);
}
.fraction-input label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #444;
font-size: 0.95em;
}
.fraction-input input[type="number"] {
width: calc(100% – 20px);
padding: 10px;
margin-bottom: 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box;
}
.fraction-input input[type="number"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 0 2px rgba(0, 123, 255, 0.25);
}
.calculator-buttons {
text-align: center;
margin-bottom: 30px;
}
.calculator-buttons button {
background-color: #007bff;
color: white;
border: none;
padding: 12px 25px;
margin: 0 8px;
border-radius: 5px;
cursor: pointer;
font-size: 1.05em;
transition: background-color 0.3s ease, transform 0.2s ease;
min-width: 100px;
}
.calculator-buttons button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.calculator-buttons button:active {
background-color: #004085;
transform: translateY(0);
}
.calculator-result {
background-color: #eaf6ff;
border: 1px solid #b3d9ff;
border-radius: 6px;
padding: 20px;
text-align: center;
font-size: 1.4em;
font-weight: bold;
color: #0056b3;
min-height: 60px;
display: flex;
flex-direction: column;
justify-content: center;
align-items: center;
}
.calculator-result h3 {
margin-top: 0;
color: #0056b3;
font-size: 1.2em;
}
#rationalResult {
margin-top: 10px;
color: #003366;
}
@media (max-width: 600px) {
.calculator-inputs {
flex-direction: column;
align-items: center;
}
.fraction-input {
width: 100%;
min-width: unset;
}
.calculator-buttons button {
margin: 8px 5px;
padding: 10px 20px;
font-size: 1em;
}
}
// Function to calculate the Greatest Common Divisor (GCD)
function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
// Main calculation function
function calculateRationals(operation) {
var num1 = parseFloat(document.getElementById('num1').value);
var den1 = parseFloat(document.getElementById('den1').value);
var num2 = parseFloat(document.getElementById('num2').value);
var den2 = parseFloat(document.getElementById('den2').value);
var resultDiv = document.getElementById('rationalResult');
// 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':
// (a/b) + (c/d) = (ad + bc) / bd
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
break;
case 'subtract':
// (a/b) – (c/d) = (ad – bc) / bd
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
break;
case 'multiply':
// (a/b) * (c/d) = ac / bd
resultNum = num1 * num2;
resultDen = den1 * den2;
break;
case 'divide':
// (a/b) / (c/d) = ad / bc
if (num2 === 0) {
resultDiv.innerHTML = "Cannot divide by zero (second numerator is zero).";
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDiv.innerHTML = "Invalid operation.";
return;
}
// Simplify the fraction
var commonDivisor = gcd(resultNum, resultDen);
var simplifiedNum = resultNum / commonDivisor;
var simplifiedDen = resultDen / commonDivisor;
// Handle negative signs correctly
if (simplifiedDen < 0) {
simplifiedNum = -simplifiedNum;
simplifiedDen = -simplifiedDen;
}
// Display result
if (simplifiedDen === 1) {
resultDiv.innerHTML = simplifiedNum;
} else if (simplifiedNum === 0) {
resultDiv.innerHTML = "0";
} else {
resultDiv.innerHTML = simplifiedNum + " / " + simplifiedDen;
}
}
Understanding Rational Numbers
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. The set of rational numbers includes all integers (e.g., 5 can be written as 5/1), finite decimals (e.g., 0.75 can be written as 3/4), and repeating decimals (e.g., 0.333… can be written as 1/3).
Rational numbers are fundamental in mathematics and everyday life, allowing us to represent parts of a whole, ratios, and precise measurements that cannot be expressed as whole numbers.
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: Add 1/2 and 3/4
(1/2) + (3/4) = (1*4 + 3*2) / (2*4) = (4 + 6) / 8 = 10/8
Simplifying 10/8 by dividing both numerator and denominator by their GCD (2) gives 5/4.
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) = (a * c) / (b * d)
Example: Multiply 1/2 by 3/4
(1/2) * (3/4) = (1 * 3) / (2 * 4) = 3/8
3. Division
To divide rational numbers, you multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction c/d is d/c.
Formula: (a/b) / (c/d) = (a/b) * (d/c) = (a * d) / (b * c)
Example: Divide 1/2 by 3/4
(1/2) / (3/4) = (1/2) * (4/3) = (1 * 4) / (2 * 3) = 4/6
Simplifying 4/6 by dividing both numerator and denominator by their GCD (2) gives 2/3.
Simplifying Fractions
After performing an operation, the resulting fraction should always be simplified to its lowest terms. This is done by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). For example, 10/8 simplifies to 5/4 because the GCD of 10 and 8 is 2.
How to Use the Calculator
- Enter the numerator and denominator for your first rational number in the "Fraction 1" fields.
- Enter the numerator and denominator for your second rational number in the "Fraction 2" fields.
- Click on the button corresponding to the operation you wish to perform (Add, Subtract, Multiply, or Divide).
- The simplified result will be displayed in the "Result" area.
The calculator automatically handles common denominators, performs the operation, and simplifies the final fraction for you.