.calculator-container {
background-color: #f9f9f9;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
font-family: Arial, sans-serif;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-input-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group input[type="number"],
.input-group select {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
width: 100%;
box-sizing: border-box;
}
.calculator-container button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
cursor: pointer;
transition: background-color 0.3s ease;
}
.calculator-container button:hover {
background-color: #0056b3;
}
.calculator-result {
background-color: #e9ecef;
border: 1px solid #ced4da;
padding: 15px;
border-radius: 4px;
margin-top: 20px;
}
.calculator-result h3 {
color: #333;
margin-top: 0;
margin-bottom: 10px;
}
.calculator-result #result {
font-size: 20px;
font-weight: bold;
color: #007bff;
word-wrap: break-word;
}
/* Responsive adjustments */
@media (max-width: 480px) {
.calculator-input-grid {
grid-template-columns: 1fr;
}
}
// Helper function to find 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;
}
// Helper function to simplify a fraction
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { num: numerator, den: 0 }; // Indicate error or undefined
}
if (numerator === 0) {
return { num: 0, den: 1 };
}
var commonDivisor = gcd(numerator, denominator);
var simplifiedNum = numerator / commonDivisor;
var simplifiedDen = denominator / commonDivisor;
// Ensure denominator is positive
if (simplifiedDen < 0) {
simplifiedNum *= -1;
simplifiedDen *= -1;
}
return { num: simplifiedNum, den: simplifiedDen };
}
// Helper function to raise a fraction to an exponent
function powerFraction(numerator, denominator, exponent) {
if (denominator === 0) {
return { num: numerator, den: 0 }; // Error: base is undefined
}
if (exponent === 0) {
return { num: 1, den: 1 }; // Any non-zero number to the power of 0 is 1
}
if (numerator === 0 && exponent 0) {
return { num: 0, den: 1 }; // 0 to a positive power is 0
}
var resultNum, resultDen;
if (exponent < 0) {
// (a/b)^-n = (b/a)^n
var positiveExp = Math.abs(exponent);
resultNum = Math.pow(denominator, positiveExp);
resultDen = Math.pow(numerator, positiveExp);
} else {
resultNum = Math.pow(numerator, exponent);
resultDen = Math.pow(denominator, exponent);
}
return simplifyFraction(resultNum, resultDen);
}
// Helper functions for fraction arithmetic
function addFractions(f1_num, f1_den, f2_num, f2_den) {
var commonDen = f1_den * f2_den;
var resultNum = (f1_num * f2_den) + (f2_num * f1_den);
return simplifyFraction(resultNum, commonDen);
}
function subtractFractions(f1_num, f1_den, f2_num, f2_den) {
var commonDen = f1_den * f2_den;
var resultNum = (f1_num * f2_den) – (f2_num * f1_den);
return simplifyFraction(resultNum, commonDen);
}
function multiplyFractions(f1_num, f1_den, f2_num, f2_den) {
var resultNum = f1_num * f2_num;
var resultDen = f1_den * f2_den;
return simplifyFraction(resultNum, resultDen);
}
function divideFractions(f1_num, f1_den, f2_num, f2_den) {
if (f2_num === 0) {
return { num: 0, den: 0 }; // Division by zero
}
var resultNum = f1_num * f2_den;
var resultDen = f1_den * f2_num;
return simplifyFraction(resultNum, resultDen);
}
function calculateFractionExponent() {
var num1 = parseFloat(document.getElementById("num1").value);
var den1 = parseFloat(document.getElementById("den1").value);
var exp1Str = document.getElementById("exp1").value;
var exp1 = exp1Str === "" ? NaN : parseFloat(exp1Str);
var operation = document.getElementById("operation").value;
var num2 = parseFloat(document.getElementById("num2").value);
var den2 = parseFloat(document.getElementById("den2").value);
var exp2Str = document.getElementById("exp2").value;
var exp2 = exp2Str === "" ? NaN : parseFloat(exp2Str);
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 numerators and denominators.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = "Denominator cannot be zero.";
return;
}
if (!isNaN(exp1) && !Number.isInteger(exp1)) {
resultDiv.innerHTML = "Exponent 1 must be an integer.";
return;
}
if (!isNaN(exp2) && !Number.isInteger(exp2)) {
resultDiv.innerHTML = "Exponent 2 must be an integer.";
return;
}
// — Process Fraction 1 —
var fraction1 = { num: num1, den: den1 };
if (!isNaN(exp1)) {
fraction1 = powerFraction(fraction1.num, fraction1.den, exp1);
if (fraction1.den === 0 && fraction1.num === 0) { // Undefined 0^negative
resultDiv.innerHTML = "Undefined: 0 raised to a negative exponent for Fraction 1.";
return;
}
if (fraction1.den === 0) { // Division by zero during exponentiation
resultDiv.innerHTML = "Undefined: Division by zero during exponentiation of Fraction 1.";
return;
}
}
// — Process Fraction 2 —
var fraction2 = { num: num2, den: den2 };
if (!isNaN(exp2)) {
fraction2 = powerFraction(fraction2.num, fraction2.den, exp2);
if (fraction2.den === 0 && fraction2.num === 0) { // Undefined 0^negative
resultDiv.innerHTML = "Undefined: 0 raised to a negative exponent for Fraction 2.";
return;
}
if (fraction2.den === 0) { // Division by zero during exponentiation
resultDiv.innerHTML = "Undefined: Division by zero during exponentiation of Fraction 2.";
return;
}
}
// — Perform Operation —
var finalResult;
switch (operation) {
case "add":
finalResult = addFractions(fraction1.num, fraction1.den, fraction2.num, fraction2.den);
break;
case "subtract":
finalResult = subtractFractions(fraction1.num, fraction1.den, fraction2.num, fraction2.den);
break;
case "multiply":
finalResult = multiplyFractions(fraction1.num, fraction1.den, fraction2.num, fraction2.den);
break;
case "divide":
if (fraction2.num === 0) {
resultDiv.innerHTML = "Cannot divide by zero.";
return;
}
finalResult = divideFractions(fraction1.num, fraction1.den, fraction2.num, fraction2.den);
break;
default:
resultDiv.innerHTML = "Invalid operation selected.";
return;
}
// — Display Result —
if (finalResult.den === 0) {
resultDiv.innerHTML = "Result is undefined (division by zero).";
return;
}
var decimalResult = finalResult.num / finalResult.den;
var resultString = "";
if (finalResult.den === 1) {
resultString = finalResult.num.toString();
} else {
resultString = finalResult.num + " / " + finalResult.den;
}
resultDiv.innerHTML = "Simplified Fraction: " + resultString + "";
resultDiv.innerHTML += "Decimal Value: " + decimalResult.toFixed(8); // Display with some precision
}
Understanding Fractions and Exponents in Mathematics
Fractions and exponents are fundamental concepts in mathematics, essential for everything from basic arithmetic to advanced algebra and calculus. This calculator helps you perform operations involving both, simplifying complex expressions into their simplest fractional and decimal forms.
What is a Fraction?
A fraction represents a part of a whole. It is written as a ratio of two numbers, a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 1⁄2, 1 is the numerator and 2 is the denominator. The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.
Numerator: The number above the line, indicating how many parts are taken.
Denominator: The number below the line, indicating the total number of equal parts in the whole. It can never be zero.
Fractions can be proper (numerator less than denominator, e.g., 3⁄4), improper (numerator greater than or equal to denominator, e.g., 7⁄4), or mixed numbers (a whole number and a proper fraction, e.g., 1 3⁄4).
Operations with Fractions
Performing arithmetic with fractions requires specific rules:
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 and convert the fractions. Then, you add or subtract the numerators and keep the common denominator.
Example: 1⁄3 + 1⁄2 = 2⁄6 + 3⁄6 = 5⁄6
Multiplication: To multiply fractions, you simply multiply the numerators together and the denominators together.
Example: 1⁄2 × 3⁄4 = (1 × 3)⁄(2 × 4) = 3⁄8
Division: To divide fractions, you "flip" the second fraction (find its reciprocal) and then multiply.
Example: 1⁄2 ÷ 3⁄4 = 1⁄2 × 4⁄3 = 4⁄6 = 2⁄3
What is an Exponent?
An exponent (also called a power or index) indicates how many times a number (the base) is multiplied by itself. It is written as a small number to the upper right of the base number. For example, in 23, 2 is the base and 3 is the exponent, meaning 2 × 2 × 2 = 8.
Negative Exponents: Indicate the reciprocal of the base raised to the positive exponent (e.g., 2-3 = 1⁄23 = 1⁄8).
Zero Exponent: Any non-zero number raised to the power of zero is 1 (e.g., 70 = 1).
Exponents with Fractions
When a fraction is raised to an exponent, both the numerator and the denominator are raised to that power.
Example: (2⁄3)3 = 23⁄33 = 8⁄27
If the exponent is negative, you first take the reciprocal of the fraction and then apply the positive exponent.
Example: (2⁄3)-2 = (3⁄2)2 = 32⁄22 = 9⁄4
How to Use the Calculator
This calculator allows you to perform arithmetic operations on two fractions, each of which can optionally be raised to an integer exponent. Follow these steps:
Enter Numerator 1 and Denominator 1: Input the top and bottom numbers for your first fraction.
Enter Exponent 1 (Optional): If you want to raise the first fraction to a power, enter an integer exponent here. Leave blank if not needed.
Select Operation: Choose whether you want to add, subtract, multiply, or divide the two fractions.
Enter Numerator 2 and Denominator 2: Input the top and bottom numbers for your second fraction.
Enter Exponent 2 (Optional): If you want to raise the second fraction to a power, enter an integer exponent here. Leave blank if not needed.
Click "Calculate": The calculator will process your input and display the result as a simplified fraction and its decimal equivalent.
This calculator is a powerful tool for students, educators, and anyone needing to quickly solve expressions involving fractions and exponents, ensuring accuracy and simplifying the results.