Perform addition, subtraction, multiplication, and division of fractions.
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Understanding and Using Fraction Operations
Fractions represent a part of a whole. The number above the line is the numerator (the count of parts), and the number below the line is the denominator (the total number of equal parts the whole is divided into). The iPhone calculator app, like many others, has built-in functionalities to handle these numbers, making complex calculations straightforward.
Basic Fraction Operations
Our calculator performs the four fundamental arithmetic operations on fractions:
Addition: To add fractions, they must have a common denominator. If they don't, find the least common multiple (LCM) of the denominators, convert each fraction to an equivalent fraction with the LCM as its denominator, and then add the numerators.
(a/b) + (c/d) = (ad + bc) / bd
Subtraction: Similar to addition, find a common denominator. Subtract the numerators after converting the fractions.
(a/b) - (c/d) = (ad - bc) / bd
Multiplication: Multiply the numerators together and multiply the denominators together.
(a/b) * (c/d) = ac / bd
Division: To divide by a fraction, multiply by its reciprocal (invert the second fraction).
(a/b) / (c/d) = (a/b) * (d/c) = ad / bc
Simplifying Fractions
After performing an operation, the resulting fraction is often simplified to its lowest terms. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Why Use a Fraction Calculator?
While the iPhone calculator can handle basic operations, dedicated fraction calculators (or features within general calculators) are invaluable for:
Accuracy: Eliminates manual calculation errors.
Efficiency: Speeds up complex fraction arithmetic.
Education: Helps students visualize and understand fraction operations.
Practical Applications: Useful in fields like cooking (recipes), carpentry (measurements), engineering, and finance.
This calculator is designed to mimic the ease of use found on a smartphone, allowing you to quickly input fractions and select an operation to get an immediate, simplified result.
function gcd(a, b) {
var a = Math.abs(a);
var b = Math.abs(b);
while(b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function simplifyFraction(num, den) {
if (den === 0) return "Division by zero!";
var commonDivisor = gcd(num, den);
num /= commonDivisor;
den /= commonDivisor;
if (den < 0) {
num = -num;
den = -den;
}
if (den === 1) {
return num.toString();
}
return num + "/" + den;
}
function calculateFraction() {
var num1 = parseInt(document.getElementById("num1").value);
var den1 = parseInt(document.getElementById("den1").value);
var num2 = parseInt(document.getElementById("num2").value);
var den2 = parseInt(document.getElementById("den2").value);
var operation = document.getElementById("operation").value;
var resultDiv = document.getElementById("result");
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDiv.textContent = "Error: Please enter valid integers for numerators and denominators.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.textContent = "Error: 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":
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDiv.textContent = "Error: Invalid operation.";
return;
}
if (resultDen === 0) {
resultDiv.textContent = "Error: Division by zero occurred.";
return;
}
var simplifiedResult = simplifyFraction(resultNum, resultDen);
resultDiv.textContent = "Result: " + simplifiedResult;
}