Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.
This calculator performs the four basic arithmetic operations on two fractions: addition, subtraction, multiplication, and division. Understanding how these operations work is crucial for various applications, from cooking and construction to advanced engineering and scientific research.
How the Calculations Work:
Let the two fractions be a/b and c/d, where a and c are numerators, and b and d are denominators.
1. Addition (a/b + c/d):
To add fractions, they must have a common denominator. The formula is:
(a*d + c*b) / (b*d)
The calculator finds the common denominator by multiplying the two denominators (b*d) and then adjusts the numerators accordingly before adding them.
2. Subtraction (a/b – c/d):
Similar to addition, fractions need a common denominator. The formula is:
(a*d - c*b) / (b*d)
The calculator computes this by finding the common denominator and then subtracting the adjusted numerators.
3. Multiplication (a/b * c/d):
Multiplying fractions is straightforward. You multiply the numerators together and the denominators together:
(a*c) / (b*d)
This operation does not require a common denominator.
4. Division (a/b รท c/d):
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of c/d is d/c. The formula is:
(a/b) * (d/c) = (a*d) / (b*c)
The calculator implements this by inverting the second fraction and then performing multiplication.
Simplifying Fractions:
While this calculator presents the direct result of the operation, it's often useful to simplify fractions to their lowest terms. This is done by finding the Greatest Common Divisor (GCD) of the numerator and denominator and dividing both by it. For example, 4/8 simplifies to 1/2 because the GCD of 4 and 8 is 4.
Use Cases:
Cooking & Baking: Adjusting recipe ingredient quantities (e.g., doubling or halving a recipe).
Construction & DIY: Measuring and cutting materials accurately, calculating proportions for mixtures.
Finance: Understanding ratios, proportions, and calculating portions of investments or costs.
Science & Engineering: Performing calculations involving ratios, rates, and proportions in various formulas.
Everyday Math: Sharing items, calculating discounts, understanding time durations.
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(numerator, denominator) {
if (denominator === 0) {
return { num: numerator, den: denominator }; // Avoid division by zero
}
var commonDivisor = gcd(numerator, denominator);
return {
num: numerator / commonDivisor,
den: denominator / commonDivisor
};
}
function calculateFraction(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");
var errorDiv = document.getElementById("errorMessage");
errorDiv.textContent = ""; // Clear previous errors
resultDiv.textContent = ""; // Clear previous result
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
errorDiv.textContent = "Please enter valid numbers for all fields.";
return;
}
if (den1 === 0 || den2 === 0) {
errorDiv.textContent = "Denominator cannot be zero.";
return;
}
var resultNum, resultDen;
if (operation === '+') {
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
} else if (operation === '-') {
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
} else if (operation === '*') {
resultNum = num1 * num2;
resultDen = den1 * den2;
} else if (operation === '/') {
if (num2 === 0) {
errorDiv.textContent = "Cannot divide by zero.";
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
}
// Simplify the result
var simplified = simplifyFraction(resultNum, resultDen);
// Handle potential negative denominator after simplification
if (simplified.den < 0) {
simplified.num = -simplified.num;
simplified.den = -simplified.den;
}
// Display the result
if (simplified.den === 1) {
resultDiv.textContent = simplified.num; // Display as integer if denominator is 1
} else if (simplified.den === 0) {
errorDiv.textContent = "Result is undefined (division by zero).";
}
else {
resultDiv.textContent = simplified.num + " / " + simplified.den;
}
}