function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var t = b;
b = a % b;
a = t;
}
return a;
}
function calculateFractions() {
var w1 = parseInt(document.getElementById('whole1').value) || 0;
var n1 = parseInt(document.getElementById('num1').value) || 0;
var d1 = parseInt(document.getElementById('den1').value) || 1;
var w2 = parseInt(document.getElementById('whole2').value) || 0;
var n2 = parseInt(document.getElementById('num2').value) || 0;
var d2 = parseInt(document.getElementById('den2').value) || 1;
var op = document.getElementById('operation').value;
var errorBox = document.getElementById('error-box');
var resultBox = document.getElementById('result-box');
if (d1 === 0 || d2 === 0) {
errorBox.style.display = 'block';
resultBox.style.display = 'none';
return;
}
errorBox.style.display = 'none';
// Convert to improper fractions
// If whole is negative, treat the entire fraction as negative
var impNum1 = (Math.abs(w1) * d1 + n1) * (w1 < 0 ? -1 : 1);
var impDen1 = d1;
var impNum2 = (Math.abs(w2) * d2 + n2) * (w2 < 0 ? -1 : 1);
var impDen2 = d2;
var resNum, resDen;
if (op === 'add') {
resNum = impNum1 * impDen2 + impNum2 * impDen1;
resDen = impDen1 * impDen2;
} else if (op === 'subtract') {
resNum = impNum1 * impDen2 – impNum2 * impDen1;
resDen = impDen1 * impDen2;
} else if (op === 'multiply') {
resNum = impNum1 * impNum2;
resDen = impDen1 * impDen2;
} else if (op === 'divide') {
if (impNum2 === 0) {
alert("Cannot divide by zero fraction.");
return;
}
resNum = impNum1 * impDen2;
resDen = impDen1 * impNum2;
}
// Handle negative denominator
if (resDen < 0) {
resNum = -resNum;
resDen = -resDen;
}
var common = gcd(resNum, resDen);
var simplifiedNum = resNum / common;
var simplifiedDen = resDen / common;
var finalDisplay = "";
if (simplifiedDen === 1) {
finalDisplay = simplifiedNum;
} else {
var wholePart = Math.trunc(simplifiedNum / simplifiedDen);
var remNum = Math.abs(simplifiedNum % simplifiedDen);
if (wholePart === 0 && simplifiedNum < 0) {
finalDisplay = "- " + remNum + "/" + simplifiedDen;
} else if (wholePart === 0) {
finalDisplay = remNum + "/" + simplifiedDen;
} else {
finalDisplay = wholePart + " " + remNum + "/" + simplifiedDen;
}
}
document.getElementById('result-text').innerText = finalDisplay;
document.getElementById('decimal-text').innerText = "Decimal Value: " + (resNum / resDen).toFixed(4);
resultBox.style.display = 'block';
}
Understanding Fractions with Whole Numbers
A mixed number is a combination of a whole number and a proper fraction. For example, 2 1/2 (two and a half) is a mixed number. While these are common in everyday life—like in cooking recipes or carpentry measurements—performing mathematical operations with them requires a specific set of steps.
How to Add or Subtract Mixed Numbers
To calculate fractions with whole numbers manually, follow these core steps:
Convert to Improper Fractions: Multiply the whole number by the denominator and add the numerator. Place this over the original denominator. For 3 1/4, (3 * 4) + 1 = 13, so the fraction is 13/4.
Find a Common Denominator: If adding or subtracting, ensure the bottom numbers match.
Perform the Operation: Add or subtract the numerators while keeping the denominator the same.
Simplify: Convert the result back into a mixed number and reduce the fraction to its lowest terms.
Rules for Multiplication and Division
When multiplying or dividing, you must convert the mixed numbers into improper fractions first. You cannot simply multiply the whole numbers and the fractions separately, as this leads to incorrect results.
Multiplication: Multiply numerators together and denominators together.
Division: Flip the second fraction (the divisor) to its reciprocal and multiply.
Real-World Example
Imagine you have 2 3/4 cups of flour and you need to add 1 1/2 cups more.
Convert 2 3/4 to 11/4.
Convert 1 1/2 to 3/2, then to 6/4 for a common denominator.
11/4 + 6/4 = 17/4.
Convert 17/4 back to a mixed number: 4 1/4.
Frequently Asked Questions
Q: Can a whole number be negative?
A: Yes. If the whole number is negative, the entire mixed number is treated as a negative value.
Q: What is the difference between a proper and improper fraction?
A: A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than the denominator (e.g., 7/4).
Q: How do I simplify the result?
A: Find the Greatest Common Divisor (GCD) of the numerator and denominator and divide both by that number.