Mixed fractions (or mixed numbers) consist of a whole number and a proper fraction. While they are useful for representing measurements like "2 and 1/2 cups," they can be tricky to add. Our calculator automates the math, but understanding the steps is essential for mastering fraction arithmetic.
Step-by-Step Guide
Convert to Improper Fractions: Multiply the whole number by the denominator and add the numerator. Place this over the original denominator. For example, $1 \frac{1}{2}$ becomes $\frac{(1 \times 2) + 1}{2} = \frac{3}{2}$.
Find a Common Denominator: If the denominators are different, find the Least Common Multiple (LCM). For $\frac{3}{2}$ and $\frac{11}{4}$, the common denominator is 4.
Adjust the Numerators: Multiply the numerator of each fraction by the same factor used to adjust the denominator. $\frac{3}{2}$ becomes $\frac{6}{4}$.
Add the Numerators: Add the adjusted numerators together while keeping the denominator the same. $\frac{6}{4} + \frac{11}{4} = \frac{17}{4}$.
Simplify and Convert Back: Divide the numerator by the denominator to get the new whole number and remainder. $\frac{17}{4} = 4 \frac{1}{4}$.
Real-World Example
Imagine you are building a shelf. You have one piece of wood that is $3 \frac{3}{4}$ feet long and another that is $2 \frac{1}{2}$ feet long. To find the total length:
Convert to improper: $\frac{15}{4}$ and $\frac{5}{2}$.
Common denominator (4): $\frac{15}{4}$ and $\frac{10}{4}$.
Add: $\frac{25}{4}$.
Final Result: $6 \frac{1}{4}$ feet.
function calculateMixedFractions() {
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;
if (d1 === 0 || d2 === 0) {
alert("Denominator cannot be zero.");
return;
}
// Step 1: Improper fractions
var impN1 = (w1 * d1) + n1;
var impN2 = (w2 * d2) + n2;
// Step 2: Addition (n1/d1 + n2/d2 = (n1*d2 + n2*d1) / (d1*d2))
var resN = (impN1 * d2) + (impN2 * d1);
var resD = d1 * d2;
// Step 3: Simplify fraction (GCD)
function getGCD(a, b) {
return b ? getGCD(b, a % b) : a;
}
var commonDivisor = Math.abs(getGCD(resN, resD));
var simplifiedN = resN / commonDivisor;
var simplifiedD = resD / commonDivisor;
// Step 4: Convert back to mixed
var finalWhole = Math.floor(simplifiedN / simplifiedD);
var finalNum = simplifiedN % simplifiedD;
var resultDiv = document.getElementById('fractionResult');
var stepDetails = document.getElementById('stepDetails');
var finalAnswer = document.getElementById('finalAnswer');
resultDiv.style.display = 'block';
var stepsHtml = "1. Convert to improper: " + impN1 + "/" + d1 + " and " + impN2 + "/" + d2 + "";
stepsHtml += "2. Common denominator sum: " + resN + "/" + resD + "";
stepsHtml += "3. Simplified improper: " + simplifiedN + "/" + simplifiedD + "";
stepDetails.innerHTML = stepsHtml;
if (finalNum === 0) {
finalAnswer.innerHTML = "Final Sum: " + finalWhole;
} else if (finalWhole === 0) {
finalAnswer.innerHTML = "Final Sum: " + finalNum + "/" + simplifiedD;
} else {
finalAnswer.innerHTML = "Final Sum: " + finalWhole + " " + finalNum + "/" + simplifiedD;
}
}