Mixed Fraction Multiplication Calculator
Use this calculator to multiply two mixed fractions. A mixed fraction combines a whole number and a proper fraction (e.g., 2 1/2).
Understanding Mixed Fraction Multiplication
Mixed fractions are numbers that consist of a whole number and a proper fraction. For example, 2 1/2 means two whole units plus one-half of another unit. Multiplying mixed fractions requires a few steps to ensure accuracy.
How to Multiply Mixed Fractions:
- Convert Mixed Fractions to Improper Fractions: Before you can multiply, each mixed fraction must be converted into an improper fraction. An improper fraction is one where the numerator is greater than or equal to the denominator (e.g.,
5/2). To do this, multiply the whole number by the denominator, then add the numerator. Keep the original denominator.
Formula: (Whole Number × Denominator) + Numerator / Denominator
- Multiply the Improper Fractions: Once both mixed fractions are converted to improper fractions, multiply them. Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
Formula: (Numerator1 × Numerator2) / (Denominator1 × Denominator2)
- Simplify the Resulting Fraction: The product you get might be an improper fraction that can be simplified. Find the Greatest Common Divisor (GCD) of the new numerator and denominator, and divide both by the GCD.
- Convert Back to a Mixed Fraction (Optional): If the resulting improper fraction is still improper (numerator is greater than denominator), you can convert it back into a mixed fraction. Divide the numerator by the denominator. The quotient becomes the new whole number, and the remainder becomes the new numerator over the original denominator.
Example: Multiplying 2 1/2 by 1 1/3
- Convert to Improper Fractions:
2 1/2 → (2 × 2) + 1 / 2 → 5/21 1/3 → (1 × 3) + 1 / 3 → 4/3
- Multiply the Improper Fractions:
5/2 × 4/3 → (5 × 4) / (2 × 3) → 20/6
- Simplify the Resulting Fraction:
- The fraction is
20/6. The Greatest Common Divisor (GCD) of 20 and 6 is 2.
- Divide both by 2:
20 ÷ 2 / 6 ÷ 2 → 10/3
- Convert Back to a Mixed Fraction:
10 ÷ 3 is 3 with a remainder of 1.- So,
10/3 → 3 1/3
Therefore, 2 1/2 × 1 1/3 = 3 1/3.
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 25px;
background: #f9f9f9;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
border: 1px solid #ddd;
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width: 70px;
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
margin-right: 5px;
-moz-appearance: textfield; /* Firefox */
}
.input-group input[type="number"]::-webkit-outer-spin-button,
.input-group input[type="number"]::-webkit-inner-spin-button {
-webkit-appearance: none;
margin: 0;
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.fraction-separator {
font-size: 1.5em;
margin: 0 5px;
color: #666;
}
.fraction-slash {
font-size: 1.5em;
margin: 0 5px;
color: #666;
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 15px;
}
button:hover {
background-color: #0056b3;
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margin-top: 25px;
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border-radius: 8px;
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@media (max-width: 600px) {
.input-group label {
flex: 1 0 100%;
margin-bottom: 5px;
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.input-group input[type="number"] {
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.fraction-separator, .fraction-slash {
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// 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;
}
function calculateMixedFractionMultiplication() {
var whole1 = parseFloat(document.getElementById('whole1').value);
var num1 = parseFloat(document.getElementById('num1').value);
var den1 = parseFloat(document.getElementById('den1').value);
var whole2 = parseFloat(document.getElementById('whole2').value);
var num2 = parseFloat(document.getElementById('num2').value);
var den2 = parseFloat(document.getElementById('den2').value);
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = "; // Clear previous results
// Input validation
if (isNaN(whole1) || isNaN(num1) || isNaN(den1) ||
isNaN(whole2) || isNaN(num2) || isNaN(den2)) {
resultDiv.innerHTML = '
Please enter valid numbers for all fields.';
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = '
Denominator cannot be zero.';
return;
}
if (whole1 < 0 || num1 < 0 || den1 < 1 ||
whole2 < 0 || num2 < 0 || den2 < 1) {
resultDiv.innerHTML = '
Whole numbers and numerators must be non-negative. Denominators must be positive.';
return;
}
// Convert mixed fractions to improper fractions
var improperNum1 = (whole1 * den1) + num1;
var improperDen1 = den1;
var improperNum2 = (whole2 * den2) + num2;
var improperDen2 = den2;
// Multiply the improper fractions
var productNum = improperNum1 * improperNum2;
var productDen = improperDen1 * improperDen2;
// Simplify the resulting fraction
var commonDivisor = gcd(productNum, productDen);
var simplifiedNum = productNum / commonDivisor;
var simplifiedDen = productDen / commonDivisor;
// Convert back to mixed fraction
var finalWhole = Math.floor(simplifiedNum / simplifiedDen);
var finalNum = simplifiedNum % simplifiedDen;
var finalDen = simplifiedDen;
var outputHtml = '
Improper Fraction: ' + simplifiedNum + '/' + simplifiedDen + ";
if (finalNum === 0) {
outputHtml += '
Mixed Fraction: ' + finalWhole;
} else if (finalWhole === 0) {
outputHtml += '
Mixed Fraction: ' + finalNum + '/' + finalDen;
} else {
outputHtml += '
Mixed Fraction: ' + finalWhole + ' ' + finalNum + '/' + finalDen;
}
resultDiv.innerHTML = outputHtml;
}