Multiple Fractions Calculator
Use this calculator to perform addition, subtraction, multiplication, or division on multiple fractions. Enter the numerator and denominator for each fraction you wish to include in the calculation. You can use up to five fractions.
.fraction-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 25px;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
max-width: 700px;
margin: 30px auto;
border: 1px solid #e0e0e0;
}
.fraction-calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
font-size: 1.8em;
}
.fraction-calculator-container p {
color: #555;
text-align: center;
margin-bottom: 25px;
line-height: 1.6;
}
.calculator-form {
display: flex;
flex-direction: column;
gap: 15px;
}
.fraction-input-group {
display: flex;
align-items: center;
gap: 10px;
background-color: #fff;
padding: 12px 15px;
border-radius: 8px;
border: 1px solid #ddd;
}
.fraction-input-group label {
flex-basis: 90px;
color: #444;
font-weight: bold;
font-size: 0.95em;
}
.fraction-input-group input[type="number"] {
flex-grow: 1;
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
-moz-appearance: textfield; /* Firefox */
}
.fraction-input-group input[type="number"]::-webkit-outer-spin-button,
.fraction-input-group input[type="number"]::-webkit-inner-spin-button {
-webkit-appearance: none;
margin: 0;
}
.fraction-input-group span {
font-size: 1.2em;
font-weight: bold;
color: #666;
}
.operation-selection {
display: flex;
align-items: center;
gap: 15px;
background-color: #fff;
padding: 12px 15px;
border-radius: 8px;
border: 1px solid #ddd;
}
.operation-selection label {
color: #444;
font-weight: bold;
font-size: 0.95em;
}
.operation-selection select {
flex-grow: 1;
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1em;
background-color: #fefefe;
cursor: pointer;
}
.fraction-calculator-container button {
background-color: #007bff;
color: white;
padding: 12px 25px;
border: none;
border-radius: 8px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease, transform 0.2s ease;
width: 100%;
margin-top: 10px;
}
.fraction-calculator-container button:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.calculator-result {
margin-top: 25px;
padding: 18px;
background-color: #e9f7ef;
border: 1px solid #c3e6cb;
border-radius: 8px;
font-size: 1.2em;
color: #28a745;
text-align: center;
font-weight: bold;
min-height: 50px;
display: flex;
align-items: center;
justify-content: center;
word-break: break-word;
}
.calculator-result.error {
background-color: #f8d7da;
border-color: #f5c6cb;
color: #dc3545;
}
@media (max-width: 600px) {
.fraction-input-group {
flex-direction: column;
align-items: flex-start;
gap: 5px;
}
.fraction-input-group label {
width: 100%;
margin-bottom: 5px;
}
.fraction-input-group input {
width: calc(100% – 22px); /* Adjust for padding/border */
}
.operation-selection {
flex-direction: column;
align-items: flex-start;
gap: 5px;
}
.operation-selection label {
width: 100%;
margin-bottom: 5px;
}
.operation-selection select {
width: 100%;
}
}
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 simplifyFraction(fraction) {
if (fraction.n === 0) {
return { n: 0, d: 1 };
}
var commonDivisor = gcd(fraction.n, fraction.d);
var simplifiedN = fraction.n / commonDivisor;
var simplifiedD = fraction.d / commonDivisor;
// Ensure denominator is positive
if (simplifiedD < 0) {
simplifiedN = -simplifiedN;
simplifiedD = -simplifiedD;
}
return { n: simplifiedN, d: simplifiedD };
}
function addFractions(f1, f2) {
var n = f1.n * f2.d + f2.n * f1.d;
var d = f1.d * f2.d;
return simplifyFraction({ n: n, d: d });
}
function subtractFractions(f1, f2) {
var n = f1.n * f2.d – f2.n * f1.d;
var d = f1.d * f2.d;
return simplifyFraction({ n: n, d: d });
}
function multiplyFractions(f1, f2) {
var n = f1.n * f2.n;
var d = f1.d * f2.d;
return simplifyFraction({ n: n, d: d });
}
function divideFractions(f1, f2) {
if (f2.n === 0) {
return { error: "Division by zero is not allowed." };
}
var n = f1.n * f2.d;
var d = f1.d * f2.n;
return simplifyFraction({ n: n, d: d });
}
function calculateFractions() {
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "";
resultDiv.classList.remove("error");
var fractionsToProcess = [];
for (var i = 1; i <= 5; i++) {
var numInput = document.getElementById("numerator" + i);
var denInput = document.getElementById("denominator" + i);
var num = parseFloat(numInput.value);
var den = parseFloat(denInput.value);
if (!isNaN(num) && !isNaN(den) && den !== 0) {
fractionsToProcess.push({ n: num, d: den });
} else if ((numInput.value !== "" || denInput.value !== "") && (isNaN(num) || isNaN(den) || den === 0)) {
resultDiv.innerHTML = "Please enter valid numbers for all filled fractions, and ensure denominators are not zero.";
resultDiv.classList.add("error");
return;
}
}
if (fractionsToProcess.length < 2) {
resultDiv.innerHTML = "Please enter at least two fractions to perform an operation.";
resultDiv.classList.add("error");
return;
}
var operation = document.getElementById("operation").value;
var currentResult = fractionsToProcess[0];
for (var j = 1; j Math.abs(finalFraction.d) && finalFraction.d !== 0) {
var wholePart = Math.floor(finalFraction.n / finalFraction.d);
var remainderN = finalFraction.n % finalFraction.d;
if (remainderN !== 0) {
mixedNumber = " (" + wholePart + " " + Math.abs(remainderN) + "/" + Math.abs(finalFraction.d) + ")";
} else {
mixedNumber = " (" + wholePart + ")";
}
} else if (finalFraction.d === 0) {
resultDiv.innerHTML = "Error: Resulting denominator is zero.";
resultDiv.classList.add("error");
return;
}
resultDiv.innerHTML = "Result:
" + finalFraction.n + "/" + finalFraction.d + "" + mixedNumber + " (Decimal: " + decimalValue.toFixed(4) + ")";
}
Understanding Fractions and Their Operations
Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.
Why Use a Multiple Fractions Calculator?
Working with fractions can be complex, especially when dealing with multiple fractions or different operations. This calculator simplifies the process by:
- Handling Multiple Inputs: Easily combine several fractions in a single calculation.
- Performing Various Operations: Add, subtract, multiply, or divide fractions with a single click.
- Simplifying Results: Automatically reduces the final fraction to its lowest terms.
- Providing Decimal Equivalents: Offers both the fractional and decimal representation of the answer.
How to Use the Calculator
- Enter Fractions: For each fraction you want to include, enter its numerator in the first box and its denominator in the second box. You can use up to five fractions. Leave fields blank for fractions you don't need.
- Select Operation: Choose the desired operation (addition, subtraction, multiplication, or division) from the dropdown menu.
- Calculate: Click the "Calculate Result" button to see the simplified fraction and its decimal equivalent.
Examples of Fraction Operations
1. Adding Multiple Fractions
When adding fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators and convert each fraction. The numerators are then added, and the denominator remains the same. Finally, simplify the result.
Example: Calculate 1/2 + 1/3 + 1/4
- Enter 1 for Numerator 1, 2 for Denominator 1.
- Enter 1 for Numerator 2, 3 for Denominator 2.
- Enter 1 for Numerator 3, 4 for Denominator 3.
- Select "Add (+)" as the operation.
- The calculator will show: 13/12 (Decimal: 1.0833)
2. Subtracting Multiple Fractions
Similar to addition, subtraction requires a common denominator. Once fractions share a common denominator, subtract the numerators and keep the denominator. Simplify the final fraction.
Example: Calculate 3/4 – 1/2 – 1/8
- Enter 3 for Numerator 1, 4 for Denominator 1.
- Enter 1 for Numerator 2, 2 for Denominator 2.
- Enter 1 for Numerator 3, 8 for Denominator 3.
- Select "Subtract (-)" as the operation.
- The calculator will show: 1/8 (Decimal: 0.1250)
3. Multiplying Multiple Fractions
Multiplying fractions is straightforward: multiply all the numerators together to get the new numerator, and multiply all the denominators together to get the new denominator. Then, simplify the resulting fraction.
Example: Calculate 2/3 * 1/4 * 3/5
- Enter 2 for Numerator 1, 3 for Denominator 1.
- Enter 1 for Numerator 2, 4 for Denominator 2.
- Enter 3 for Numerator 3, 5 for Denominator 3.
- Select "Multiply (*)" as the operation.
- The calculator will show: 3/30, which simplifies to 1/10 (Decimal: 0.1000)
4. Dividing Multiple Fractions
To divide by a fraction, you "keep, change, flip": keep the first fraction, change the division sign to multiplication, and flip (invert) the second fraction. For multiple divisions, you apply this rule sequentially. For example, A/B / C/D / E/F becomes (A/B * D/C) * F/E.
Example: Calculate 1/2 / 1/4 / 2/3
- Enter 1 for Numerator 1, 2 for Denominator 1.
- Enter 1 for Numerator 2, 4 for Denominator 2.
- Enter 2 for Numerator 3, 3 for Denominator 3.
- Select "Divide (/)" as the operation.
- The calculator will show: 3/1 (Decimal: 3.0000)