Use this calculator to perform addition, subtraction, multiplication, or division on two mixed fractions. Enter the whole number, numerator, and denominator for each fraction, select your desired operation, and click "Calculate".
Fraction 1
+
–
*
/
Fraction 2
Result:
// 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 to simplify a fraction
function simplifyFraction(num, den) {
if (num === 0) {
return { num: 0, den: 1 };
}
var commonDivisor = gcd(num, den);
return { num: num / commonDivisor, den: den / commonDivisor };
}
// Function to convert a mixed fraction to an improper fraction
function mixedToImproper(whole, num, den) {
if (den === 0) {
return { num: NaN, den: NaN }; // Indicate error
}
var improperNum;
if (whole < 0) {
improperNum = -(Math.abs(whole) * den + num);
} else {
improperNum = whole * den + num;
}
return { num: improperNum, den: den };
}
// Function to convert an improper fraction to a mixed fraction
function improperToMixed(num, den) {
if (den === 0) {
return { whole: NaN, num: NaN, den: NaN }; // Indicate error
}
if (num === 0) {
return { whole: 0, num: 0, den: 1 };
}
var isNegative = false;
if (num < 0) {
isNegative = true;
num = Math.abs(num);
}
if (den < 0) { // Should ideally not happen with validated inputs, but for robustness
isNegative = !isNegative;
den = Math.abs(den);
}
var wholePart = Math.floor(num / den);
var remainderNum = num % den;
if (remainderNum === 0) {
return { whole: isNegative ? -wholePart : wholePart, num: 0, den: 1 };
} else {
var simplified = simplifyFraction(remainderNum, den);
return { whole: isNegative ? -wholePart : wholePart, num: simplified.num, den: simplified.den };
}
}
function calculateMixedFractions() {
var whole1 = parseFloat(document.getElementById("whole1").value);
var numerator1 = parseFloat(document.getElementById("numerator1").value);
var denominator1 = parseFloat(document.getElementById("denominator1").value);
var operation = document.getElementById("operation").value;
var whole2 = parseFloat(document.getElementById("whole2").value);
var numerator2 = parseFloat(document.getElementById("numerator2").value);
var denominator2 = parseFloat(document.getElementById("denominator2").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous result
// Input validation
if (isNaN(whole1) || isNaN(numerator1) || isNaN(denominator1) ||
isNaN(whole2) || isNaN(numerator2) || isNaN(denominator2)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (!Number.isInteger(whole1) || !Number.isInteger(numerator1) || !Number.isInteger(denominator1) ||
!Number.isInteger(whole2) || !Number.isInteger(numerator2) || !Number.isInteger(denominator2)) {
resultDiv.innerHTML = "Please enter whole numbers for all fields.";
return;
}
if (denominator1 === 0 || denominator2 === 0) {
resultDiv.innerHTML = "Denominator cannot be zero.";
return;
}
if (numerator1 < 0 || numerator2 < 0) {
resultDiv.innerHTML = "Numerator must be non-negative. If the fraction is negative, include the sign in the whole number.";
return;
}
if (denominator1 < 1 || denominator2 < 1) {
resultDiv.innerHTML = "Denominator must be a positive integer (1 or greater).";
return;
}
// Convert mixed fractions to improper fractions
var improper1 = mixedToImproper(whole1, numerator1, denominator1);
var improper2 = mixedToImproper(whole2, numerator2, denominator2);
if (isNaN(improper1.num) || isNaN(improper2.num)) {
resultDiv.innerHTML = "An error occurred during fraction conversion. Please check inputs.";
return;
}
var resultNum, resultDen;
// Perform the selected operation
switch (operation) {
case "add":
resultNum = improper1.num * improper2.den + improper2.num * improper1.den;
resultDen = improper1.den * improper2.den;
break;
case "subtract":
resultNum = improper1.num * improper2.den – improper2.num * improper1.den;
resultDen = improper1.den * improper2.den;
break;
case "multiply":
resultNum = improper1.num * improper2.num;
resultDen = improper1.den * improper2.den;
break;
case "divide":
if (improper2.num === 0) {
resultDiv.innerHTML = "Cannot divide by zero.";
return;
}
resultNum = improper1.num * improper2.den;
resultDen = improper1.den * improper2.num;
break;
default:
resultDiv.innerHTML = "Invalid operation selected.";
return;
}
// Handle potential negative denominator from division if improper2.num was negative
if (resultDen < 0) {
resultNum = -resultNum;
resultDen = -resultDen;
}
// Simplify the resulting improper fraction
var simplifiedResult = simplifyFraction(resultNum, resultDen);
var finalImproperNum = simplifiedResult.num;
var finalImproperDen = simplifiedResult.den;
// Convert the simplified improper fraction back to a mixed fraction
var finalMixed = improperToMixed(finalImproperNum, finalImproperDen);
// Format and display the result
var resultString = "";
var sign = "";
if (finalMixed.whole < 0 || (finalMixed.whole === 0 && finalMixed.num < 0)) {
sign = "-";
}
var absWhole = Math.abs(finalMixed.whole);
var absNum = Math.abs(finalMixed.num);
var absDen = Math.abs(finalMixed.den);
if (absWhole === 0 && absNum === 0) {
resultString = "0";
} else if (absNum === 0) {
resultString = sign + absWhole;
} else if (absWhole === 0) {
resultString = sign + absNum + "/" + absDen;
} else {
resultString = sign + absWhole + " " + absNum + "/" + absDen;
}
resultDiv.innerHTML = "" + resultString + " (Improper: " + finalImproperNum + "/" + finalImproperDen + ")";
}
.mixed-fraction-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 25px;
max-width: 700px;
margin: 20px auto;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
color: #333;
}
.mixed-fraction-calculator-container h2 {
text-align: center;
color: #2c3e50;
margin-bottom: 20px;
font-size: 1.8em;
}
.mixed-fraction-calculator-container h3 {
color: #34495e;
margin-top: 15px;
margin-bottom: 10px;
font-size: 1.2em;
}
.mixed-fraction-calculator-container p {
line-height: 1.6;
margin-bottom: 15px;
}
.calculator-inputs {
display: flex;
flex-wrap: wrap;
justify-content: center;
align-items: flex-end;
gap: 20px;
margin-bottom: 25px;
}
.fraction-input-group {
background-color: #ffffff;
border: 1px solid #e0e0e0;
border-radius: 6px;
padding: 15px;
flex: 1;
min-width: 200px;
box-shadow: 0 2px 5px rgba(0, 0, 0, 0.05);
}
.fraction-input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
font-size: 0.95em;
}
.fraction-input-group input[type="number"] {
width: calc(100% – 20px);
padding: 10px;
margin-bottom: 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box;
}
.operation-selector {
text-align: center;
margin-top: 20px;
min-width: 100px;
}
.operation-selector label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #555;
font-size: 0.95em;
}
.operation-selector select {
padding: 10px 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1.1em;
background-color: #eaf4f7;
cursor: pointer;
appearance: none; /* Remove default arrow */
-webkit-appearance: none;
-moz-appearance: none;
background-image: url('data:image/svg+xml;charset=US-ASCII,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20width%3D%22292.4%22%20height%3D%22292.4%22%3E%3Cpath%20fill%3D%22%23000%22%20d%3D%22M287%2069.4a17.6%2017.6%200%200%200-13-5.4H18.4c-5%200-9.3%201.8-12.9%205.4A17.6%2017.6%200%200%200%200%2082.2c0%205%201.8%209.3%205.4%2012.9l128%20127.9c3.6%203.6%207.8%205.4%2012.8%205.4s9.2-1.8%2012.8-5.4L287%2095c3.5-3.5%205.4-7.8%205.4-12.8%200-5-1.9-9.2-5.5-12.8z%22%2F%3E%3C%2Fsvg%3E');
background-repeat: no-repeat;
background-position: right 10px top 50%;
background-size: 12px auto;
}
.mixed-fraction-calculator-container button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #28a745;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 20px;
}
.mixed-fraction-calculator-container button:hover {
background-color: #218838;
}
.calculator-result {
margin-top: 30px;
padding: 15px;
background-color: #e9f7ef;
border: 1px solid #d4edda;
border-radius: 6px;
text-align: center;
font-size: 1.3em;
color: #155724;
font-weight: bold;
}
.calculator-result p {
margin: 0;
}
/* Responsive adjustments */
@media (max-width: 600px) {
.calculator-inputs {
flex-direction: column;
align-items: stretch;
}
.fraction-input-group, .operation-selector {
min-width: unset;
width: 100%;
}
}
Understanding and Calculating Mixed Fractions
Mixed fractions, also known as mixed numbers, combine a whole number and a proper fraction (a fraction where the numerator is smaller than the denominator). For example, 3 1/2 means three whole units plus one-half of another unit. They are commonly used in everyday life, such as in cooking recipes or measurements.
Why Use Mixed Fractions?
Mixed fractions provide a more intuitive way to express quantities greater than one, especially when dealing with physical measurements. Instead of saying 7/2 cups of flour, it's often clearer to say 3 1/2 cups.
Converting Mixed Fractions to Improper Fractions
To perform arithmetic operations (addition, subtraction, multiplication, division) with mixed fractions, it's often easiest to first convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator (e.g., 7/2).
Steps for Conversion:
Multiply the whole number by the denominator.
Add the numerator to the product from step 1. This sum becomes the new numerator.
Keep the original denominator.
Formula:Whole Number (W) N/D = (W × D + N) / D
Example: Convert 3 1/2 to an improper fraction.
Multiply the whole number (3) by the denominator (2): 3 × 2 = 6
Add the numerator (1) to the result: 6 + 1 = 7
Keep the original denominator (2).
So, 3 1/2 becomes 7/2.
If the mixed fraction is negative, like -3 1/2, you convert 3 1/2 to 7/2 first, then apply the negative sign to the improper fraction: -7/2.
Performing Operations with Mixed Fractions
1. Addition and Subtraction
To add or subtract mixed fractions, convert them to improper fractions first. Then, find a common denominator, adjust the numerators, and perform the operation.
Example (Addition): Calculate 1 1/2 + 2 1/3
Convert to improper fractions:
1 1/2 = (1 × 2 + 1) / 2 = 3/2
2 1/3 = (2 × 3 + 1) / 3 = 7/3
Find a common denominator (LCM of 2 and 3 is 6):
3/2 = (3 × 3) / (2 × 3) = 9/6
7/3 = (7 × 2) / (3 × 2) = 14/6
Add the fractions: 9/6 + 14/6 = 23/6
Convert back to a mixed fraction: 23 ÷ 6 = 3 with a remainder of 5. So, 3 5/6.
2. Multiplication
To multiply mixed fractions, convert them to improper fractions and then multiply the numerators together and the denominators together.
Example (Multiplication): Calculate 1 1/2 × 2 1/3
Convert to improper fractions:
1 1/2 = 3/2
2 1/3 = 7/3
Multiply the numerators and denominators: (3 × 7) / (2 × 3) = 21/6
Simplify the improper fraction: 21/6 can be simplified by dividing both by their GCD (3), resulting in 7/2.
Convert back to a mixed fraction: 7 ÷ 2 = 3 with a remainder of 1. So, 3 1/2.
3. Division
To divide mixed fractions, convert them to improper fractions. Then, invert the second fraction (the divisor) and multiply.
Example (Division): Calculate 3 1/2 ÷ 1 1/4
Convert to improper fractions:
3 1/2 = (3 × 2 + 1) / 2 = 7/2
1 1/4 = (1 × 4 + 1) / 4 = 5/4
Invert the second fraction and multiply: 7/2 ÷ 5/4 = 7/2 × 4/5
Multiply: (7 × 4) / (2 × 5) = 28/10
Simplify the improper fraction: 28/10 can be simplified by dividing both by their GCD (2), resulting in 14/5.
Convert back to a mixed fraction: 14 ÷ 5 = 2 with a remainder of 4. So, 2 4/5.
Converting Improper Fractions Back to Mixed Fractions
After performing operations, your result will often be an improper fraction. To convert it back to a mixed fraction:
Divide the numerator by the denominator. The whole number part of the result is the whole number of your mixed fraction.
The remainder of the division becomes the new numerator.
The denominator stays the same.
Simplify the fractional part if possible by dividing both the numerator and denominator by their greatest common divisor (GCD).
Example: Convert 23/6 to a mixed fraction.
Divide 23 by 6: 23 ÷ 6 = 3 with a remainder of 5.
The whole number is 3.
The new numerator is 5.
The denominator is 6.
So, 23/6 becomes 3 5/6. (The fraction 5/6 is already simplified).
This calculator automates these steps, making it easy to work with mixed fractions for any operation.