.calculator-container {
font-family: 'Arial', sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
max-width: 700px;
margin: 20px auto;
border: 1px solid #ddd;
}
.calculator-container h2, .calculator-container h3 {
color: #333;
text-align: center;
margin-bottom: 15px;
}
.calculator-container p {
text-align: center;
margin-bottom: 20px;
color: #555;
}
.calculator-inputs {
display: flex;
justify-content: space-around;
align-items: center;
flex-wrap: wrap;
margin-bottom: 20px;
}
.fraction-input {
background-color: #fff;
padding: 15px;
border-radius: 5px;
border: 1px solid #eee;
margin: 10px;
flex: 1;
min-width: 200px;
}
.fraction-input label {
display: block;
margin-bottom: 5px;
color: #666;
font-size: 0.9em;
}
.fraction-input input[type="number"] {
width: calc(100% – 10px);
padding: 8px;
margin-bottom: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.operation-selector {
margin: 0 20px;
text-align: center;
}
.operation-selector label {
display: block;
margin-bottom: 5px;
color: #666;
font-size: 0.9em;
}
.operation-selector select {
padding: 8px;
border: 1px solid #ccc;
border-radius: 4px;
background-color: #fff;
font-size: 1.1em;
min-width: 60px;
}
.calculator-container 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;
}
.calculator-container button:hover {
background-color: #0056b3;
}
.calculator-result {
background-color: #e9f7ef;
border: 1px solid #d4edda;
padding: 15px;
border-radius: 5px;
margin-top: 20px;
text-align: center;
}
.calculator-result #result {
font-size: 1.4em;
color: #28a745;
font-weight: bold;
word-wrap: break-word;
}
@media (max-width: 600px) {
.calculator-inputs {
flex-direction: column;
}
.fraction-input, .operation-selector {
width: 100%;
margin: 10px 0;
}
}
// 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 convert a mixed fraction to an improper fraction
function toImproper(whole, num, den) {
if (den === 0) {
return { num: NaN, den: NaN }; // Indicate error
}
var improperNum = whole * den + num;
return { num: improperNum, den: den };
}
// Function to convert an improper fraction to a mixed fraction (or simplified proper fraction)
function toMixed(num, den) {
if (den === 0) {
return "Undefined (denominator is zero)";
}
if (num === 0) {
return "0";
}
var sign = 1;
if (num < 0) {
sign = -1;
num = Math.abs(num);
}
if (den 0) {
result += whole + " ";
}
result += simplifiedNum + "/" + simplifiedDen;
if (sign === -1) {
return "-" + result;
}
return result;
}
function calculateMixedFractions() {
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 operation = document.getElementById("operation").value;
var resultDiv = document.getElementById("result");
// 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 (num1 < 0 || num2 < 0) {
resultDiv.innerHTML = "Numerators should be non-negative. Please adjust the whole number for negative mixed fractions.";
return;
}
// Convert mixed fractions to improper fractions
var improper1 = toImproper(whole1, num1, den1);
var improper2 = toImproper(whole2, num2, den2);
var resNum, resDen;
switch (operation) {
case "add":
resNum = improper1.num * improper2.den + improper2.num * improper1.den;
resDen = improper1.den * improper2.den;
break;
case "subtract":
resNum = improper1.num * improper2.den – improper2.num * improper1.den;
resDen = improper1.den * improper2.den;
break;
case "multiply":
resNum = improper1.num * improper2.num;
resDen = improper1.den * improper2.den;
break;
case "divide":
if (improper2.num === 0) {
resultDiv.innerHTML = "Cannot divide by zero.";
return;
}
resNum = improper1.num * improper2.den;
resDen = improper1.den * improper2.num;
break;
default:
resultDiv.innerHTML = "Invalid operation selected.";
return;
}
// Simplify the result
var commonDivisor = gcd(resNum, resDen);
var finalNum = resNum / commonDivisor;
var finalDen = resDen / commonDivisor;
// Convert back to mixed fraction for display
resultDiv.innerHTML = toMixed(finalNum, finalDen);
}
Understanding Mixed Fractions and How to Calculate Them
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, 1 1/2 is a mixed fraction, representing one whole unit plus half of another unit.
Why Use Mixed Fractions?
Mixed fractions are often used in everyday life to describe quantities that are more than a whole but not an exact whole number. Think about recipes (2 3/4 cups of flour), measurements (5 1/2 feet tall), or time (1 1/4 hours). They provide a more intuitive way to express these values compared to improper fractions (e.g., 11/4 for 2 3/4).
Converting Between Mixed and Improper Fractions
To perform arithmetic operations on mixed fractions, it's often easiest to convert them into improper fractions first. An improper fraction has a numerator that is greater than or equal to its denominator (e.g., 3/2).
Mixed to Improper:
Multiply the whole number by the denominator, then add the numerator. Keep the original denominator.
Example: Convert 1 1/2 to an improper fraction.
- Whole number (1) × Denominator (2) = 2
- Add Numerator (1): 2 + 1 = 3
- Resulting improper fraction:
3/2
Improper to Mixed:
Divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator over the original denominator. Simplify the fractional part if possible.
Example: Convert 7/4 to a mixed fraction.
- 7 ÷ 4 = 1 with a remainder of 3
- Whole number: 1
- New numerator: 3
- Original denominator: 4
- Resulting mixed fraction:
1 3/4
Performing Operations with Mixed Fractions
1. Addition and Subtraction
The easiest way to add or subtract mixed fractions is to convert them to improper fractions first. Then, find a common denominator, perform the operation, and convert the result back to a mixed fraction.
Example (Addition): 1 1/2 + 2 3/4
- Convert to improper:
1 1/2 = 3/2, 2 3/4 = 11/4
- Find common denominator (4):
3/2 = 6/4
- Add:
6/4 + 11/4 = 17/4
- Convert back to mixed:
17/4 = 4 1/4
2. Multiplication
Convert mixed fractions to improper fractions. Multiply the numerators together and the denominators together. Simplify the result.
Example (Multiplication): 1 1/2 * 2 1/3
- Convert to improper:
1 1/2 = 3/2, 2 1/3 = 7/3
- Multiply:
(3/2) * (7/3) = (3*7) / (2*3) = 21/6
- Simplify and convert to mixed:
21/6 = 7/2 = 3 1/2
3. Division
Convert mixed fractions to improper fractions. Then, "keep, change, flip": keep the first fraction, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction. Finally, multiply and simplify.
Example (Division): 2 1/2 / 1 1/4
- Convert to improper:
2 1/2 = 5/2, 1 1/4 = 5/4
- Keep, Change, Flip:
(5/2) * (4/5)
- Multiply:
(5*4) / (2*5) = 20/10
- Simplify:
20/10 = 2
How to Use the Calculator
Our Mixed Fractions Calculator simplifies these steps for you:
- Enter Fraction 1: Input the whole number, numerator, and denominator for your first mixed fraction.
- Select Operation: Choose whether you want to add, subtract, multiply, or divide.
- Enter Fraction 2: Input the whole number, numerator, and denominator for your second mixed fraction.
- Click "Calculate": The calculator will instantly display the result as a simplified mixed fraction or whole number.
This tool is perfect for students, teachers, or anyone needing quick and accurate calculations involving mixed fractions without the manual hassle.