Mixed Number Fractions Calculator
:root {
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–success-green: #28a745;
–light-background: #f8f9fa;
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–border-color: #ccc;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–dark-text);
line-height: 1.6;
margin: 0;
padding: 20px;
display: flex;
flex-direction: column;
align-items: center;
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.loan-calc-container {
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border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
padding: 30px;
width: 100%;
max-width: 700px;
margin-bottom: 40px;
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h1, h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 20px;
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.input-group {
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margin-bottom: 8px;
font-weight: bold;
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.input-group input[type="number"],
.input-group input[type="text"] {
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padding: 12px;
border: 1px solid var(–border-color);
border-radius: 5px;
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font-size: 1rem;
transition: border-color 0.3s ease;
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font-weight: bold;
transition: background-color 0.3s ease, transform 0.2s ease;
width: 100%;
margin-top: 10px;
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button:hover {
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.result-container h3 {
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.result {
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.explanation-section {
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.fraction-input input[type="number"] {
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button {
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}
Mixed Number Fractions Calculator
Understanding and Adding Mixed Number Fractions
Mixed numbers combine a whole number with a proper fraction (where the numerator is smaller than the denominator). For example, 3 ½ means 3 whole units and half of another unit.
Adding mixed numbers involves two primary steps:
- Convert to Improper Fractions: First, convert each mixed number into an improper fraction. An improper fraction has a numerator that is greater than or equal to its denominator. The formula to convert a mixed number (whole $\frac{numerator}{denominator}$) to an improper fraction is:
$$ \text{Improper Fraction} = \frac{(\text{Whole} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}} $$
- Add the Improper Fractions: Once both mixed numbers are converted into improper fractions, you can add them.
- If the denominators are the same, add the numerators and keep the common denominator.
- If the denominators are different, find a common denominator (usually the least common multiple or LCM) and adjust the numerators accordingly before adding.
The formula for adding two fractions $\frac{a}{b}$ and $\frac{c}{d}$ is:
$$ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} $$
If a common denominator $D$ is found, and the fractions are converted to $\frac{a'}{D}$ and $\frac{c'}{D}$, then:
$$ \frac{a'}{D} + \frac{c'}{D} = \frac{a' + c'}{D} $$
- Convert Back to Mixed Number (Optional but Recommended): After adding, if the resulting improper fraction has a numerator larger than its denominator, you can convert it back to a mixed number by dividing the numerator by the denominator. The quotient becomes the new whole number, the remainder becomes the new numerator, and the denominator stays the same.
Calculator Usage:
This calculator simplifies the process. Simply input the whole number, numerator, and denominator for each of the two mixed numbers you wish to add. Click "Add Fractions", and the calculator will provide the sum, both as an improper fraction and converted back into a mixed number for clarity.
Examples:
- Example 1: Add 2 $\frac{1}{3}$ and 1 $\frac{1}{2}$
- Convert to improper fractions:
- 2 $\frac{1}{3}$ = $\frac{(2 \times 3) + 1}{3} = \frac{7}{3}$
- 1 $\frac{1}{2}$ = $\frac{(1 \times 2) + 1}{2} = \frac{3}{2}$
- Find a common denominator (LCM of 3 and 2 is 6):
- $\frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6}$
- $\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}$
- Add: $\frac{14}{6} + \frac{9}{6} = \frac{23}{6}$
- Convert back to mixed number: 23 ÷ 6 = 3 with a remainder of 5. So, 3 $\frac{5}{6}$.
- Example 2: Add 4 $\frac{2}{5}$ and 3 $\frac{1}{5}$
- Denominators are already the same.
- Add whole numbers: 4 + 3 = 7
- Add fractions: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$
- Combine: 7 $\frac{3}{5}$
function gcd(a, b) {
var a = Math.abs(a);
var b = Math.abs(b);
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
function lcm(a, b) {
return (a * b) / gcd(a, b);
}
function addMixedFractions() {
var whole1 = parseFloat(document.getElementById("whole1").value);
var num1 = parseFloat(document.getElementById("numerator1").value);
var den1 = parseFloat(document.getElementById("denominator1").value);
var whole2 = parseFloat(document.getElementById("whole2").value);
var num2 = parseFloat(document.getElementById("numerator2").value);
var den2 = parseFloat(document.getElementById("denominator2").value);
var resultDiv = document.getElementById("result");
var resultContainer = document.getElementById("result-container");
// Input validation
if (isNaN(whole1) || isNaN(num1) || isNaN(den1) ||
isNaN(whole2) || isNaN(num2) || isNaN(den2)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
resultContainer.style.backgroundColor = "#dc3545"; // Red for error
resultContainer.style.display = "block";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = "Denominators cannot be zero.";
resultContainer.style.backgroundColor = "#dc3545"; // Red for error
resultContainer.style.display = "block";
return;
}
// Convert to improper fractions
var impNum1 = (whole1 * den1) + num1;
var impDen1 = den1;
var impNum2 = (whole2 * den2) + num2;
var impDen2 = den2;
// Find a common denominator
var commonDen = lcm(impDen1, impDen2);
// Adjust numerators
var adjustedNum1 = impNum1 * (commonDen / impDen1);
var adjustedNum2 = impNum2 * (commonDen / impDen2);
// Add numerators
var finalNum = adjustedNum1 + adjustedNum2;
var finalDen = commonDen;
// Simplify the result
var commonDivisor = gcd(finalNum, finalDen);
finalNum /= commonDivisor;
finalDen /= commonDivisor;
// Convert back to a mixed number
var finalWhole = Math.floor(finalNum / finalDen);
var finalRemainderNum = finalNum % finalDen;
var resultString = "";
if (finalWhole !== 0) {
resultString += finalWhole + " ";
}
if (finalRemainderNum !== 0) {
resultString += finalRemainderNum + "/" + finalDen;
} else if (finalWhole === 0) {
resultString = "0"; // Handle case where sum is zero
}
// Display the result
resultDiv.innerHTML = resultString || finalNum + "/" + finalDen; // Display as improper if whole is 0 and num is 0
resultContainer.style.backgroundColor = "var(–success-green)"; // Green for success
resultContainer.style.display = "block";
}