Advanced Arithmetic Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
display: flex;
justify-content: center;
align-items: flex-start; /* Align items to the top */
min-height: 100vh;
}
.loan-calc-container {
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
width: 100%;
max-width: 700px;
margin-top: 20px; /* Add margin to separate from header */
}
h1 {
color: #004a99;
text-align: center;
margin-bottom: 25px;
font-size: 2.2em;
}
h2 {
color: #004a99;
margin-top: 30px;
margin-bottom: 15px;
border-bottom: 2px solid #004a99;
padding-bottom: 5px;
}
.input-group {
margin-bottom: 20px;
display: flex;
align-items: center;
gap: 15px;
}
.input-group label {
flex: 1;
min-width: 120px; /* Ensure labels have a consistent minimum width */
font-weight: bold;
color: #555;
text-align: right;
}
.input-group input[type="number"],
.input-group input[type="text"] {
flex: 2;
padding: 10px 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
}
.input-group input[type="number"]:focus,
.input-group input[type="text"]:focus {
outline: none;
border-color: #007bff;
box-shadow: 0 0 5px rgba(0, 123, 255, 0.25);
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.button-group {
text-align: center;
margin-top: 30px;
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button {
background-color: #004a99;
color: white;
padding: 12px 25px;
border: none;
border-radius: 5px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
margin: 0 10px;
}
button:hover {
background-color: #003366;
}
#result {
margin-top: 30px;
padding: 20px;
background-color: #e7f3ff;
border-left: 5px solid #28a745;
border-radius: 5px;
text-align: center;
font-size: 1.8em;
font-weight: bold;
color: #004a99;
min-height: 60px; /* Ensure it has some height even when empty */
display: flex;
justify-content: center;
align-items: center;
word-break: break-all; /* Prevent long results from overflowing */
}
#result.error {
background-color: #f8d7da;
border-left-color: #dc3545;
color: #721c24;
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padding: 25px;
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.article-content ul, .article-content ol {
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margin-bottom: 15px;
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.article-content li {
margin-bottom: 8px;
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.article-content strong {
color: #004a99;
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/* Responsive adjustments */
@media (max-width: 600px) {
.input-group {
flex-direction: column;
align-items: stretch;
gap: 10px;
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.input-group label {
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min-width: auto;
}
.input-group input[type="number"],
.input-group input[type="text"] {
flex: none;
width: 100%;
}
button {
width: calc(100% – 20px); /* Full width minus margin */
margin: 10px 0;
}
.loan-calc-container {
padding: 20px;
}
h1 {
font-size: 1.8em;
}
#result {
font-size: 1.5em;
}
}
Advanced Arithmetic Calculator
Enter numbers and select an operator
Understanding Advanced Arithmetic: Negatives and Fractions
This calculator is designed to handle a broader range of arithmetic operations than basic calculators, specifically focusing on calculations involving negative numbers and fractions. Understanding how to work with these number types is fundamental in mathematics and has numerous practical applications.
Working with Negative Numbers
Negative numbers represent values less than zero. They are essential for representing concepts like debt, temperatures below freezing, or altitudes below sea level. When performing arithmetic with negative numbers, follow these rules:
- Addition: Adding a negative number is the same as subtracting its positive counterpart.
(5 + (-3) = 5 - 3 = 2). Adding two negative numbers results in a more negative number. (-4 + (-2) = -4 - 2 = -6).
- Subtraction: Subtracting a negative number is the same as adding its positive counterpart.
(7 - (-3) = 7 + 3 = 10). Subtracting a positive number from a negative number results in a more negative number. (-5 - 4 = -9).
- Multiplication: Multiplying two numbers with the same sign (both positive or both negative) results in a positive number.
(6 * 3 = 18), (-6 * -3 = 18). Multiplying two numbers with different signs results in a negative number. (6 * -3 = -18), (-6 * 3 = -18).
- Division: Similar to multiplication, dividing two numbers with the same sign results in a positive number, and dividing two numbers with different signs results in a negative number.
(18 / 6 = 3), (-18 / -6 = 3), (18 / -6 = -3), (-18 / 6 = -3).
Working with Fractions
Fractions represent parts of a whole. A fraction consists of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar.
- Addition/Subtraction: To add or subtract fractions, they must have a common denominator. Find the least common multiple (LCM) of the denominators, convert each fraction to an equivalent fraction with the LCM as the denominator, and then add or subtract the numerators.
(1/3 + 1/4 = 4/12 + 3/12 = 7/12).
- Multiplication: Multiply the numerators together and the denominators together. Simplify the resulting fraction if possible.
(2/5 * 3/4 = (2*3) / (5*4) = 6/20 = 3/10).
- Division: To divide fractions, invert the second fraction (find its reciprocal) and then multiply.
(1/2 / 3/4 = 1/2 * 4/3 = (1*4) / (2*3) = 4/6 = 2/3).
Combining Negatives and Fractions
This calculator handles combinations of negative numbers and fractions seamlessly. For example, you can calculate -1/2 + 3/4 or -5 * -2/3. The calculator processes these inputs by first converting them into a usable format, performing the arithmetic according to the rules above, and then presenting the result, often in its simplest fractional form.
Use Cases
- Scientific and Engineering Calculations: Many formulas in physics, engineering, and advanced mathematics involve negative values and fractional coefficients.
- Financial Modeling: Representing losses (negative values) and proportions (fractions) is common in finance.
- Academic Learning: This calculator serves as a valuable tool for students learning and practicing arithmetic with negative numbers and fractions.
- Complex Data Analysis: When dealing with datasets that contain negative values or require proportional adjustments, this type of calculator can be useful.
By providing precise results for operations involving negatives and fractions, this calculator empowers users to tackle more complex mathematical problems with confidence.
function gcd (a, b) {
return b === 0 ? a : gcd(b, a % b);
}
function parseFraction (fractionStr) {
if (typeof fractionStr !== 'string' || fractionStr.trim() === ") {
return NaN;
}
fractionStr = fractionStr.replace(/\s/g, "); // Remove whitespace
if (fractionStr.includes('/')) {
var parts = fractionStr.split('/');
if (parts.length !== 2) return NaN;
var numerator = parseFloat(parts[0]);
var denominator = parseFloat(parts[1]);
if (isNaN(numerator) || isNaN(denominator)) return NaN;
if (denominator === 0) return NaN; // Division by zero
return numerator / denominator;
} else {
var num = parseFloat(fractionStr);
return isNaN(num) ? NaN : num;
}
}
function formatFraction (number) {
if (isNaN(number)) {
return "Invalid Input";
}
if (number === 0) {
return "0";
}
var tolerance = 1e-10; // Tolerance for floating point comparisons
var decimalPart, integerPart = Math.floor(number);
// Check if it's very close to an integer
if (Math.abs(number – integerPart) < tolerance) {
return integerPart.toString();
}
// Attempt to find a simple fractional representation
var maxDenominator = 1000; // Limit complexity
for (var denominator = 1; denominator <= maxDenominator; denominator++) {
var numerator = number * denominator;
var roundedNumerator = Math.round(numerator);
if (Math.abs(numerator – roundedNumerator) < tolerance) {
var common = gcd(Math.abs(roundedNumerator), denominator);
var finalNumerator = roundedNumerator / common;
var finalDenominator = denominator / common;
if (finalDenominator < 0) { // Ensure denominator is positive
finalNumerator = -finalNumerator;
finalDenominator = -finalDenominator;
}
if (finalDenominator === 1) {
return finalNumerator.toString();
} else {
return finalNumerator + "/" + finalDenominator;
}
}
}
// If no simple fraction found, return as decimal (limited precision)
return number.toFixed(6);
}
function calculate() {
var operand1Str = document.getElementById("operand1").value;
var operand2Str = document.getElementById("operand2").value;
var operator = document.getElementById("operator").value;
var resultDiv = document.getElementById("result");
var operand1 = parseFraction(operand1Str);
var operand2 = parseFraction(operand2Str);
if (isNaN(operand1) || isNaN(operand2)) {
resultDiv.innerHTML = "Error: Invalid number format. Use integers, decimals, or fractions (e.g., 3/4, -1/2).";
resultDiv.className = "error";
return;
}
var result;
switch (operator) {
case '+':
result = operand1 + operand2;
break;
case '-':
result = operand1 – operand2;
break;
case '*':
result = operand1 * operand2;
break;
case '/':
if (operand2 === 0) {
resultDiv.innerHTML = "Error: Division by zero is not allowed.";
resultDiv.className = "error";
return;
}
result = operand1 / operand2;
break;
default:
resultDiv.innerHTML = "Error: Unknown operator.";
resultDiv.className = "error";
return;
}
resultDiv.innerHTML = formatFraction(result);
resultDiv.className = ""; // Remove error class if calculation is successful
}
function resetFields() {
document.getElementById("operand1").value = "";
document.getElementById("operand2").value = "";
document.getElementById("operator").value = "+";
document.getElementById("result").innerHTML = "Enter numbers and select an operator";
document.getElementById("result").className = "";
}