Algebraic Phrase Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #eef2f7;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
display: flex;
justify-content: center;
align-items: flex-start;
min-height: 100vh;
}
.loan-calc-container {
background-color: #ffffff;
padding: 30px;
border-radius: 10px;
box-shadow: 0 5px 15px rgba(0, 74, 153, 0.1);
width: 100%;
max-width: 700px;
margin-bottom: 40px;
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
font-weight: bold;
margin-bottom: 8px;
color: #004a99;
}
.input-group input[type="text"],
.input-group input[type="number"] {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 1rem;
box-sizing: border-box;
}
button {
background-color: #004a99;
color: white;
border: none;
padding: 12px 25px;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
width: 100%;
margin-top: 10px;
transition: background-color 0.3s ease;
}
button:hover {
background-color: #003366;
}
#result {
background-color: #d4edda; /* Light green for success */
color: #155724; /* Dark green for text */
padding: 20px;
margin-top: 25px;
border-radius: 8px;
text-align: center;
font-size: 1.4rem;
font-weight: bold;
border: 1px solid #c3e6cb;
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#result span {
font-size: 1.2rem;
font-weight: normal;
display: block;
margin-top: 5px;
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padding: 25px;
border-radius: 8px;
margin-top: 30px;
border: 1px solid #e9ecef;
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.article-section h2 {
text-align: left;
margin-bottom: 15px;
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.article-section p, .article-section ul {
margin-bottom: 15px;
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.article-section ul {
padding-left: 20px;
}
.article-section li {
margin-bottom: 8px;
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strong {
color: #004a99;
}
input[type="text"]:focus, input[type="number"]:focus {
outline: none;
border-color: #004a99;
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
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.error-message {
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font-weight: bold;
margin-top: 10px;
text-align: center;
width: 100%;
}
Algebraic Phrase Calculator
Understanding the Algebraic Phrase Calculator
This calculator is designed to evaluate an algebraic expression (or "phrase") given specific numerical values for its variables, typically 'x' and 'y'. Algebraic expressions are fundamental in mathematics, providing a way to represent relationships and perform calculations involving unknown quantities.
How it Works:
The calculator takes three inputs:
- Value of Variable 'x': A numerical value assigned to the variable 'x'.
- Value of Variable 'y': A numerical value assigned to the variable 'y'.
- Algebraic Phrase: An expression containing variables (like 'x' and 'y'), numbers, and mathematical operators. Common operators include:
- Addition:
+
- Subtraction:
-
- Multiplication:
* (essential to distinguish from variable concatenation)
- Division:
/
- Exponentiation:
^ (e.g., x^2 for x squared)
Once these inputs are provided, the calculator substitutes the given numerical values for 'x' and 'y' into the algebraic phrase and performs the operations according to the standard order of operations (PEMDAS/BODMAS – Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right). The final numerical result of this evaluation is then displayed.
Use Cases:
- Mathematics Education: Students can use this tool to check their manual calculations of algebraic expressions, reinforcing their understanding of substitution and order of operations.
- Problem Solving: In scenarios where a formula or relationship is defined algebraically, this calculator can quickly provide results for different input values.
- Prototyping & Exploration: Quickly test the outcome of simple mathematical models or financial formulas (e.g., calculating costs based on a formula involving quantity and price per unit).
- Data Analysis (Simple): Evaluating derived metrics based on basic formulas and input data points.
Mathematical Concepts Involved:
- Variables: Symbols (like x, y) representing unknown or changing quantities.
- Expressions: Combinations of numbers, variables, and operators.
- Substitution: Replacing variables with their numerical values.
- Order of Operations (PEMDAS/BODMAS): The standard convention for the sequence in which mathematical operations are performed to ensure a consistent result.
Example: If x = 5, y = 3, and the phrase is 2*x + y^2, the calculation would be:
2*(5) + (3)^2
10 + 9
19
This calculator simplifies the process of performing these evaluations accurately and efficiently.
function calculatePhrase() {
var xInput = document.getElementById("variableX");
var yInput = document.getElementById("variableY");
var phraseInput = document.getElementById("phrase");
var resultDiv = document.getElementById("result");
var errorDiv = document.getElementById("errorMessage");
errorDiv.textContent = ""; // Clear previous errors
resultDiv.innerHTML = ""; // Clear previous result
var xVal = parseFloat(xInput.value);
var yVal = parseFloat(yInput.value);
var phrase = phraseInput.value.trim();
if (isNaN(xVal)) {
errorDiv.textContent = "Please enter a valid number for the value of 'x'.";
return;
}
if (isNaN(yVal)) {
errorDiv.textContent = "Please enter a valid number for the value of 'y'.";
return;
}
if (phrase === "") {
errorDiv.textContent = "Please enter an algebraic phrase to evaluate.";
return;
}
// Basic sanitization and replacement for calculation
// Replace variable names with their values
var expression = phrase.replace(/x/gi, '(' + xVal + ')');
expression = expression.replace(/y/gi, '(' + yVal + ')');
// Replace exponentiation symbol '^' with Math.pow()
// This requires a more robust parsing or eval-like approach.
// For simplicity and safety, we'll use a basic regex replacement and eval,
// but acknowledge the security risks of eval with untrusted input.
// A safer approach would involve a dedicated expression parser.
// Replace common exponentiation patterns like x^n or (expr)^n
expression = expression.replace(/\(([^)]+)\)\^(\d+(\.\d+)?)/g, 'Math.pow($1, $2)');
expression = expression.replace(/(\d+(\.\d+)?|\(\s*-?\d+(\.\d+)?\s*\))\^(\d+(\.\d+)?)/g, 'Math.pow($1, $3)');
expression = expression.replace(/x\^(\d+(\.\d+)?)/g, 'Math.pow(' + xVal + ', $1)');
expression = expression.replace(/y\^(\d+(\.\d+)?)/g, 'Math.pow(' + yVal + ', $1)');
// Handle simple base^exponent where base is number literal
expression = expression.replace(/(\d+(\.\d+)?)\^(\d+(\.\d+)?)/g, 'Math.pow($1, $3)');
// Ensure multiplication is explicit where needed (e.g., 2x -> 2*x)
// This is complex and error-prone with simple regex. Using eval is often chosen
// for convenience in calculators like this, despite risks.
// We'll rely on the user inputting explicit '*' for multiplication.
try {
// WARNING: Using eval() can be a security risk if the input phrase
// comes from an untrusted source. For this specific calculator
// where the user is directly inputting, it's often accepted,
// but a proper parser is recommended for production systems.
// Ensure valid operators and numbers are present.
// A more robust check would be needed for full security.
if (!/^[0-9\s\.\+\-\*\/\(\)xXyYMath\.\^]+$/.test(phrase)) {
throw new Error("Invalid characters detected in the phrase.");
}
// Replace '^' with Math.pow for cases not caught by regex above
expression = expression.replace(/\^/g, ', '); // prepare for Math.pow(base, exponent) structure
// Need to wrap the exponent part correctly after replacing ^
// This gets complicated quickly with nested structures.
// A simplified approach might just replace ^ with **, but JS doesn't support ** natively before ES7.
// Let's stick to Math.pow replacement.
// Using Function constructor is slightly safer than direct eval
var allowedNames = { x: xVal, y: yVal, Math: Math };
var evaluator = new Function('x', 'y', 'Math', 'return ' + expression.replace(/x/gi, 'x').replace(/y/gi, 'y'));
var result = evaluator(xVal, yVal, Math);
// Check for results like Infinity or NaN which might indicate issues
if (result === Infinity || result === -Infinity || isNaN(result)) {
throw new Error("Calculation resulted in an invalid number (e.g., division by zero, undefined operation).");
}
resultDiv.innerHTML = "Result: " + result.toFixed(4) + "
(Evaluated from '" + phrase + "')";
} catch (e) {
errorDiv.textContent = "Error evaluating phrase: " + e.message;
console.error("Evaluation error:", e);
}
}