Simplify and evaluate algebraic expressions by substituting variable values.
Result:
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Understanding Algebraic Expressions
Algebraic expressions are fundamental building blocks in mathematics. They are mathematical phrases that can contain numbers, variables (like x, y, or z), and operation symbols (like +, -, *, /). Unlike algebraic equations, expressions do not have an equals sign and therefore cannot be "solved" in the same way. Instead, they can be simplified or evaluated.
Simplification involves rewriting an expression to make it shorter or easier to understand, often by combining like terms or performing operations. For example, 2x + 3x simplifies to 5x.
Evaluation, which this calculator focuses on, means finding the numerical value of an expression by substituting specific numbers for its variables. This is incredibly useful in various fields:
Science and Engineering: To calculate physical quantities, test hypotheses, or model systems. For instance, the expression for kinetic energy is (1/2)mv², where m is mass and v is velocity. You can evaluate this to find the energy for specific objects.
Computer Science: To determine performance metrics, resource allocation, or algorithm efficiency.
Economics and Finance: To model costs, revenues, profits, or predict market trends. A simple profit calculation might be Revenue – Costs, where Revenue could be (Price per Unit * Number of Units Sold).
Everyday Problem Solving: To calculate distances, time, or costs based on changing conditions. For example, if you have an expression for the total cost of a trip based on distance and fuel price, you can evaluate it for different trip lengths.
This calculator allows you to input an algebraic expression and then assign numerical values to its variables. It will then compute and display the resulting numerical value of the expression. This tool is valuable for quickly checking calculations, exploring how changes in variables affect an outcome, and understanding the practical application of algebraic concepts.
function calculateExpression() {
var expressionStr = document.getElementById("expression").value;
var varName1 = document.getElementById("variable1").value.trim();
var varValue1 = parseFloat(document.getElementById("value1").value);
var varName2 = document.getElementById("variable2").value.trim();
var varValue2 = parseFloat(document.getElementById("value2").value);
var varName3 = document.getElementById("variable3").value.trim();
var varValue3 = parseFloat(document.getElementById("value3").value);
var resultValueElement = document.getElementById("resultValue");
resultValueElement.style.color = "#28a745"; // Default to green for success
if (!expressionStr) {
resultValueElement.textContent = "Please enter an expression.";
resultValueElement.style.color = "red";
return;
}
try {
var scope = {};
if (varName1 && !isNaN(varValue1)) {
scope[varName1] = varValue1;
}
if (varName2 && !isNaN(varValue2)) {
scope[varName2] = varValue2;
}
if (varName3 && !isNaN(varValue3)) {
scope[varName3] = varValue3;
}
// Basic validation for variable names (avoiding conflicts with JS keywords if possible, though a full parser is complex)
var validVarNames = /^[a-zA-Z_][a-zA-Z0-9_]*$/;
if ((varName1 && !validVarNames.test(varName1)) ||
(varName2 && !validVarNames.test(varName2)) ||
(varName3 && !validVarNames.test(varName3))) {
throw new Error("Invalid variable name. Use letters, numbers, and underscores, starting with a letter or underscore.");
}
// A very basic substitution and evaluation.
// For complex expressions, a dedicated math parsing library would be better.
// This handles simple cases and common operators.
// It replaces variable names with their values.
var evaluatedExpression = expressionStr;
// Order of replacement matters if variable names are substrings of others (e.g., 'x' and 'xx')
// Replace longer variable names first if there's overlap, or ensure unique names.
// For simplicity here, we assume unique or non-overlapping names.
if (varName1 && scope[varName1] !== undefined) {
var regex1 = new RegExp("\\b" + varName1 + "\\b", "g");
evaluatedExpression = evaluatedExpression.replace(regex1, varValue1.toString());
}
if (varName2 && scope[varName2] !== undefined) {
var regex2 = new RegExp("\\b" + varName2 + "\\b", "g");
evaluatedExpression = evaluatedExpression.replace(regex2, varValue2.toString());
}
if (varName3 && scope[varName3] !== undefined) {
var regex3 = new RegExp("\\b" + varName3 + "\\b", "g");
evaluatedExpression = evaluatedExpression.replace(regex3, varValue3.toString());
}
// Now, evaluate the string. Using eval is risky in production for untrusted input,
// but for a calculator tool where the user provides the expression, it's often used.
// A safer approach involves a parser.
// We'll use eval for demonstration purposes, assuming the user intends to evaluate math.
var result = eval(evaluatedExpression);
if (isNaN(result)) {
throw new Error("Result is Not a Number.");
}
resultValueElement.textContent = result;
} catch (error) {
resultValueElement.textContent = "Error: " + error.message;
resultValueElement.style.color = "red";
}
}