This calculator is designed to solve various mathematical expressions and provide a step-by-step breakdown of the calculation process. It adheres to the standard order of operations (PEMDAS/BODMAS) to ensure accurate results for complex equations.
What is the Order of Operations?
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed in an expression to ensure a consistent and correct outcome. The most common acronyms used are PEMDAS and BODMAS:
PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
BODMAS: Brackets, Orders (powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Essentially, you solve operations within grouping symbols first, then exponents, then multiplications and divisions as they appear from left to right, and finally, additions and subtractions as they appear from left to right.
How This Calculator Works:
This calculator takes your input expression and applies the order of operations systematically. It identifies and performs operations in the correct sequence, simplifying the expression at each stage. The 'Steps' section will show you how the original expression was transformed through each significant operation, making it easier to follow the logic and learn how to solve similar problems manually.
Use Cases:
Students: Verify homework answers and understand how to solve multi-step math problems.
Educators: Use as a teaching aid to demonstrate the order of operations.
Everyday Users: Quickly solve calculations without manual errors, especially when dealing with more complex arithmetic.
Problem Solving: Break down and solve real-world problems that involve mathematical expressions.
The goal is to provide not just an answer, but also the educational insight into the mathematical process.
function calculateMath() {
var expression = document.getElementById('expression').value;
var resultElement = document.getElementById('result');
var stepsElement = document.getElementById('steps');
var steps = [];
var currentExpression = expression;
// Clear previous results and steps
resultElement.textContent = 'Calculating…';
stepsElement.innerHTML = ";
// Basic validation: Check if the expression is empty
if (!expression || expression.trim() === ") {
resultElement.textContent = 'Please enter a math expression.';
return;
}
try {
// — Step 1: Handle Parentheses/Brackets —
var regexParentheses = /\(([^()]*)\)/;
while (regexParentheses.test(currentExpression)) {
var match = regexParentheses.exec(currentExpression);
var subExpression = match[1];
var subResult = evaluateSimpleExpression(subExpression);
if (isNaN(subResult)) {
throw new Error("Invalid expression inside parentheses.");
}
steps.push("Inside parentheses: " + subExpression + " = " + subResult);
currentExpression = currentExpression.replace(match[0], subResult.toString());
}
steps.push("After removing parentheses: " + currentExpression);
// — Step 2: Handle Exponents (Simplified – this example doesn't support complex exponents directly, focus on basic arithmetic) —
// For a true step-by-step exponent solver, a more complex parser would be needed.
// This basic version will treat numbers followed by ^ and another number as multiplication if not handled by regex below.
// A more robust solution would require parsing and evaluating powers.
// — Step 3: Handle Multiplication and Division (Left to Right) —
var regexMulDiv = /(-?\d*\.?\d+)\s*([\*\/])\s*(-?\d*\.?\d+)/;
while (regexMulDiv.test(currentExpression)) {
var match = regexMulDiv.exec(currentExpression);
var num1 = parseFloat(match[1]);
var operator = match[2];
var num2 = parseFloat(match[3]);
var result;
if (operator === '*') {
result = num1 * num2;
} else { // operator === '/'
if (num2 === 0) throw new Error("Division by zero.");
result = num1 / num2;
}
steps.push("Multiply/Divide: " + num1 + " " + operator + " " + num2 + " = " + result);
currentExpression = currentExpression.replace(match[0], result.toString());
}
steps.push("After multiplication/division: " + currentExpression);
// — Step 4: Handle Addition and Subtraction (Left to Right) —
// Need to handle signs carefully, especially with negative numbers.
// Normalize the expression: replace '–' with '+', '+-' with '-', '-+' with '-'
currentExpression = currentExpression.replace(/–/g, '+');
currentExpression = currentExpression.replace(/\+-/g, '-');
currentExpression = currentExpression.replace(/-\+/g, '-');
var regexAddSub = /(-?\d*\.?\d+)\s*([\+\-])\s*(-?\d*\.?\d+)/;
// This loop needs to be careful to handle chained operations correctly and signs
while (true) {
// Find the next addition or subtraction, but ensure it's not part of a number like -5.5
// A simple regex might get confused by '-5' vs '5-'.
// Let's try to find the *first* operator not preceded by another operator or start of string.
var addSubMatch = currentExpression.match(/(-?\d*\.?\d+)([\+\-])(\d*\.?\d+)/);
if (!addSubMatch) {
// Handle cases like just a single number or already simplified
if (!isNaN(parseFloat(currentExpression))) {
break;
} else {
// This might indicate an error or a very simple expression like "-5"
// If it's just a number, it should be handled by the final parseFloat
break;
}
}
var num1Str = addSubMatch[1];
var operator = addSubMatch[2];
var num2Str = addSubMatch[3];
var num1 = parseFloat(num1Str);
var num2 = parseFloat(num2Str);
var result;
if (operator === '+') {
result = num1 + num2;
} else { // operator === '-'
result = num1 – num2;
}
steps.push("Add/Subtract: " + num1 + " " + operator + " " + num2 + " = " + result);
// Replace only the *first* occurrence of the matched pattern to maintain left-to-right processing
currentExpression = currentExpression.replace(addSubMatch[0], result.toString());
currentExpression = currentExpression.replace(/–/g, '+'); // Re-normalize after replacement
currentExpression = currentExpression.replace(/\+-/g, '-');
currentExpression = currentExpression.replace(/-\+/g, '-');
}
var finalResult = parseFloat(currentExpression);
if (isNaN(finalResult)) {
throw new Error("Could not parse the final result. Ensure the expression is valid.");
}
resultElement.textContent = "Result: " + finalResult.toString();
// Display steps
if (steps.length > 0) {
var stepsHtml = "
Calculation Steps:
";
steps.forEach(function(step, index) {
stepsHtml += "Step " + (index + 1) + ": " + step + "";
});
stepsElement.innerHTML = stepsHtml;
} else {
stepsElement.innerHTML = "No intermediate steps to display for this simple expression.";
}
} catch (error) {
resultElement.textContent = "Error: " + error.message;
stepsElement.innerHTML = "; // Clear steps on error
}
}
// Helper function to evaluate simple expressions (used for parentheses)
// This function assumes no nested parentheses and only basic arithmetic
function evaluateSimpleExpression(expr) {
// Trim whitespace
expr = expr.trim();
// Remove any remaining parentheses that might have been missed or are empty
expr = expr.replace(/[()]/g, ");
// Prioritize multiplication and division
var regexMulDiv = /(-?\d*\.?\d+)\s*([\*\/])\s*(-?\d*\.?\d+)/;
while (regexMulDiv.test(expr)) {
var match = regexMulDiv.exec(expr);
var num1 = parseFloat(match[1]);
var operator = match[2];
var num2 = parseFloat(match[3]);
var result;
if (operator === '*') {
result = num1 * num2;
} else { // operator === '/'
if (num2 === 0) throw new Error("Division by zero.");
result = num1 / num2;
}
expr = expr.replace(match[0], result.toString());
}
// Handle addition and subtraction
expr = expr.replace(/–/g, '+');
expr = expr.replace(/\+-/g, '-');
expr = expr.replace(/-\+/g, '-');
var regexAddSub = /(-?\d*\.?\d+)([\+\-])(\d*\.?\d+)/;
while (true) {
var addSubMatch = expr.match(/(-?\d*\.?\d+)([\+\-])(\d*\.?\d+)/);
if (!addSubMatch) {
break;
}
var num1 = parseFloat(addSubMatch[1]);
var operator = addSubMatch[2];
var num2 = parseFloat(addSubMatch[3]);
var result;
if (operator === '+') {
result = num1 + num2;
} else { // operator === '-'
result = num1 – num2;
}
expr = expr.replace(addSubMatch[0], result.toString());
expr = expr.replace(/–/g, '+');
expr = expr.replace(/\+-/g, '-');
expr = expr.replace(/-\+/g, '-');
}
var finalResult = parseFloat(expr);
if (isNaN(finalResult)) {
throw new Error("Invalid simple expression.");
}
return finalResult;
}