Long division is a standard algorithm used to solve division problems involving multi-digit numbers. It breaks down a complex division problem into a series of simpler steps: divide, multiply, subtract, and bring down. By repeating these steps, you can find exactly how many times a divisor fits into a dividend and what amount is left over as a remainder.
Real-World Example:
Imagine you have 130 cookies and you want to pack them into boxes that hold 12 cookies each. Using long division:
Dividend: 130
Divisor: 12
Quotient: 10 (You can fill 10 full boxes)
Remainder: 10 (You will have 10 cookies left over)
How to Use This Long Division Calculator
Using this tool is straightforward and designed for both students and professionals who need quick, accurate results:
Enter the Dividend: This is the total quantity you have.
Enter the Divisor: This is the size of the groups you are dividing into.
Click Calculate: The tool will instantly provide the whole number quotient, the remainder, and the decimal equivalent.
The Anatomy of Division
To master long division, it's essential to understand the four key components:
Dividend: The number being divided (the "big" number).
Divisor: The number you are dividing by.
Quotient: The primary result (how many times the divisor goes in).
Remainder: The amount left over that is smaller than the divisor.
Step-by-Step Manual Calculation
If you were to solve 485 ÷ 12 manually:
See how many times 12 goes into 48. It goes 4 times exactly (4 x 12 = 48).
Subtract 48 from 48 to get 0.
Bring down the 5.
See how many times 12 goes into 5. It goes 0 times.
The 5 becomes your remainder.
Final Answer: 40 R 5.
function performLongDivision() {
var dividendInput = document.getElementById('dividend').value;
var divisorInput = document.getElementById('divisor').value;
var dividend = parseFloat(dividendInput);
var divisor = parseFloat(divisorInput);
var display = document.getElementById('resultDisplay');
var qOut = document.getElementById('quotientRes');
var rOut = document.getElementById('remainderRes');
var dOut = document.getElementById('decimalRes');
var sOut = document.getElementById('stepsOutput');
if (isNaN(dividend) || isNaN(divisor)) {
alert("Please enter valid numbers.");
return;
}
if (divisor === 0) {
alert("Division by zero is not possible.");
return;
}
display.style.display = 'block';
// Core Calculations
var quotient = Math.floor(Math.abs(dividend) / Math.abs(divisor));
var remainder = Math.abs(dividend) % Math.abs(divisor);
var decimalResult = dividend / divisor;
// Handle sign for negative numbers
if ((dividend 0) || (dividend > 0 && divisor < 0)) {
quotient = -quotient;
}
// Update Results
qOut.innerHTML = "Quotient (Whole Number): " + quotient;
rOut.innerHTML = "Remainder: " + remainder;
dOut.innerHTML = "Decimal Result: " + decimalResult.toLocaleString(undefined, {maximumFractionDigits: 10});
// Generate Step-by-Step string
var steps = "Step-by-step logic for " + dividend + " ÷ " + divisor + ":\n\n";
steps += "1. Divide " + Math.abs(dividend) + " by " + Math.abs(divisor) + ".\n";
steps += "2. " + Math.abs(divisor) + " goes into " + Math.abs(dividend) + " a total of " + Math.floor(Math.abs(dividend) / Math.abs(divisor)) + " times.\n";
steps += "3. Multiply: " + Math.floor(Math.abs(dividend) / Math.abs(divisor)) + " × " + Math.abs(divisor) + " = " + (Math.floor(Math.abs(dividend) / Math.abs(divisor)) * Math.abs(divisor)) + ".\n";
steps += "4. Subtract: " + Math.abs(dividend) + " – " + (Math.floor(Math.abs(dividend) / Math.abs(divisor)) * Math.abs(divisor)) + " = " + remainder + ".\n";
steps += "5. Result: " + quotient + " with a remainder of " + remainder + ".";
sOut.innerText = steps;
}