Long division is a standard algorithm used to divide multi-digit numbers. It breaks down a complex division problem into a series of simpler steps involving basic division, multiplication, and subtraction. This method is essential for understanding how numbers interact and is a core component of elementary mathematics.
Key Terms in Long Division
Dividend: The total amount you have that you want to divide up.
Divisor: The number you are dividing by (how many groups you are making).
Quotient: The result of the division (the answer).
Remainder: The amount left over that cannot be evenly divided by the divisor.
How to Perform Long Division Step-by-Step
To use this calculator, simply enter your dividend and divisor. The tool follows the "DMSB" method:
Divide: See how many times the divisor goes into the first digit(s) of the dividend.
Multiply: Multiply that partial quotient by the divisor.
Subtract: Subtract that result from the partial dividend.
Bring Down: Bring down the next digit of the dividend and repeat.
Example Calculation
If you divide 485 by 12:
12 goes into 48 four times (12 x 4 = 48).
Subtract 48 from 48 to get 0.
Bring down the 5.
12 goes into 5 zero times.
The final quotient is 40 with a remainder of 5.
function calculateLongDivision() {
var dividendInput = document.getElementById('dividend').value;
var divisorInput = document.getElementById('divisor').value;
var resultArea = document.getElementById('ld-result-area');
var summaryText = document.getElementById('ld-summary-text');
var stepsDisplay = document.getElementById('ld-steps-display');
if (!dividendInput || !divisorInput) {
alert("Please enter both a dividend and a divisor.");
return;
}
var dividendVal = parseFloat(dividendInput);
var divisorVal = parseFloat(divisorInput);
if (divisorVal === 0) {
alert("Division by zero is undefined.");
return;
}
// Convert to absolute integers for step processing
var dividendStr = Math.abs(Math.floor(dividendVal)).toString();
var divisor = Math.abs(Math.floor(divisorVal));
var isNegative = (dividendVal < 0) ^ (divisorVal < 0);
var currentPart = "";
var quotient = "";
var steps = "";
var padding = " ";
steps += " " + Math.floor(dividendVal / divisorVal) + " (Quotient)\n";
steps += " " + " ".repeat(divisor.toString().length) + "______\n";
steps += divisor + " | " + dividendStr + "\n";
var remainder = 0;
var currentVal = 0;
var stepBuffer = "";
for (var i = 0; i = divisor) {
var qDigit = Math.floor(currentVal / divisor);
var product = qDigit * divisor;
var newRemainder = currentVal – product;
var lineIndent = " ".repeat(divisor.toString().length + 3 + i – (product.toString().length – 1));
stepBuffer += lineIndent + product + "\n";
stepBuffer += " ".repeat(divisor.toString().length + 3) + "-".repeat(i + 1) + "\n";
quotient += qDigit;
currentPart = newRemainder.toString();
var remIndent = " ".repeat(divisor.toString().length + 3 + i – (newRemainder.toString().length – 1));
// Only add remainder line if not last step or if remainder > 0
if (i < dividendStr.length – 1) {
// Visualize "bringing down" next digit
}
} else {
quotient += "0";
}
}
var finalQuotient = Math.floor(Math.abs(dividendVal) / Math.abs(divisorVal));
var finalRemainder = Math.abs(dividendVal) % Math.abs(divisorVal);
if (isNegative && finalQuotient !== 0) {
finalQuotient = -finalQuotient;
}
summaryText.innerHTML = "Result: " + finalQuotient + " Remainder: " + finalRemainder + "";
// Simplified Visual Step Logic
var visualSteps = "Manual Calculation for " + dividendStr + " รท " + divisor + ":\n\n";
var tempDividend = "";
var runningRemainder = 0;
for (var j = 0; j " + times + " times.\n";
visualSteps += " " + times + " x " + divisor + " = " + sub + "\n";
runningRemainder = workingValue – sub;
visualSteps += " Subtract: " + workingValue + " – " + sub + " = " + runningRemainder + "\n";
if (j < dividendStr.length – 1) {
visualSteps += " Bring down " + dividendStr[j+1] + " to make " + (runningRemainder * 10 + parseInt(dividendStr[j+1])) + "\n\n";
} else {
visualSteps += " Final Remainder: " + runningRemainder + "\n";
}
}
stepsDisplay.innerText = visualSteps;
resultArea.style.display = 'block';
}