How to Calculate Long division with Remainders?


The long division method is a means of dividing large numbers by multiple steps following a set sequence. Like regular division problems, the dividend is divided by the divisor, resulting in the quotient, and sometimes there is a remainder as well.

How to Calculate Long Division?

The long division equation is

“Dividend = Divisor × Quotient + Remainder”.

How to Calculate Long division with Remainders?

Divide the number using the long division symbol or the long division bracket, then put 32, the divisor, on the outside of the bracket, and the dividend, 487, on the inside. Divide the number by the divisor, 32.

Short Method of Long Division

1. Start Simple

In the long division equation, there are many different parts, so make sure how to identify them.

long division

In the first step, introduce an equation that does not have a remainder.

It might be difficult to understand the concept of 2 times 4, so use the idea of sharing: If you want to share 4 objects between 2 people, how many objects do each person get?

After you have come to the correct answer, put 4 above 2, and then repeat the steps with the second digit.

2. Remainder in the Ones

First, see the problem with a remainder in the ones: how to do long division one step at a time. Now, begin working with the tens column: 5 goes into 5 only once, so there’s nothing left, but how many times does 5 go into 7, and how do you handle the leftovers?

See the new steps:

Divide the one’s column dividend by the divisor Multiply the divisor by the quotient in the right column

Subtract the product from the one column

To get the remainder, divide the one-column dividend by the divisor.

During this multiply the divisor by the quotient and add the remainder, the answer should be the same as the dividend they started with.

3. Remainder in the Tens

Where the divisor is impossible to fit neatly into either a tens or a one’s column. The steps are more or less the same, with one exception:

Divide the tens column dividend by the divisor and multiply the divisor by the quotient in the tens place column.

Subtract the product from the divisor, and then bring down the dividend in the one’s column.

To begin with, start with one-digit divisors and two-digit dividends to keep things simple, take the time to model the problems on the board, discuss why the steps work, and explain how place value plays an important role in how long division works.

4. Introduce Bigger Numbers, Gradually

The steps remain the same no matter how big the problem, is and help them “guess-and-check” multiplication as they go.

5. How to do Long Division with Decimals

Practice long division with large and small numbers, and keep reinforcing the connection between division and other mathematics that you’re learning.

However, the process is not yet complete – you still have to understand how to do long division with decimals. First, let’s get back to one of the fundamental principles of division: place value. However, this time you will move backward instead of forwards.

When you reach the step where you would normally stop with a remainder, have them place a decimal point at the end of the quotient and the divided, and add several zeros after the dividend.

Then you can continue with regular division steps to the nearest two digits, bringing the zeros down, and then you can connect the decimal to a fraction, and then finally convert the quotient, with the decimal, to an improper fraction. This should help you better understand fractions and place value, and can also be a good opportunity to cover fraction basics.

Examples of Long Division

Example 1:


3) 1641







Example 2: 


73) 5738





Example 3:







Example 4:







Example 5:








As part of our core principles, Cuemath helps children develop their ability to analyze and solve complex problems through reasoning. Another core principle is conceptual learning, where every math concept is introduced either through activities or pictorial models. Additionally, Cuemath teachers do not give away the answers. Want to try
then, visit website to book a free session and get the detailed explanation


Please enter your comment!
Please enter your name here