How to Do Long Division? A Step-by-Step Guide

At first glance, long division looks quite tricky and complicated, especially for a primary school student. However, this article will show how easy it really is for anyone to do long division. Knowing how to do long division is an extremely important maths skill to have in your toolbox, because it is used in almost every type of maths as you progress through school. This article goes through what long division is, the parts and terms of long division, how to properly do long division, and it will even show you a few examples of long division questions. Learn how to do long division here!

What is Long Division?

Long division is a method to divide big numbers, breaking down large numbers into much smaller numbers in a sequential fashion. Long division also serves as one of the ways we use our four basic mathematical operations in primary school (addition, subtraction and multiplication being the others).

The process of long division can be done in just a few short steps. Let’s learn these steps in this article, along with a few easy examples to help get you started to make long division as easy as possible, whether you’re working with 2 digits, or 2000 digits.

Elements of Long Division

There are four major elements you need to do long division. They are as follows:

Dividend – The number that you want to divide into.

Divisor – The number you want to divide by.

Quotient – The answer of the long division problem. Sometimes this word is also a synonym for division (For example, the quotient of 30 and 6 is 5).

Remainder – How much is left over if the divisor does not perfectly go in the dividend.

Below is an example of all four terms in practice.

For a lot of long division exercises, the dividend is generally bigger than the divisor. If the divisor is bigger than the dividend, then you’ve got yourself a fraction. 

If you can understand these four terms, then long division becomes a lot easier to handle.

Long Division Step-By-Step

If your child is more of a visual learner, then this visual step-by-step chart below could help.

STEP 1: We work from left to right in long division. So, the first thing to do is to look at the first digit of the dividend. If we can, let’s ask ourselves ‘How many times does the divisor go into the digit of the dividend’? 

STEP 2: Write the quotient (result of the previous step) at the top of your sum. 

STEP 3: Multiply the new digit with the divisor.

STEP 4: Once we have the answer at the top, we need to subtract (take away) the new quotient digit with the multiple of the digit’s dividend we were looking at.

STEP 5: And so, after this process we just went through with the first digit, we move onto the next digit on the right. We bring that number down next to the subtracted answer. 

STEP 6: Repeat steps 1-5 until you run out of numbers in the dividend. Once every number of the dividend has been completed, you will have come to your long division answer!

STEP 7: Check your answer. To check your answer, remember:

Dividend = Divisor x Quotient + Remainder

Visual Guide: 

STEP 1: Divide the digits first.

4 goes into 6 once, with some remainder. 

(6 ÷ 4 = 1) 

We can now write 1 above the 6.

STEP 2: Write the quotient at the top. 

Remember to put the quotient above the correct digit!

STEP 3: Multiply the result with the divisor.

1 x 4 is 4

STEP 4: Subtract! 

6 – 4 is 2, so the remainder is 2.

STEP 5: Bring the next column down.

We bring down the 8 next to the 2, so it becomes 28

STEP 6: Repeat previous steps until result. 

We’ve finished with the left column, so it’s time to work with the right column.

STEP 7: Check your answer!

68 = 4 x 17

It’s always important to check.

Long Division Examples

 1. 935 ÷ 5:

So, 935 ÷ 5 is 187.

Now, what happens when you divide numbers that don’t go evenly into each other. In other words, what happens when you have a remainder? In this same example, let’s also take a look where the first digit of the dividend is smaller than the divisor, and where the divisor has two digits.

2. 203 ÷ 15

If we were to look at the first digit of the dividend (203), we can see that 15 cannot go into 2. In this case, we now must look at both the first and second digits. Here, 15 can now go into 20.

Sometimes, there will be worded questions you can solve by using long division. Let’s try one.

3. Simon grew 393 oranges on his farm this year. He wants to sell those oranges to three buyers, who all get the same number of oranges. How many oranges does each buyer get?

The dividend will be 393, and the divisor will be 3. So, the problem we need to look at is 393÷3.

So, each buyer gets 131 oranges from Simon.


Learning Long Division Can Be Simple!

So, there you have it. Long division is a lot less tricky than it looks, but with these simple steps, anybody can do long division easily!

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