How to Divide Large Numbers Long Division & Alternative Methods

How to Divide Large Numbers Long Division & Alternative Methods

Before we begin:

The length of the division is not what's important, If you know the steps of division well, having an extra three digits in the dividend will only slightly delay you, but you will find the result. The important thing is to understand the logic of division well.

Example 1:

There's no 26 in 11, so I need to check how many 26 are there in 117.

Determining this might be easier if you round the numbers. Don't immediately say that you don't know what rounding is or the rules of rounding, you don't necessarily have to stick to the rules.
Just think of a number that is closer to the original but allows for easier calculations, a smoother number. For example, if our number is 126, you could consider it as 130.

If we take 26 as 30, we can consider 117 as 120 as well.

The quotient should be approximately 4, it could be 3, it could be 4, it could even be 5.

Let's give 4 and see how close we get to the result.

So, we need to give 4.

26 is found 4 times in 117. So, where should we write the 4? Above the left-hand 1 ? Above the middle 1 , or above the 7 ? 

The short answer is we need to write it above the smallest digit, which is 7 in 117, so it goes above the 7. But why is it so?

I am multiplying 26 by 4 and subtracting it from 117.

I am bringing down the 0. Now, I need to look at how many times 26 is in 130.

26 fits exactly 5 times into 130. We've done this before, if you've forgotten you can try it by rounding.

Result is 45, There's no remainder.

Example 2

Let's divide 29 110 by 142

How many times does 142 fit into 291 ? You can round the numbers to make an estimate.

We can consider 142 as 140 and 291 as 290.

140+140 = 280, so 2 times!

I am writing 2 over 1 to the quotient.

Multiplying 2 by 142 and subtracting the result from 291.

I am bringing down the 2 next to the 1, our number becomes 71.

How many times is 142 in 71? None! Therefore, I am writing 0 in the quotient.

I am bringing down the 0. Now, I need to ask how many times 142 is in 710.

it is 5 times! 

I am writing 5 over the 0.

I am multiplying 5 by 142 and subtracting the result from 710, the result is 0. I have no remainder.

Alternative Methods

We need to find how many times 26 is in 1170. 

I call this method the 'bite method,' we proceed piece by piece until the entire number is divided.

10 times 26 equals 260. This is a bit too little.  100 times 26 equals 2600, which is quite a lot more than 1170. 
Why am I trying to estimate with 10, 100, or 1000? Because multiplying by 10, 100, 1000 is very simple..

"Think of it as each time I'm eating a number that's ten times a 26, until I have no number left. To speed up the process, you can try 20 times, 30 times, 50 times, etc. instead of 10 times, Of course, if your numbers are suitable..

We might be able to speed up the process like this;

Another example

Let's divide 29 110 by 142

First, read the number to be divided and imagine how large a number it is in your mind.

Let's start by taking bites as multiples of 10, 100, or 1000 of the divisor, whichever makes sense, and repeat this.