### Theory:

Suppose you want to find the difference between two numbers.

Let us calculate the difference of \(8\) and \(3\).

That is \(8 - 3 = 5\).

This is a simple subtraction method. It gives the difference between the two numbers.

But now, we have to find the numbers between any two whole number.

Let's take a look at that method with an example.

James and Ranvir standing in a straight line at a school prayer. But a few students are standing between them. James was standing first in the line and Ranvir was standing as the sixth person.

Now tell me how many students are standing between Ranvir and James?

If we calculate it as the position of Ranvir minus the position of James, we get \(6 - 1= 5\).

Is this a correct way to calculate the numbers between the two numbers?

If you're thinking the above calculation is wrong, you're correct.

This is not the correct way to calculate the numbers between two whole numbers.

So what is the right way? Now we will take a look at that method.

**Steps to find the numbers between any two whole numbers:**

1. Subtract the two given numbers.

2. Subtract \(1\) from the obtained difference.

3. The number obtained after subtracting \(1\) is the actual numbers lying between the two given numbers.

2. Subtract \(1\) from the obtained difference.

3. The number obtained after subtracting \(1\) is the actual numbers lying between the two given numbers.

Important!

The numbers between \(x\) and \(y\) \(= x - y - 1\) if \(x > y\).

Where \(x\) and \(y\) are whole numbers.

Example:

1. Let us find the solution for the example discussed above.

James was standing first in the line and Ranvir was standing as the sixth person. We have to find how many students are standing between Ranvir and James?

Let us apply the steps to solve this problem.

Subtracting the two position, \(6-1 = 5\).

Now subtract \(1\) from the obtained difference.

That is, \(5-1 = 4\).

Thus, there are \(4\) standing between James and Ranvir.

2. Take \(8\) pencils and arrange it in a straight line. Now find how many pencils are there between the \(7th\) pencil and \(2nd\) pencil?

Let us apply the steps to solve this problem.

First, find the difference of \(7th\) pencil and \(2nd\) pencil. That is \(7 - 2= 5\).

Next, subtract this number by \(1\) then we get the number of pencils between \(7th\) and \(2nd\) pencil.

That is \(5 -1 = 4\). Therefore, there are \(4\) pencils between \(7th\) and \(2nd\) pencil.

Reference:

Image credits: https://commons.wikimedia.org/wiki/File:School_Assembly.jpg