Question

How many whole numbers are there between $ 1032{\text{ and 1209}} $ ?

Answer 1

Hint:
We have two numbers and we need to find the total whole numbers that lie between the given two numbers. So if we have two whole numbers $ a{\text{ and }}b $ and suppose that $ b > a $ then the whole numbers between them are $ (b - a) - 1 $ .

Complete step by step solution:
Here we are given the two whole numbers. All the non-negative integers are called the whole numbers. So we can say that whole numbers are $ 0,1,2,3,4,...........\infty $
Here also we are given the two whole numbers $ 1032{\text{ and 1209}} $ and we need to find the total number of whole numbers that lie between the given two numbers. So we can understand it clearly by the example. Most of the students would simply subtract the two numbers and get the number of whole numbers between them. But this is the wrong way. For example: If we consider two whole numbers $ 3{\text{ and 7}} $ we know that there are whole numbers $ 4,5,6 $ that lie between the two whole numbers. So we can say there are three whole numbers between them. If we subtract the two values which means smaller from the larger value we will get:
Difference $ 7 - 3 = 4 $ which is not equal to $ 3 $
Hence we can say that the total number of whole numbers that lie between the two whole numbers is one less than the difference between the two whole numbers.
So if we have two whole numbers $ a{\text{ and }}b $ and suppose that $ b > a $ then the number of whole numbers between them are $ (b - a) - 1 $
Now we have two whole numbers $ 1032{\text{ and 1209}} $
So we can say the total number of whole numbers that lie between them will be one less than the difference between the given two numbers. We must take care that the subtraction is done from the larger to the smaller number because the number of whole numbers cannot be negative.
So total number of whole numbers between them $ = 1209 - 1032 - 1 = 176 $

So there are $ 176 $ whole numbers between $ 1032{\text{ and 1209}} $ .

Note:
Here the student must know that the subtraction will only be done from the larger whole number and the number of whole numbers will not be the difference between the two whole numbers but will be one less than that difference.