NCERT Solutions for Class 6 Maths Chapter 2 Exercise 2.2

Class VI Mathematics NCERT textbook Ex. 2.2 of chapter 2 Whole Numbers in PDF file format free to download or use online without any login or password. All the Maths solution is updated for CBSE current academic session providing the best way to solve the questions. Class 6 Maths NCERT solutions are useful for the students studying in state board also.

We know that subtraction is the inverse process of addition. It means that subtracting 13 from 27 is the same as finding a whole number which when added to 13 gives 27.
Thus, 27 – 13 = ….is the same as …… + 13 = 27
i.e., 27 – 13 = 14 is the same as 14 + 13 = 27
Similarly, 33 – 16 = 17 is the same as 17 + 16 = 33.
Let us see what happens when we subtract 38 from 25. Can you find a whole number which when added to 38 gives 25? No.
Thus, we cannot subtract a greater whole number from a smaller whole number.

If we subtract two equal whole numbers, we get the whole number 0.
Examples: 5 – 5 = 0, 9 – 9 = 0, 14 – 14 = 0, etc.
Again, if we subtract a smaller whole number from a larger one, the result is clearly a whole number. Examples: 9 – 7 = 2, 10 – 6 = 4, 19 – 16 = 3, etc.
But, what happens if we subtract 14 from 7?
Clearly, there is no whole number which when added to 14, gives 7.
So, (7 – 14) is not a whole number.

If a and b are two whole numbers such that a > b or a = b then a – b is a whole number, otherwise subtraction is not possible in whole numbers.

Let us now examine whether the property 2 of addition holds good for subtraction.
We know that 9 – 3 = 6 but 3 – 9 is not possible in whole numbers.
Again, 18 – 5 = 13 but 13 – 18 is not possible in whole numbers.

If a and b are two whole numbers then, in general, a – b is not equal to b – a.

Let us see whether the property 3 of addition holds good for subtraction.
We know that, 3 – 0 = 3 but 0 – 3 is not defined in whole numbers; 9 – 0 = 9 but 0 – 9 is not defined in whole numbers.

If a is any whole number, then a – 0 = a but 0 – a is not defined in whole numbers.

Let us now examine whether the property 4 of addition holds good for subtraction.
Take three numbers, say 5, 2, 1.
We have, (5 – 2) – 1 = 3 – 1 = 2 and 5 – (2 – 1) = 5 – 1 = 4. Thus, (5 – 2) – 1 is not equal to 5 – (2 – 1).
This shows that the associative law is not applicable to subtraction on whole numbers.

If a, b, c are three whole numbers then, in general, (a – b) – c is not equal to a – (b – c).

We know that multiplication is a repeated addition. Instead of adding the same number many times, we multiply it by the number equal to the number of times it is added. For example, if we have to add 4 six times. We add like this: 4 + 4 + 4 + 4 + 4 + 4 = 24. This may be written as 4 × 6 = 24, which is read as 4 taken 6 times is equal to 24 or 4 multiplied by 6 is 24. If the numbers to be multiplied are small, we can perform the operation mentally and find the product. But if the numbers are large we use the multiplication tables to find the product as you have learnt in the earlier classes.

Let us take a few pairs of whole numbers and check in each case whether their product is a whole number.

What do we conclude?
We conclude that if we multiply two whole numbers, the product is also a whole number.
So, we have the following property, called the closure property of multiplication.