Class 7 Maths Chapter 1 Integers Exercise 1.2 pdf notes:-

**Exercise 1.2** Class 7 maths Chapter 1 Pdf Notes:-

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## Ncert Solution for Class 6 Maths Chapter 1 Integers Exercise 1.2 Tips:-

**Introduction:-**

**Closure under Addition**

We have learnt that sum of two whole numbers is again a whole number. For example,

17 + 24 = 41 which is again a whole number. We know that, this property is known as the

closure property for addition of the whole numbers.

**Commutative Property**

We know that 3 + 5 = 5 + 3 = 8, that is, the whole numbers can be added in any order. In

other words, addition is commutative for whole numbers.

Can we say the same for integers also?

We have 5 + (ā 6) = ā1 and (ā 6) + 5 = ā1

So, 5 + (ā 6) = (ā 6) + 5

Are the following equal?

(i) (ā 8) + (ā 9) and (ā 9) + (ā 8)

(ii) (ā 23) + 32 and 32 + (ā 23)

(iii) (ā 45) + 0 and 0 + (ā 45)

Try this with five other pairs of integers. Do you find any pair of integers for which the

sums are different when the order is changed? Certainly not. We say that addition is

commutative for integers.

In general, for any two integers a and b, we can say

a + b = b + a

ļ¬ We know that subtraction is not commutative for whole numbers. Is it commutative

for integers?

Consider the integers 5 and (ā3).

Is 5 ā (ā3) the same as (ā3) ā5? No, because 5 ā ( ā3) = 5 + 3 = 8, and (ā3) ā 5

= ā 3 ā 5 = ā 8.

Take atleast five different pairs of integers and check this.

We conclude that subtraction is not commutative for integers.

1.3.4 Associative Property

Observe the following examples:

Consider the integers ā3, ā2 and ā5.

Look at (ā5) + [(ā3) + (ā2)] and [(ā5) + (ā3)] + (ā2).

In the first sum (ā3) and (ā2) are grouped together and in the second (ā5) and (ā3)

are grouped together. We will check whether we get different results.

TRY THESE

In both the cases, we get ā10.

i.e., (ā5) + [(ā3) + (ā2)] = [(ā5) + (ā2)] + (ā3)

Similarly consider ā3 , 1 and ā7.

( ā3) + [1 + (ā7)] = ā3 + ** _** =

*_*[(ā3) + 1] + (ā7) = ā2 +

**=***_**_*Is (ā3) + [1 + (ā7)] same as [(ā3) + 1] + (ā7)?

Take five more such examples. You will not find any example for which the sums are

different. Addition is associative for integers.

In general for any integers a, b and c, we can say

a + (b + c) = (a + b) + c

1.3.5 Additive Identity

When we add zero to any whole number, we get the same whole number. Zero is an

additive identity for whole numbers. Is it an additive identity again for integers also?

Observe the following and fill in the blanks:

(i) (ā 8) + 0 = ā 8 (ii) 0 + (ā 8) = ā 8

(iii) (ā23) + 0 =

*_ (iv) 0 + (ā37) = ā37 (v) 0 + (ā59) = (vi) 0 + = ā 43*

(vii) ā 61 + = ā 61 (viii) + 0 = _(vii) ā 61 + = ā 61 (viii) + 0 = _

The above examples show that zero is an additive identity for integers.

You can verify it by adding zero to any other five integers.

In general, for any integer a

a + 0 = a = 0 + a

- Write a pair of integers whose sum gives

(a) a negative integer (b) zero

(c) an integer smaller than both the integers. (d) an integer smaller than only one of the integers.

(e) an integer greater than both the integers. - Write a pair of integers whose difference gives

(a) a negative integer. (b) zero.

(c) an integer smaller than both the integers. (d) an integer greater than only one of the integers.

(e) an integer greater than both the integers