Q.1 Fill in the blanks and write the name of the property used in each case

(i) -16+(-5) = -5 +—

(ii) -561 + —=-561

(iii) -18+(-4)=—

Q.2 For a=-12 and ,b=4 and c =-25 find whether

(i) a and b are closed under addition

(ii) a+b=b+a

(iii) a-b=b-a

Q.3 Find a pair of integers whose

(a) Sum is -9

(b) Difference is -16

(c) Sum is -100

Q.4 Find a negative integer and a positive integer whose sum is -10 .

Q.5 The sum of two integers is -156 .If one of the integers is -283 ,find the other

Q.6 The difference of two integers is -63 .If one of the integers is 105 ,find the other

Answer key

Problem : 01

Fill in the blanks and write the name of the property used in each case

(i) -16+(-5) = -5 +—

(ii) -561 + —=-561

(iii) -18+(-4)=—

Solution:

(i) -16+(-5) = -5 +—

Add the LHS of the equation

-16+(-5)=-21

For RHS ,look for a number which when added with -5 give -21 as result

Let the required number is X

∴ -5+X=-21

X=-21+5

X=-16

Thus ,required number is -16

Then ,given equation can be written as

-16+(-5) = -5 +(-16)

The property this equation satisfies is Commutative property

(ii) -561 + —=-561

Note: When addition of two number is same as one of given number ,then other number must be zero

In the given problem

-561 + —=-561

It is only possible when — replace with 0 .There is no other number which can satisfy this situation

These types of problem are example of Existence of Additive Identity

(iii) -18+(-4)=—

Add these integers

-18+(-4)=-22 which is also a integer

Thus ,It is closed under addition

Problem: 02

For a=-12 and ,b=4 and c =-25 find whether

(i) a and b are closed under addition

(ii) a+b=b+a

(iii) a-b=b-a

Solution:

(i) For a and b are closed under addition , sum of a and b should be a integer

a+b=-12+4=-8 which is also a integer

Hence , a and b are closed under addition

(ii) a+b=b+a

a+b=-12+4=-8

b+a=4+(-12)=-8

∴ a+b=b+a

(iii) a-b=b-a

a-b=(-12)-4=-16

b-a=4-(-12)=16

So, a-b≠b-a

Problem: 03

Find a pair of integers whose

(a) Sum is -9

(b) Difference is -16

(c) Sum is -100

(d) Sum is 0

Solution:

(i) Pair whose sum is -9 are (-3 ,-6) ,(-5,-4) ,(-2,-7) etc

(ii) Pair whose difference is -16 are (-20,-4 ) ,( -25,-9) etc

(iii) Pair whose sum is -100 are (-80,-20) ,(-120,20) ,(-50,-50) etc

(iv) Pair whose sum is 0 are (-5,5) ,(-8,8) ,(-5,5) etc

Problem: 04

Find a negative integer and a positive integer whose sum is -10 .

Solution:

A negative integer=-15

A positive integer =5

Adding these integers ,we get -15+5=-10

Let’s take another pair

A negative integer=-12

A positive integer =2

Adding these integers ,we also get -12+2=-10

In this way ,we can find lot of pairs whose sum is -10

Problem: 05

The sum of two integers is -156 .If one of the integers is -283 ,find the other

Solution:

Given:

Sum of two integers is -156

One integer is -283

Let another required integer is X

∴ -283+X=-156

X=-156+283

X= 127

So, required integer is 127