Worksheet on properties of integer

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 

 

 

 

 

 

 

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