RD Sharma Solutions Class 6 Maths Chapter 5 Negative Numbers and Integers

Exercise 5.1

Question 1:  Write the opposite of each of the following:

(i) Increase in population

(ii) Depositing money in a bank

(iii) Earning money

(iv) Going North

(v) Gaining a weight of 4kg

(vi) A loss of Rs. 1000

(vii) 25

(viii) – 15 

Solution 1:

(i) Decrease in population is the opposite of Increase in population.

(ii) Withdrawing money from a bank is the opposite of depositing money in a bank

(iii) Spending money is the opposite of earning money

(iv) Going south is the opposite of Going North.

(v) Losing a weight of 4kg is the opposite of gaining a weight of 4kg

(vi) A gain of Rs. 1000 is the opposite of A loss of Rs. 1000. 

(vii) – 25 is the opposite of 25.

(viii) 15 is the opposite of -15.

Question 2:  Indicate the following by using integers:

(i)  25° above zero.

(ii) 5° below zero.

(iii) A profit of Rs. 800.

(iv) A deposit of Rs. 2500.

(v) 3 km above sea level.

(vi) 2 km below level. 

Solution 2:

(i) +25°.

(ii) – 5°.

(iii) + Rs. 800.

(iv) + Rs. 2500.

(v) + 3.

(vi) – 2.

Question 3:  Mark the following integers on a number line:

(i) 7

(ii) -4

(iii) 0 

Solution 3:

Question 4:  Which number in each of the following pairs is smaller?

(i) 0, -4

(ii) -3 , 12

(iii) 8, 13

(iv) – 15, -27 

Solution 4:

Question 5:  Which number in each of the following pairs is larger?

(i) 3, -4

(ii) – 12, – 8

(iii) 0, 7

(iv) 12, – 18 

Solution 5:

Question 6:  Write all integers between:

(i) – 7 and 3

(ii) – 2 and 2

(iii) – 4 and 0

(iv) 0 and 3 

Solution 6:

(i) – 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2 is the integers between – 7 and 3.

(ii) -1, 0, 1 is the integers between – 2 and 2.

(iii) -3, -2, -1 is the integers between – 4 and 0.

(iv) 1, 2 is the integers between 0 and 3.

Question 7:  How many integers are between?

(i) – 4 and 3

(ii) 5 and 12

(iii) – 9 and – 2

(iv) 0 and 5

Solution 7:

(i) -3, -2, -1, 0, 1, 2 is the integers between – 4 and 3.

Hence, number of integers between – 4 and 3 are 6.

(ii) 6, 7, 8, 9, 10, 11 is the integers between 5 and 12.

Hence, number of integers between 5 and 12 are 6.

(iii) -8, -7, -6, -5, -4, -3 is the integers between – 9 and – 2.

Hence, number of integers between -9 and -2 are 6.

(iv) 1, 2, 3, 4 is the integers between 0 and 5 are

Hence, number of integers between 0 and 5 are 4.

Question 8:  Replace * in each of the following by < or > so that the statement is true:

(i) 2 * 5

(ii) 0 * 3

(iii) 0 * – 7

(iv) – 18 * 15

(v) – 235 * – 532

(vi) – 20 * 20 

Solution 8:

Question 9:  Write the following integers in increasing order:

(i) – 8, 5, 0, -12, 1, -9, 15

(ii) – 106, 107, – 320, – 7, 185 

Solution 9:

(i) The increasing order of given numbers is – 12 < – 9 < – 8 < 0 < 1 < 5 < 15. 

(ii) The increasing order of given numbers is -320 < – 106 < – 7 < 107 < 185.

Question 10:  Write the following integers in decreasing order:

(i) – 15, 0, -2, -9, 7, 6, -5, 8

(ii) -154, 123, -205, -89, -74 

Solution 10:

(i) The decreasing order of given numbers is 8 > 7 > 6 > 0 > -2 > -5 > -9 > -15. 

(ii) The decreasing order of given numbers is 123 > – 74 > – 89 > – 154 > – 205.

Question 11:  Using the number line, write the integer which is:

(i) 2 more than 3

(ii) 5 less than 3

(iii) 4 more than – 9 

Solution 11:

Question 12:  Write the absolute value of each of the following:

(i) 14

(ii) – 25

(iii) 0

(iv) – 125

(v) – 248

(vi) a – 7, if a is greater than 7

(vii) a – 7, if a – 2 is less than 7

(viii) a + 4, if a is greater than -4

(ix) a + 4 if a is less than – 4

(x) |-3|

(xi) -|-5|

(xii) |12 – 5|

Solution 12:

Question 13:  

(i) Write 4 negative integers less than – 10.

(ii) Write 6 negative integers just greater than – 12. 

Solution 13:

(i) – 11, – 12, – 13, – 14 are the 4 negative integers less than – 10. 

(ii) -11, – 10, – 9, – 8, – 7, – 6 are the 6 negative integers just greater than – 12.

Question 14:  Which of the following statements are true?

(i) The smallest integer is zero.

(ii) The opposite of zero is zero.

(iii) Zero is not an integer.

(iv) 0 is larger than every negative integer.

(v) The absolute value of an integer is greater than the integer.

(vi) A positive integer is greater than its opposite.

(vii) Every negative integer is less than every natural number.

(viii) 0 is the smallest positive integer.

Solution 14:

Exercise 5.2 

Question 1:  Draw a number line and represent each of the following on it:

(i) 5 + (-2)

(ii) (-9) + 4

(iii) (-3) + (-5)

(iv) 6 + (-6)

(v) (-1) + (-2) + 2

(vi) (-2) + 7 + (-9) 

Solution 1:

Question 2:  Find the sum of

(i) -557 and 488

(ii) -522 and -160

(iii) 2567 and – 325

(iv) -10025 and 139

(v) 2547 and -2548

(vi) 2884 and -2884 

Solution 2:

(i) – 557 and 488

= – 557 + 488 (we know that-,+,=,-)

= 557 – 488

= 69.

(ii) – 522 and – 160

= – 522 + (-160) (we know that +,-,=,-)

= – 522 – 160

= – 682

(iii) 2567 and – 325

= 2567 + (-325) (we know that  +,-,=,-)

= 2567 – 325

= 2242

(iv) -10025 and 139

= -10025 + 139 (we know that-,+,=,-)

= -10025 + 139

= -9886

(v) 2547 and -2548

= 2547 + (-2548) (we know that +,-,=,-)

= 2547 – 2548

= -1

(vi) 2884 and -2884

= 2884 + (-2884) (we know that +,-,=,-)

= 2884 – 2884

= 0

Exercise 5.3

Question 1:  Find the additive inverse of each of the following integers:

(i) 52

(ii) – 176

(iii) 0

(iv) 1 

Solution 1:

(i) – 52 is the additive inverse of 52.

(ii) 176 is the additive inverse of – 176.

(iii) 0 is the additive inverse of 0.

(iv) – 1 is the additive inverse of 1.

Solution 2:  Find the successor of each of the following integers:

(i) – 42

(ii) -1

(iii) 0

(iv) – 200

(v) -99 

Solution 2:

(i) For successor we should add 1 in each value.

Successor of – 42 is 

(ii) For successor we should add 1 in each value.

Successor of – 1 is 

(iii) For successor we should add 1 in each value.

Successor of 0 is 

(iv) For successor we should add 1 in each value.

Successor of – 200 is 

(v) For successor we should add 1 in each value.

Successor of – 99 is 

Question 3:  Find the predecessor of each of the following integers:

(i) 0

(ii) 1

(iii) – 1

(iv) – 125

(v) 1000 

Solution 3:

(i) For predecessor we should subtract 1 in each value.

Predecessor of 0 is

= 0 – 1

= – 1

(ii) For predecessor we should subtract 1 in each value.

Predecessor of 1 is

= 1 – 1

= 0

(iii) For predecessor we should subtract 1 in each value.

Predecessor of -1 is

= -1 – 1

= -2

(iv) For predecessor we should subtract 1 in each value.

Predecessor of – 125 is

= -125 – 1

= – 126

(v) For predecessor we should subtract 1 in each value.

Predecessor of 1000 is

= 1000 – 1

= 999

Question 4:  Which of the following statements are true?

(i) The sum of a number and its opposite is zero.

(ii) The sum of two negative integers is a positive integer.

(iii) The sum of a negative integer and a positive integer is always a negative integer.

(iv) The successor of – 1 is 1.

(v) The sum of three different integers can never be zero. 

Solution 4:

(i) True

Reason:- 1 – 1 = 0

(ii) False

Reason:- -1 – 1 = -2

(iii) False

Reason:- – 2 + 3 = 1

(iv) False

Reason:- Successor of – 1 is 0.

(v) False

Reason:- 1 + 2 – 3 = 0

Question 5:  Write all integers whose absolute values are less than 5. 

Solution 5:

-4, – 3, – 2, – 1, 0, 1, 2, 3, 4

Hence, above are the integers whose absolute values are less than 5:-

Question 6:   Which of the following is false:

(i) |4 + 2| = |4| + |2|

(ii) |2 – 4| = |2| + |4|

(iii) |4 – 2| = |4| – |2|

(iv) |(-2) + (-4)| = |-2| + |-4| 

Solution 6:

(i) True

Reason :-

|4+2|= |4|+|2

|6|=4+2

6  =  6

(ii) False

Reason :-

|2 - 4| = |2|+|4|

|-2| = 2+4

2 = 6 

(iii) True

Reason :- 

|4-2|= |4|-|2|

|2|=4 - 2

2  =  2

(iv) True

Reason :-

|(-2) + (-4)| = |-2| + |-4|

|-2-4| = 2 + 4

|-6| = 6

6 = 6

Question 7:  Complete the following table:

From the above table:

(i) Write all the pairs of integers whose sum is 0.

(ii) Is (-4) + (-2) = (-2) + (-4)?

(iii) Is 0 + (-6) = -6? 

Solution 7:

(i) (6, -6), (4, – 4), (2, – 2), (0, 0) are the pairs of integers whose sum is 0.

(ii) By using commutatively of addition

(-4) + (-2) = (-2) + (-4)

- 4 – 2 = - 2 – 4

- 6 = - 6

Hence, it is a correct statement.

(iii) By using additive identity

 0 + (-6)

= -6.

Question 8:  Find an integer x such that

(i) x + 1 = 0

(ii) x + 5 = 0

(iii) – 3 + x = 0

(iv) x + (-8) = 0

(v) 7 + x = 0

(vi) x + 0 = 0 

Solution 8:

(i) x + 1 = 0 (Subtracting 1 on both sides)

x + 1 – 1 = 0 – 1

x = -1

(ii) x + 5 = 0 (Subtracting 5 on both sides)

x + 5 – 5 = 0 – 5

x = -5

(iii) – 3 + x = 0 (Adding 3 on both sides)

-3 + x + 3 = 0 + 3

x = 3

(iv) x + (-8) = 0 (Adding 8 on both sides)

x – 8 + 8 = 0 + 8

x = 8

(v) 7 + x = 0 (Subtracting 7 on both sides)

7 + x – 7 = 0 – 7

x = – 7

(vi) x + 0 = 0

x = 0

Exercise 5.4

Question 1:  Subtract the first integer from the second in each of the following:

(i) 12, -5

(ii) – 12, 8

(iii) – 225, – 135

(iv) 1001, 101

(v) – 812, 3126

(vi) 7560, – 8

(vii) – 3978, – 4109

(viii) 0, – 1005 

Solution 1:

(i) 12, -5