Page No.5.11, Negative Numbers And Integers, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

Question 1: Find the additive inverse of each of the following integers:
(i) 52
(ii) −176
(iii) 0
(iv) 1
ANSWER: THE ADDITIVE INVERSE OF THE NUMBER A  IS THE NUMBER ADDED TO A,  YIELDS ZERO.  SO, WE FIND THE FOLLOWING:

(i) 52 + (−52) = 0Here, −52 is the additive inverse of 52.

(ii) (−176) + 176 = 0Here, 176 is the additive inverse of −176.

(iii) 0 + 0 = 0Here, 0 itself is its inverse.

(iv) 1 + (−1) = 0Here, −1 is the additive inverse of 1.

Question 2:

Find the successor of each of the following integers:
(i) −42
(ii) −1
(iii) 0
(iv) −200
(v) −99

Question 3:

Find the predecessor of each of the following integers:
(i) 0
(ii) 1
(iii) −1
(iv) −125
(v) 1000

ANSWER:

For the integer a, the predecessor is (a − 1).
(i)  −1 is the predecessor of 0.
(ii) 0 is the predecessor of  1.
(iii) −2 is the predecessor of −1.
(iv) −126 is the predecessor of −125.
(v) 999 is the predecessor of 1000

Question 4:

Which of the following statements are true?
(i) The sum of a number and its opposite zero.
(ii) The sum of two negative integer is 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.

ANSWER:

(i) True − It is the definition of additive inverse; for example, 5 + (−5) = 0.
(ii) False − For example, −2 − 3 = −5; it is a negative integer.
(iii) False − −3 +  5 = 2; it is a positive integer.
(iv) False − 0 is the successor of −1.
(v) False − It can be zero like (−2) + (−1) + (3).

Question 5:

∴ -5 < x < 5

=> x = ] -4, 4 [

These are the nine integers whose absolute values are less than 5, namely, -4, -3, -2, -1, 0, 1, 2, 3 and 4.

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|