RD Sharma Solutions -Page No.5.11, Negative Numbers And Integers, Class 6, Maths Class 6 Notes | EduRev

RD Sharma Solutions for Class 6 Mathematics

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Class 6 : RD Sharma Solutions -Page No.5.11, Negative Numbers And Integers, Class 6, Maths Class 6 Notes | EduRev

The document RD Sharma Solutions -Page No.5.11, Negative Numbers And Integers, Class 6, Maths Class 6 Notes | EduRev is a part of the Class 6 Course RD Sharma Solutions for Class 6 Mathematics.
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PAGE NO 5.11:


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

ANSWER: For the integer a, a + 1 will be its successor.
(i) −41 is the successor of −42.
(ii) 0 is the successor of −1.
(iii) 1 is the successor of 0.
(iv) −199 is the successor of 200.
(v) −98 is the successor of −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:

Write all integers whose absolute values are less than 5.
ANSWER:
Let x be an integer such that |x| < 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|

ANSWER:
(i) |4|+ |2| = 6 = |4| + |2|; True
(ii) |2 − 4| = |−2| = 2 ≠ 2 + 4 = 6; False
(iii) |4 − 2| = 2 = |4| − |2|; True
(iv) |(−2) + (−4)| = |−6| = 6 = |−2| + |(−4)|; True

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