Page No.5.18, Negative Numbers And Integers, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

PAGE NO 5.18:

Question 9: Calculate:
1 − 2 + 3 − 4 + 5 − 6 +......+ 15 − 16

ANSWER:1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10 + 11 − 12 + 13  − 14 + 15 − 16

= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16)

= 64 − 72

= −8

Question 10: Calculate the sum:
5 + (−5) + 5 (−5) + .....
(i) if the number of terms is 10.
(ii) if the number of terms is 11.

ANSWER:

(i) If the number of terms is 10, then 5 + (−5) + 5 + (−5) + 5 + (−5) + 5 + (−5) + 5 + (−5) = 0.
(ii) If the number of terms is 11, then 5 + (−5) + 5 + (−5) + 5 + (−5) + 5 + (−5) + 5 + (−5) + 5 = 5.

Question 11: Replace * by '<' or '>' in each of the following to make the statement true:
(i) (−6) + (−9) * (−6) − (−9)
(ii) (−12) − (−12) * (−12) + (−12)
(iii) (−20) − (−20) * 20 − (65)
(iv) 28 − (−10) * (−16) − (−76)

ANSWER:

(i) (−6) + (−9) = −15 < (−6) − (−9) = −6 + 9 = 3
(ii) (−12) − (−12) = −12 + 12 = 0 > (−12) + (−12) = −12 − 12 = −24
(iii) (−20) − (−20) = −20 + 20 = 0 > 20 − 65 = −45
(iv) 28 − (−10) = 28 + 10 = 38 < −16 − (−76) = −16 + 76 = 60

Question 12: If ∆ is an operation on integers such that a ∆ b = −a + b − (−2) for all integers a, b. Find the value of
(i) 4 ∆ 3
(ii) (−2) ∆ (−3)
(iii) 6 ∆ (−5)
(iv) (−5) ∆ 6

ANSWER:

(i) −4 + 3 − (−2)
= −4 + (3 + 2)
= −4 + 5
= 1
(ii) −(−2) + (−3) − (−2)
= (2 − 3) + 2
= −1 + 2
= 1
(iii) −6 + (−5) − (−2)
= −6 + (−5 + 2)
= −6 − 3
= −9
(iv) −(−5) + 6 − (−2)
= 5 + (6 + 2)
= 5 + 8
= 13

Question 13: If a and b are two integers such that a is predecessor of b. Find the value of a − b.

ANSWER: a and b are integers such that a is the predecessor of b, that is, a = b − 1.
∴ (a − b)
= (b − 1) − b
=  b − 1 − b
= −1 

Question 14: If a and b are two integers such that a  is the successor of b. Find the value of a − b.

ANSWER: a and b are two integers such that a is the successor of b, that is, a = b + 1.
∴ a − b
= b + 1 − b
= 1

Question 15:

Which of the following statements are true:
(i) −13 > −8 − (−2)
(ii) −4 + (−2) < 2.
(iii) The negative of a negative integer is positive.
(iv) If a and b are two integers such that  a > b, then a − b is always positive integer,
(v) The difference of two integers is an integer.
(vi) Additive inverse of a negative integer is negative.
(vii) Additive inverse of a positive integer is negative.
(viii)  Additive inverse of a negative is positive.

ANSWER:

(i) False; It should be −13 < −8 + 2 = −6.
(ii) True; −4 − 2 = −6 < 2
(iii) True; For example: −(−2) = 2
(iv) True; a > b
(v) True; For example: 3 − 2 = 1, which is a integer.
(vi) False; For example: −2 + 2 = 0. Here, 2 is the additive inverse of −2; it is positive.
(vii) True  
(viii) True

Question 16: Fill in the blanks:
(i) −7 + ...... = 0
(ii) 29 + ...... = 0
(iii) 132 + (−132) = ......
(iv) −14 + ....= 22
(v) −1256 + ..... = −742
(vi) ..... −1234 = −4539.

ANSWER:

(i) −7 + 7 = 0  (−a and a are the negative and additive inverses of each other.)
(ii) 29 + (−29) = 0  (−a and a are the negative and additive inverses of each other.)
(iii) 132 + (−132) = 0  (−a and a are the negative and additive inverses of each other.)
(iv) −14 + 36 = 22
(v) −1256 + 514 = −742
(vi) −3305 − 1234 = −4539

Question 1: Which of the following statement is true?
(a) − 7 > − 5              
(b) − 7 < − 5                
(c) (− 7) + (− 5) > 0                      
(d) (− 7) − (− 5) > 0

ANSWER:

(a)
On the number line, − 7 is to the left of − 5, so − 7 < − 5.
(c)
Here, (− 7) + (− 5) = − ( 7 + 5) = − 12.
On the number line, − 12 is to the left of 0, so (− 7) + (− 5) < 0.
(d)
Here, (− 7) − (− 5) = (− 7) + (additive inverse of − 5) = (− 7) + (5) = − (7 − 5) = − 2
On the number line, − 2 is to the left of 0, so (− 7) − (− 5) < 0.
Hence, the correct option is (b).

Question 2: 5 less than − 2 is
(a) 3      
(b) − 3  
(c) − 7    
(d) 7

ANSWER:

Here, 5 less than − 2 = (− 2) − (5) = − 2 − 5 = − 7.
Hence, the correct option is (c).

Question 3: 6 more than − 7 is
(a) 1                            
(b) − 1                        
(c) 13                                
(d) − 13

ANSWER:

6 more than − 7 = (− 7) + 6
= − ( 7 − 6)
= − 1
Hence, the correct option is (b).