Page No.5.19, Negative Numbers And Integers, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

PAGE NO 5.19:

Question 4: If x is a positive integer, then
(a) x + |x| = 0
(b) x − |x| = 0  
(c) x + |x| = −2x    
(d) x = − |x|

ANSWER:

If x is positive integer, then |x| = x. So, x + |x| = x + x = 2x and x − |x| = x − x = 0.             Hence, the correct option is (b).

Question 5: If x is a negative integer, then
(a) x + |x| = 0              
(b) x − |x| = 0                    
(c) x + |x| = 2x                
(d) x − |x| = − 2x

ANSWER:

If x is negative integer, then |x| = −x. So
x + |x| = x − x = 0
x − |x| = x − (− x) = x + x = 2x
Hence, the correct option is (a).

Question 6: If x is greater than 2, then |2 − x| =
(a) 2 − x              
(b) x − 2                    
(c) 2 + x                
(d) − x − 2

ANSWER:

If a is negative integer, then |a| = − a.
Here, x is greater than 2. So, 2 − x is negative.
Therefore, |2 − x| = − (2 − x) = − 2 + x = x − 2.
Hence, the correct option is (b).

Question 7: 9 + |− 4| is equal to

(a) 5                        
(b) − 5                      
(c) 13                            
(d) −13

ANSWER:

Here, |− 4| = 4. Therefore
9 + |− 4| = 9 + 4 = 13
Hence, the correct option is (c).

Question 8: (− 35) + (− 32) is equal to
(a) 67                        
(b) − 67                      
(c) − 3                            
(d) 3

ANSWER:

(− 35) + (− 32) = − (35 + 32) = − 67
Hence, the correct option is (b).

Question 9: (− 29) + 5 is equal to
(a) 24                        
(b) 34                      
(c) − 34                            
(d) − 24

ANSWER:

(− 29) + 5 = − (29 − 5) = − 24
Thus, the correct option is (d).

Question 10: |− |− 7| − 3| is equal to

(a) − 7                      
(b) 7                              
(c) 10                                    
(d) − 10

ANSWER:

|− |− 7| − 3| = |− 7 − 3|    (∵ |− 7| = 7)
= |− 10|                                
= 10                (∵ |− 10| = 10)
Hence, the correct option is (c).

Question 11: The successor of − 22 is

(a) − 23                      
(b) − 21                              
(c) 23                                    
(d) 21

ANSWER:

If a is an integer, then its successor is a + 1. So
Successor of − 22 = − 22 + 1 = − (22 − 1) = − 21
Hence, the correct option is (b).

Question 12: If the sum of two integers is − 26 and one of them is 14, then the other integer is
(a) − 12                      
(b) 12                              
(c) − 40                              
(d) 40

ANSWER:

Sum of two integers = − 26
One of the two numbers = 14
∴ second number = − 26 − 14
= − (26 + 14)
= − 40
Hence, the correct option is (c).

Question 13: Which of the following pairs of integers have 5 as a difference?
(a) 10, 5                      
(b) − 10, − 5                          
(c) 15, − 20                              
(d) both (a) and (b)

ANSWER:

(a) 10 − 5 = 5
(b) (− 5) − (− 10) = − 5 + 10 = 5
(c) 15 − (− 20) = 15 + 20 = 35
Hence, the correct option is (d).

Question 14: If the product of two integers is 72 and one of them is − 9, then the other integers is

(a) − 8                      
(b) 8                          
(c) 81                              
(d) 63

ANSWER:

Product of integers = 72
One of the two integers = − 9
So, the other integer is 72 ÷÷ (− 9) = − 8.
Hence, the option is (a).

Question 15: On subtracting − 7 from − 14, we get
(a) − 12                      
(b) − 7                          
(c) −14                              
(d) 21

ANSWER:

Required number = − 14 − (− 7)
= − 14 + 7
= − (14 − 7)
= − 7
Hence, the correct option is (b).

Question 16: The largest number that divides 64 and 72 and leave the remainders 12 and 7 respectively, is
(a) 17                            
(b) 13                                      
(c) 14                                      
(d) 18

ANSWER:

Subtract 12 and 7 from 64 and 72 respectively.
64 − 12 = 52
72 − 7 = 65
The required number is the HCF of 52 and 65.
Now
52 = 4 ×× 13
65 = 5 ×× 13
∴ HCF 52 and 65 = 13
Therefore, the largest number that divides 64 and 72 and leave the remainder 12 and 7 respectively, is 13.
Hence, the correct option is (b).

Question 17: The sum of two integers is − 23. If one of them is 18, then the other is
(a) −14                            
(b) 14                                    
(c) 41                                    
(d) −41
ANSWER:

Sum of integers = − 23
One of the numbers = 18
Other number = (− 23) − (18)
= − 23 − 18
= − (23 + 18)
= − 41
Therefore, the other number is − 41.
Hence, the correct option is (d).

Question 18: The sum of two integers is − 35. If one of them is 40, then the other is
(a) 5
(b) − 75  
(c) 75            
(d) − 5
ANSWER:

Sum of integers = − 35
One of the numbers = 40
Other number = (− 35) − (40)
= − 35 − 40
= − (35 + 40)
= − 75
Therefore, the other number is − 75.
Hence, the correct option is (b).

Question 19:On subtracting − 5 from 0, we get

(a) − 5                             

(b) 5                                    

(c) 50                                    

(d) 0

ANSWER: Here, 0 − (− 5) = 0 + 5 = 5.
Therefore, on subtracting − 5 from 0, we get 5.
Hence, the correct option is (b).

Question 20: (− 16) + 14 − (− 13) is equal to

(a) − 11                             

(b) 12                                    

(c) 11                                    

(d) − 15
ANSWER: (− 16) + 14 − (− 13) = (− 16) + 14 + 13           (Additive inverse of − 13 is 13)

= (− 16) + 27

= 27 − 16

= 11

Hence, the correct option is (c).

ANSWER:

(− 2) ×× (− 3) ×× 6 ×× (− 1) = (2 ×× 3) ×× 6 ×× (− 1)
= 6 ×× 6 ×× (− 1)
= 36 ×× (− 1)
= − (36 ×× 1)
= − 36
Hence, the correct option is (b).

Question 22: 86 + (−28) + 12 + (−34) is equal to
(a) − 36                            
(b) 40                                
(c) 36                                    
(d) − 40

ANSWER:

86 + (−28) + 12 + (−34) = 86 + (−28) − (34 − 12)
= 86 + (−28) − 22
= (86 − 28) − (34 − 12)
= 58 − 22
= 36
Hence, the correct option is (c).

Question 23:(−12) ×× (−9) − 6 ×× (−8) is equal to

(a) 156                            
(b) 60                                
(c) −156                                    
(d) − 60

ANSWER:(−12) ×× (−9) − 6 ×× (−8) = (12 ×× 9) − 6 ×× (−8)

= 108 − 6 ×× (−8)

= 108 + 6 ×× 8

= 108 + 48

= 156

Hence, the correct option is (a).