Important questions for rational Numbers Class 8 CBSE

Question 1
Write the additive inverse of each of the following:

1. 1
2. $\frac {-1}{9}$
3. $ \frac {-2}{3}$
4. 2
5. $\frac {-9}{1}$

Answer
(i) 1
Additive inverse = -1
(ii) $\frac {-1}{9}$
Additive inverse = $\frac {1}{9}$
(iii) $ \frac {-2}{3}$
Additive inverse = $\frac {2}{3}$
(iv)  2
Additive inverse =-2
(v) -9/1=-9
Additive inverse =9
Question 2
What is the additive identity?

1. 1
2. -1
3. 0
4. None of the above

Answer   0
Question 3 
True or False Statement

1. The difference of two rational number is a rational number
2. Addition of rational numbers is associative
3. Addition of rational numbers is commutative
4. Subtraction of rational numbers is not commutative
5. The addition or subtraction of two rational number is a rational number

Answer
All the statement are true
Question 4  
Find the multiplicative inverse of the following.

1. $ \frac {-11}{12}$
2. $ \frac {-10}{9}$
3. $ \frac {1}{2}$
4. $\frac {-5}{2} \times \frac {-2}{5}$
5. $\frac {-1}{2} \times \frac {-2}{5}$
6. - 4

Answer

1. $ \frac {-11}{12}$
   Multiplicative inverse =>$ \frac {-12}{11}$
   
2. $ \frac {-10}{9}$
   Multiplicative inverse =$ \frac {-9}{10}$
   
3. $ \frac {1}{2}$
   Multiplicative inverse =2
   
4. $\frac {-5}{2} \times \frac {-2}{5} =1$
   Multiplicative inverse =1
   
5. $\frac {-1}{2} \times \frac {-2}{5} = \frac {1}{5}$
   Multiplicative inverse =5
   
6. -4
   Multiplicative inverse =-1/4
   

Question 5
Which of these properties hold false for Multiplication of rational numbers?

1.  Associative law
2. Closure law
3. Commutative law
4. Existence of Multiplicative identity
5. None of the these

Answer
None of these
Question 6
Find the below multiplication

1. $ \frac {-1}{2} \times \frac {9}{10}$
2. $ \frac {-25}{9} \times \frac {1}{3}$
3. $\frac {7}{24} \times 10$

Answer

1. $ \frac {-1}{2} \times \frac {9}{10}$
   $=\frac { -1 \times 9}{2 \times 10} = \frac {-9}{20}$
2. $ \frac {-25}{9} \times \frac {1}{3}$
   $= \frac {-25 \times 1}{9 \times 3}= \frac {-25}{27}$
3. $\frac {7}{24} \times 10$
   $= \frac {7 \times 10}{24}= \frac {70}{24}$
   

Question 7
Find the following

1.  (1/2)^-1
2. (3)^-1
3. (-6)^-1
4. (1/-2)^-1

Answer

1. Multiplicative inverse of (1/2)   =2
2. Multiplicative inverse of (3)   =1/3
3. Multiplicative inverse of (-6)   =-1/6
4. Multiplicative inverse of (1/-2)   =-2

Question 8  
The product of two rational number is 2   , if one of the rational number is 1/7  ,what is the value of other?
Answer:
Let a   be the other number, then
$a \times \frac {1}{7} =2$
Or
$a= 2 \div \frac {1}{7}$
$a=2 \times 7=14$
Question 11
Fill in the blanks
(i)  ____   ÷  (-3)=  (-4/15)
(ii) The numbers __________ and __________ are their own reciprocals
(iii) The reciprocal of   1   is __________.
(iv)   (1/2)   ÷  (2/3)  =__________.
(v) The product of two rational numbers is always a __________.
(vi)  The reciprocal of a negative rational number is __________.

Answer:

1. 4/5
2. 1 and -1
3.  1
4. 3
5. Rational Number
6. Negative rational number

Question 12
Write five rational numbers which are smaller than 5

Answer:
  0,1,2,3,4
Question 13
Find five rational numbers between (1) and 2
Answer:
We can write as
$1= \frac {10}{10}$
$2= \frac {20}{10}$
So five rational numbers will be
11/10, 12/10, 13/10,14/10,15/10

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