CBSE Class VIII MATHS - Chapter 1 - Rational Numbers - Chapter Test - Answers

Rational Numbers Question Answers Test-1

Subjective Test

Question 1 ( 1.0 marks)
Are rational numbers closed under division? Give reasons in support of your answer.

Solution:
No, rational numbers are not closed under division.
This is because if we consider a rational number a (a ≠ 0)and the rational number 0, then
a ÷ 0 is not a rational number (since it is not defined).

Question 2 ( 1.0 marks)

Fill in the blanks:

(a) The reciprocal of the rational number a/b,(a,b ≠ 0) is __________. (1/2 mark)
(b) The rational number __________ has no multiplicative inverse. (1/2 mark)

Solution:
(a) The reciprocal of the rational number a/b,(a,b ≠ 0) is b/a.
(b) The rational number _____0_____ has no multiplicative inverse.

Question 3 ( 1.0 marks)


Isthe multiplicative inverse of 0.71? Give reason in support of your answer.


Solution:

Consider

Thus,is not the multiplicative inverse of 0.71.

Question 4 ( 1.0 marks)
Name the property under multiplication used in the expression.

Solution:
Under associative property of multiplication of rational numbers,

(a × b) × c = a × (b × c), where a, b, and c are any three rational numbers
Thus, in the expression, the associative property under multiplication has been used.

Question 5 ( 1.0 marks)
Using property of multiplication, find the value of the expression.

Solution:
Using commutative property of multiplication, the given expression can be simplified as:

Question 6 ( 2.0 marks)
(a) Define a rational number. (1 mark)
(b) Are rational numbers closed under subtraction? Give reasons. (1 mark)

Solution:
(a) A rational number is a number which can be written in the form p/q, where p and q are integers, q ≠ 0.
Example,

(b) Yes, rational numbers are closed under subtraction because when we subtract any rational number from a rational number, the result is again a rational number.

Question 7 ( 2.0 marks)
Find the additive inverse of the multiplicative inverse of the expression.

Solution:
The expression can be simplified as:

Multiplicative inverse of 
Additive inverse of 

Thus, the required number is -1/6.

Question 8 ( 3.0 marks)
Find seven rational numbers between −1 and 1 and represent them on the number line.

Solution:

Rational numbers between −1 and 1 are.
These numbers can now be represented on number line as:

Question 9 ( 3.0 marks)

(a) State distributive property of multiplication over addition and subtraction for rational numbers. (1 mark)
(b) Using the property under multiplication, simplify the expression. (2 marks)

Solution:
(a) Distributive property of multiplication over addition and subtraction states that for all rational numbers a, b, and c,

(b)
[Commutative property of multiplication]
[Distributivity of multiplication under subtraction]

Question 10 ( 6.0 marks)
(a) Find eight rational numbers between -7/5 and 3/4. (2 marks)
(b) Find four rational numbers between 1/9 and 1/3. (2 marks)
(c) How many rational numbers are there between 3 and 4? Write any two of them. (2 marks)
Solution:
∴ Eight rational numbers lying between -7/5 and 3/4 are ,.
(b) Mean of 1/9 and 

Mean of 1/9 and 2/9

Mean ofand

From (1), (2), (3), we obtain

Mean ofand

Thus,[Using (4) and (5)]
Hence, four rational numbers between 1/9 and 1/3 are 1/6, 2/9, 1/4, 5/18.
(c) We know that there are infinite numbers of rational numbers between any two rational numbers.
Hence, there are infinite number of rational numbers between 3 and 4.

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