RBSE Class 8 Maths Important Questions Chapter 1 Rational Numbers

Rajasthan Board RBSE Class 8 Maths Important Questions Chapter 1 Rational Numbers Important Questions and Answers.

RBSE Class 8 Maths Chapter 1 Important Questions Rational Numbers

Multiple Choice Questions:

Question 1.
Rational numbers are closed for
(a) addition and multiplication
(b) addition and subtraction
(c) addition, subtraction and multiplication
(c) none of these
Answer:
(c) addition, subtraction and multiplication

Question 2.
Rational numbers are not associative for:
(a) addition
(b) multiplication
(c) both (a) and (b)
(d) division
Answer:
(d) division

Question 3.
Additive inverse of $\frac{a}{b}$ is 
(a) $\frac{a}{b}$
(b) $-\frac{a}{b}$
(c) $\frac{b}{a}$
(d) a × b
Answer:
(b) $-\frac{a}{b}$

Question 4.
Which property of multiplication is illustrated by $\left(\frac{-11}{5}\right) \times\left(\frac{-3}{7}\right)=\left(\frac{-3}{7}\right) \times\left(\frac{-11}{15}\right)$
(a) Commutative
(b) Inverse
(c) Associative
(d) None of these
Answer:
(a) Commutative

Question 5.
What is the multiplicative inverse of ?
(a) $-\frac{8}{21}$
(b) 1
(c) 0
(d) $\frac{21}{8}$
Answer:
(d) $\frac{21}{8}$

Question 6.
Give one rational number between $\frac{1}{4}$ and $\frac{1}{2}$
(a) $\frac{3}{4}$
(b) 1
(c) $\frac{3}{8}$
(d) $\frac{1}{8}$
Answer:
(c) $\frac{3}{8}$

Fill in the blanks:

Question 1.
Rational numbers are __________ under subtraction.
Answer:
closed

Question 2.
The rational number __________ is the additive identity for rational numbers.
Answer:
zero

Question 3.
$\frac{3}{8}$ × ______ = 1 × $\frac{3}{8}=\frac{3}{8}$
Answer:
1

Question 4.
__________ can be represented on a number line.
Answer:
rational numbers

Question 5.
Between any two rational numbers there are rational numbers.
Answer:
countless.

Very Short Answer Type Questions:

Question 1.
Define rational numbers.
Answer:
Rational number is the quotient of two integers such that the denominator is a non-zero inter, i.e. Rational number = $\frac{p}{q}$ where p and q are integers and q ≠ 0

Question 2.
What is the multiplicative identity for rational numbers?
Answer:
1

Question 3.
Find $\frac{-2}{3} \times \frac{4}{5}$.
Answer:
$\left(\frac{-2}{3}\right) \times\left(\frac{4}{5}\right)=\frac{-8}{15}$
 
Question 4.
Write the additive inverse of $-\frac{7}{19}$ and varify.
Answer:
$-\frac{7}{19}$ additive inverse of $\frac{7}{19}$.
Verification : $\frac{-7}{19}+\frac{7}{19}=\frac{-7+7}{19}=\frac{0}{19}$ = 0

Question 5.
Find the mean of $\frac{3}{8}$ and $\frac{1}{2}$
Answer:
$\left(\frac{3}{8}+\frac{1}{2}\right) \div 2=\left(\frac{3+4}{8}\right) \div 2=\frac{7}{8} \times \frac{1}{2}=\frac{7}{16}$

Question 6.
Is 0.6 is multiplicative inverse of 1$\frac{2}{3}$? Why or why not?
Answer:
Yes, 0.6 is multiplicative of 1$\frac{2}{3}$
Because 0.6 × 1$\frac{2}{3}=\frac{6}{10} \times \frac{5}{3}=\frac{30}{30}$ = 1

Short Answer Type Questions:

Question 1.
Find the rational number between $\frac{1}{4}$ and $\frac{1}{2}$ and represent on a number line.
Answer:
1st we find out the mean of given rational numbers $\left(\frac{1}{4}+\frac{1}{2}\right)$ + 2
= $\left(\frac{1+2}{4}\right)$ + 2
= $\frac{3}{4} \times \frac{1}{2}=\frac{3}{8}$
therefore $\frac{3}{8}$ in the rational number between  $\frac{1}{4}$ and $\frac{1}{2}$
 
Represent on a number line