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