CBSE Class 8 Mathematics Rational Numbers Assignment Set 06

Fill the gap

Question. Rational numbers are _________ under the operations of _________, _________ and _________.
Answer: closed, Addition, Subtraction, Multiplication

Question. The operations addition and multiplication are _________ and _________ for rational nos.
Answer: Commutative, Associative

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

Question. The rational number _________ is the multiplicative identity for rational nos.
Answer: one

Question. The additive inverse of \( \left(\frac{a}{b}\right), b \neq 0 \) is _________
Answer: \( -\left(\frac{a}{b}\right) \)

Question. The multiplicative inverse of \( \left(\frac{a}{b}\right), b \neq 0 \) is _________
Answer: \( \left(\frac{b}{a}\right) \)

Question. Distributive property for any three rational numbers \( a, b, c \) is _________
Answer: \( a(b+c) = ab + ac \)

Question. If 'a' and 'b' are two rational nos. then _________ is a rational number lying between 'a' and 'b'
Answer: \( \frac{a+b}{2} \)

Question. Between any two rational numbers there are _________ rational numbers.
Answer: Infinite

Question. If \( a, b, c \) are three rational nos. and \( a \neq 0 \) then \( (b+c) \div a = \text{_____} + \text{_____} \)
Answer: \( b \div a + c \div a \)

Question. For a rational number \( a \neq 0 \), \( a \div a = \text{_____} \) and \( a \div (-a) = \text{_____} \)
Answer: 1 and -1

Question. If \( \frac{a}{b} \) and \( \frac{c}{d} (\neq 0) \) are two rational numbers then \( \frac{a}{b} \div \frac{c}{d} = \text{_____} \)
Answer: \( \frac{ad}{bc} \)

Question. For any three rational numbers associative property for multiplication is _________
Answer: \( a \times (b \times c) = (a \times b) \times c \)

Question. If \( \frac{a}{b}, \frac{c}{d} (\neq 0) \) are two rational numbers then closure property for addition states that _________ is a rational no.
Answer: \( \left(\frac{a}{b} + \frac{c}{d}\right) \)

Question. If 'a' and 'b' are two such rational numbers that \( a+b=0 \) then \( b \) is the _________ of \( a \).
Answer: additive inverse

Question. If 'a' and 'b' are two rational numbers then \( |a+b| \leq \text{_____} + \text{_____} \)
Answer: \( |a| + |b| \)

Question. If 'a' and 'b' are two rational numbers then \( |a \times b| \text{_____} |a| \times |b| \)
Answer: \( = \)

Question. For any rational number 'a', if \( a+0=0+a=a \) then '0' is called _________
Answer: additive identity

Question. For any two rational numbers 'a', 'b', \( (a-b) \) is a _________
Answer: rational number

Question. For any rational number, the multiplicative identity is _________
Answer: one