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Practice each question, then open the answer or worked solution.
A number which can be expressed as p/q where p and q are integers and q≠0 is
(a) natural number. (b) whole number.
(c) integer. (d) rational number
Solution:-
A number which can be expressed as p/q where p and q are integers and q≠0 is (d) rational number
A number of the form p/q is said to be a rational number if
(a) p and q are integers.
(b) p and q are integers and q ≠ 0
(c) p and q are integers and p ≠ 0
(d) p and q are integers and p ≠ 0 also q ≠ 0
Solution:-
A number of the form p/q is said to be a rational number if (b) p and q are integers and q ≠ 0
The numerical expression (3/8) + (-5/7) = (-19/56) shows that
(a) rational numbers are closed under addition.
(b) rational numbers are not closed under addition.
(c) rational numbers are closed under multiplication.
(d) addition of rational numbers is not commutative.
Solution:-
(a) rational numbers are closed under addition.
Because, (3/8) + (-5/7)
Take the LCM of the denominators of the given rational numbers.
LCM of 8 and 7 is 56
Express each of the given rational numbers with the above LCM as the common denominator.
Now,
(3/8)= [(3×7)/ (8×7)] = (21/56)
(-5/7)= [(-5×8)/ (7×8)] = (-40/56)
Then,
= (21/56) + (-40/56) … [∵ denominator is same in both the rational numbers]
= (21 – 40)/56
= (-19/56)
. Which of the following is not true?
Solution:-
(d) rational numbers are closed under division.
Because, rational numbers are closed under the operations of addition, subtraction and multiplication.
(-3/8) + (1/7) = (1/7) + (-3/8) is an example to show that
(a) addition of rational numbers is commutative.
(b) rational numbers are closed under addition.
(c) addition of rational number is associative.
(d) rational numbers are distributive under addition.
Solution:-
(a) addition of rational numbers is commutative.
The arrangement of above rational numbers is in the form of Commutative law of addition [a + b=b + a]
Which of the following expressions shows that rational numbers are associative under multiplication.
Solution:-
(a) [(2/3) × ((-6/7) × (3/5))] = [((2/3) × (-6/7)) × (3/5)]
Because, the arrangement of above rational numbers is in the form of Associative law of Multiplication [a × (b ×c)] = [(a× b) × c]
Zero (0) is
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.
Solution:-
Zero (0) is (a) the identity for addition of rational numbers.
One (1) is
(a) the identity for addition of rational numbers.
(b) the identity for subtraction of rational numbers.
(c) the identity for multiplication of rational numbers.
(d) the identity for division of rational numbers.
Solution:-
One (1) is the identity for multiplication of rational numbers.
The additive inverse of -7/19 is
(a) -7/19 (b) 7/19 (c) 19/7 (d) -19/7
Solution:-
Additive inverse of (-7/19) is (b) (7/19)
The additive inverse of the rational number -a/b is a/b and vice-versa.
Multiplicative inverse of a negative rational number is
(a) a positive rational number.
(b) a negative rational number.
(c) 0
(d) 1
Solution:-
(b) a negative rational number.
(-1/3) is a rational number so its multiplicative inverse is (-3/1)
So that their multiplication will be,
= (-1/3) × (-3/1)
= – 1 × -1
= 1