NCERT Exemplar Problems Solution Class 8 Math Unit 1 Rational Numbers
(1.) 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.
(2.) 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
(3.) 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.
(4.) Which of the following is not true?
(a) rational numbers are closed under addition.
(b) rational numbers are closed under subtraction.
(c) rational numbers are closed under multiplication.
(d) rational numbers are closed under division.
(5) -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.
(6.) Which of the following expressions shows that rational numbers are
associative under multiplication.
(a) 2/3 x (-6/7 x 3/5) = (2/3 x -6/7) x 3/5
(b) 2/3 x (-6/7 x 3/5) = 2/3 x (3/5 x -6/7)
(c) 2/3 x (-6/7 x 3/5) = (3/5 x 2/3) x -6/7
(d) (2/3 x -6/7) x 3/5 = (-6/7 x 2/3) x 3/5
(7.) 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.
Ans. (a) the identity for addition of rational numbers.
Sol. As we know from the basic concepts of rational numbers,
i.e. the rational number 0 is the additive identity for rational numbers.
(8.) 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.
Ans. (c) the identity for multiplication of rational numbers.
Sol. As we know from the basic concepts of rational numbers,
i.e. the rational numbers 1 is the multiplicative identity for rational numbers.
(9) The additive inverse of -7/19 is
(a) -7/19
(b) 7/19
(c) 19/7
(d) -19/7
(10.) Multiplicative inverse of a negative rational number is
(a) a positive rational number.
(b) a negative rational number.
(c) 0
(d) 1
(11.) If x + 0 = 0 + x = x, which is rational number, then 0 is called
(a) identity for addition of rational numbers.
(b) additive inverse of x.
(c) multiplicative inverse of x.
(d) reciprocal of x.
(12) To get the product 1, we should multiply 8/21 by
(a) 8/21
(b) -8/21
(c) 21/8
(d) -21/8
(13.) – (–x) is same as
(a) – x
(b) x
(c) 1/x
(d) -1/x
(14.) The multiplicative inverse of -1~1/7
(a) 8/7
(b) -8/7
(c) 7/8
(d) 7/-8
(15) If x be any rational number then x + 0 is equal to
(a) x
(b) 0
(c) – x
(d) Not defined
(16.) The reciprocal of 1 is
(a) 1
(b) –1
(c) 0
(d) Not defined
(17.) The reciprocal of –1 is
(a) 1
(b) –1
(c) 0
(d) Not defined
(18.) The reciprocal of 0 is
(a) 1
(b) –1
(c) 0
(d) Not defined
(19.) The reciprocal of any rational number p/q , where p and q are integers
and q ≠ 0, is
(a) p/q
(b) 1
(c) 0
(d) q/p
(20) If y be the reciprocal of rational number x, then the reciprocal of y will be
(a) x
(b) y
(c) x/y
(d) y/x
(21) The reciprocal of -3/8 x (-7/13) is
(a) 104/21
(b) -104/21
(c) 21/104
(d) -21/104
(23.) Between two given rational numbers, we can find
(a) one and only one rational number.
(b) only two rational numbers.
(c) only ten rational numbers.
(d) infinitely many rational numbers
Ans. (d) infinitely many rational numbers
Sol. According to the basic concepts of rational numbers, Between any two given rational numbers there are infinity many rational numbers.
(24) x+y/2 is a rational number.
(a) Between x and y
(b) Less than x and y both.
(c) Greater than x and y both.
(d) Less than x but greater than y.
(25.) Which of the following statements is always true?
(a) x-y/2 is a rational number between x and y.
(b) x+y/2 is a rational number between x and y.
(c) xXy/2 is a rational number between x and y.
(d) x÷y/2 is a rational number between x and y.
(26.) The equivalent of 5/7 whose numerator is 45 is ___
(27.) The equivalent rational number of 7/9 , whose denominator is 45 is _____.
(28.) Between the numbers 15/20 and 35/40 the greater number is _____
(29.) The reciprocal of a positive rational number is ___________.
Ans. Positive rational number.
Sol: According to the reciprocal property, to get result 1, which is positive, We have to multiply a positive rational number by a positive rational number [1 x 1 = 1].
(30.) The reciprocal of a negative rational number is ___________
ans. Negative rational number.
Sol: According to the reciprocal property, to get result 1, which is positive, we have to multiply a negative rational number by a negative rational number.
-1 x -1 = 1 [∵-a x -a = a]
(31.) Zero has ___________ reciprocal.
Ans. non-defined
Sol: According to the reciprocal property, the result have to be 1. As we know, multiplying a rational number by 0, the result will be 0, which is not satisfied by the reciprocal property. So ) has non defined reciprocal.
(32.) The numbers ___________ and ___________ are their own reciprocal
Ans. 1 and -1
Sol: According to reciprocal property,
1 x 1 = 1
-1 x -1 = 1
(34.) The reciprocal of 2/5 x (-4/9) is _____
(35.) (213 × 657)-1 = 213-1 × _____
(36.) The negative of 1 is ________.
(37.) For rational numbers a/b, c/d, and e/f we have a/b x (c/d + e/f) = ______ + ______.
38. -5/7 is greater than -3
Sol: -5/7 = -0.71428
0.71428 > -3
39. There are infinitely many rational numbers between two rational numbers.
Sol: According to basic concepts, we know that there are infinitely many rational numbers between two rational numbers.
40. The rational numbers 1/3 and -1/3 are on the opposite sides of zero on the number line.
Sol: As we know from the concepts of the numbers lines i.e. all positive numbers are on right side of zero and all negative numbers are on left side of zero.
(41) The negative of a negative rational number is always a positive rational number.
Sol: According to roles of algebra, -(-a) = a
Let us consider a = 1, -a = -1
-(-1) = 1
(42) Rational numbers can be added or multiplied in any order.
Sol: According to the basic concepts of rational numbers, rational numbers can be added or multiplied in an order.
(45) The rational number 10.11 in the form p/q is 1011/100
Sol: In given rational number 10.11 has 2 digits after point, to remove the point we have to multiply 10.11 by 100.
10.11 = 1011/100.
(47) The two rational numbers lying between -2 and -5 with denominator as 1 are -3/1 and -4/1
Sol. According to the given question, -2, -3/1, -4/1, -5