Chapter1: Rational Numbers

1.A number which can be expressed as pq 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 pq 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 38+(-5)7=-1956 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. -38+17=17+-38 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) 23×-67×35=23×-67×35 

(b) 23×-67×35=23×35×-67

(c) 23×-67×35=35×23×-67

(d) -67×35×35=-67×23×35 

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.
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.

9.The additive inverse of -719  is
(a)  -719              (b)  719          (c) 197      (d) -197
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 multiply821 by
(a)  821         (b)   -821        (c)  218       (d)  -218 

13. -(-x) is same as
(a) -x             (b) x          (c) 1x          (d) -1x
14.The multiplicative inverse of -117 is
(a) 87         (b) -87      (c) 78       (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 pq , where p and q are integers and q ≠ 0, is
(a) pq         (b)  1           (c) 0     (d)  qp
20.If y be the reciprocal of rational number x, then the reciprocal of y will be
(a) x          (b) y         (c) xy          (d)  yx
21.The reciprocal of -38×-713 is
(a) 10421        (b)  -10421              (c) 21104         (d)  -21104
22.Which of the following is an example of distributive property of multiplication over addition for rational numbers.

(a) -14×23+-47=-14×23+-14×-47 
(b) -14×23+-47=-14×23--47

(c) -14×23+-47=23+-14×-47

(d) -14×23+-47=23+-47-14

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.

24. x+y2 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-y2  is a rational number between x and y.
(b) x+y2  is a rational number between x and y.
(c) x×y2  is a rational number between x and y.
(d) x÷y2 is a rational number between x and y.

Fill in the blanks :

26.The equivalent of 57 , whose numerator is 45 is ___________.
27.The equivalent rational number of 79 , whose denominator is 45 is___________.
28.Between the numbers 1520 and 3540 , the greater number is __________.
29.The reciprocal of a positive rational number is ___________.
30.The reciprocal of a negative rational number is ___________.
31.Zero has ___________ reciprocal.
32.The numbers ___________ and ___________ are their own reciprocal.
33.If y be the reciprocal of x , then the reciprocal of y² in terms of x will be ___________.
34.The reciprocal of 25×-49 is ___________.
35. (213 × 657)-1 = 213-1 × ___________.
36.The negative of 1 is ___________.

37.For rational numbers ab ,cd and ef and we have  ab×cd+ef= _________ +________.
38. -57 is ________ than –3.
39.There are ________ rational numbers between any two rational numbers.
40.The rational numbers 13 and -13 are on the ________ sides of zero on the number line.
41.The negative of a negative rational number is always a ________ rational number.
42.Rational numbers can be added or multiplied in any __________.
43.The reciprocal of -57 is ________.
44.The multiplicative inverse of 43 is _________.
45.The rational number 10.11 in the from pq is _________.

46.  15×27+38=15×27+ _________.
47.The two rational numbers lying between –2 and –5 with denominator as 1 are _________ and _________.