We provide rational numbers practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on rational numbers skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of rational numbers Questions

Question No | Questions | Class |
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1 | A prime number is squared and then added to a different prime number. The number thus obtained is: I. An even number II. An odd number III. A positive number A. I only B. II only c. ॥ only D. I and III only E . ।, ॥।, and III | 7 |

2 | The property satisfied by the division of whole numbers is A. closure property B. Commutative property c. Associative property D. None of these | 8 |

3 | 3. Which of the following rational numbers is in the standard form? fa tla rse | 8 |

4 | 7. The denominator of a rational number cannot be …… | 8 |

5 | The value of the fraction ( frac{1}{3}+frac{3}{4} ) is equal to A ( cdot frac{1}{12} ) в. ( frac{13}{12} ) ( c cdot frac{16}{12} ) D. none of the above | 7 |

6 | 9. Find five rational numbers between. | 8 |

7 | Arrange ( frac{5}{8}, frac{3}{16},-frac{1}{4} ) and ( frac{17}{32} ) in descending order of their magnitudes, the sum of the lowest and the largest of these fractions is | 7 |

8 | If the multiplicative inverse of ( frac{x+1}{x} ) is ( frac{2}{3}, ) then find ( x ) | 8 |

9 | By what number should ( (2)^{-7} ) be multiplied so that the product is 1 | 8 |

10 | Ifa is reciprocal of b, then the reciprocal of bis …. prolofany number | 8 |

11 | Check the distributive property for the stated triples of rational numbers: ( frac{1}{8}, frac{1}{9}, frac{1}{10} ) | 8 |

12 | Subtraction of ( frac{11}{35} ) from ( frac{12}{15} ) gives A ( cdot frac{84}{35} ) в. ( frac{33}{35} ) c. ( frac{11}{15} ) D. ( frac{17}{35} ) | 7 |

13 | 57. (1-1)(-1)(-5)–(-5)=- (3) 7 14 2-1 | 7 |

14 | Check the distributive property for the stated triples of rational numbers: ( frac{3}{8}, 0, frac{13}{7} ) | 8 |

15 | A rational number whose product with a given rational number is equal to a rational number A. True B. False | 8 |

16 | Simplify : ( [mathbf{0 . 9}-{mathbf{2 . 3}-mathbf{3 . 2}-(mathbf{7 . 1}-mathbf{5 . 4}-mathbf{3 . 5})}] ) ( A ) B. 0.9 ( c .0 .8 ) ( D ) | 7 |

17 | There are ……. rational number which when multiplied by ( 0, ) gives product as 1. A . 0 B. 2 ( c cdot 4 ) D. infinite | 8 |

18 | Find the multiplicative inverse of each of the following numbers: ( 2, frac{6}{11}, frac{-8}{15}, frac{19}{18}, frac{1}{1000} ) | 8 |

19 | Write the negative (additive inverse) of each of the following: ( frac{-16}{13} ) | 8 |

20 | The multiplicative inverse of ( frac{-13}{19} ) is ( frac{-19}{q}, ) then the value of ( q ) is equal to ( ? ) | 8 |

21 | The sum of two numbers is ( frac{-1}{3} . ) If one of the number is ( frac{-12}{3}, ) find the other | 7 |

22 | The value of ( (-32) div(-4) ) is equal to ( A cdot+8 ) B. -18 ( c cdot+18 ) D. – 8 | 7 |

23 | Is 0.21 the multiplicative inverse of ( 4 frac{16}{21} ) ( ? ) A. Yes B. No c. cannot say D. None | 8 |

24 | 1. Column-I (A) Distributive law (B) Commutative law Column-II (p) Ifa & bare rational number, then a +bis rational (q) Ifa & bare rational numbers, then a+b=b+a If a, b & c are rational numbers, then a +(b + c) =(a+b)+ (s) If a, b & c are ratioan numbers, then ax (b+c) = ab + ac © Associative law (D) Closure law | 8 |

25 | Prove that ( 3+sqrt{5} ) is an rational number. | 7 |

26 | Prove that ( (-1) times(-1)=1 ) | 8 |

27 | (1 4. What should be added to + to get 3? | 8 |

28 | 5. Insert three rational numbers between and | 8 |

29 | 71. The value of 3+ ਡ ‘ ‘ – 1s (1) 3+3 3) 1 (2) 3 (4) 0 | 8 |

30 | Choose the correct option for following statement. Subtraction of rational numbers is not | 8 |

31 | Rational numbers are closed under A. addition B. subtraction c. multiplication D. all of the above | 8 |

32 | 2 | 8 |

33 | Find the unknown number: ( dots dots dots-. . ) ( frac{3}{7}=frac{3}{7} ) ( mathbf{A} cdot mathbf{0} ) в. 1 ( c cdot frac{3}{7} ) D. | 7 |

34 | f ( x, y ) are rational numbers such that ( (x+y)+(x-2 y) sqrt{2}=2 x-y+ ) ( (x-y-1) sqrt{5} ) then A. ( x=1, y=1 ) B. ( x=2, y=1 ) c. ( x=5, y=1 ) D. ( x ) and ( y ) can take infinitely many values | 8 |

35 | Simplify using associative property : ( frac{7}{16} timesleft(frac{-24}{49} times frac{28}{15}right) ) A ( cdot frac{28}{15} ) B. ( frac{2}{5} ) c. ( frac{-2}{5} ) D. ( frac{-3}{15} ) | 8 |

36 | Use distributive property of multiplication of rational numbers and simplify: (i) ( frac{-5}{4} timesleft(frac{8}{9}+frac{5}{7}right) ) (ii) ( frac{2}{7} timesleft(frac{1}{4}-frac{1}{2}right) ) | 8 |

37 | For any two rational numbers ( x ) and ( y ) which of the following is/are correct, if ( x ) is positive and ( y ) is negative? (1) ( boldsymbol{x}y ) A. Both 1 and 2 B. Both 2 and 3 c. only 3 D. 1,2 and 3 | 7 |

38 | If ( k>0 ) ( mathbf{A}:(-mathbf{1})(-mathbf{2})(-boldsymbol{k}) ) ( mathrm{B}:(1)(2)(k) ) Then A. Quantity in A is greater than B B. Quantity in B is greater than A. c. Both quantities are equal. D. The relationship cannot be determined from the information given. | 7 |

39 | -6 6. The additive inverse of – is not equal to | 8 |

40 | 7. The value of 4 — 3+ 1 | 8 |

41 | The property under multiplication used in each of the following. ( frac{-4}{5} times 1=1 times frac{-4}{5}=-frac{4}{5} ) This question has multiple correct options A. Commutative Property B. Associative Property c. Distributive Property D. Identity Property | 8 |

42 | 6. All rational numbers can be represented on a number line. | 8 |

43 | Find a rational number between -1 and 1 ( mathbf{A} cdot mathbf{0} ) B. ( frac{1}{sqrt{-2}} ) ( c cdot frac{-8}{5} ) D. ( frac{3}{2} ) | 7 |

44 | For any real number a, prove that ( a times ) ( mathbf{0}=mathbf{0} ) | 8 |

45 | PUU au yolu -9 8. -2 5 Represent 1111 on the number line. | 8 |

46 | ( G ) is a set of all rational numbers except -1 and ( * ) is defined by ( a * b=a+b+ ) ( a b ) for all ( a, b in G, ) in the group ( (G, *) ) the solution of ( 2^{-1} * x * 3^{-1}=5 ) is ( mathbf{A} cdot 71 ) B. 68 c. ( 63 / 5 ) D. ( 72 / 5 ) | 8 |

47 | 1. Simplity – R B D | 8 |

48 | Multiply ( frac{6}{13} ) by the reciprocal of ( frac{-7}{16} ) is ( frac{-96}{q}, ) then ( q ) is equal to | 7 |

49 | The value of ( 2 frac{1}{2} times 10-4 frac{1}{3} times 10 ) is A ( cdot frac{-3}{55} ) в. ( frac{3}{55} ) c. ( frac{55}{3} ) D. ( frac{-55}{3} ) | 8 |

50 | 3. G-G)«(-7) Sumpit Simp 13 | 8 |

51 | Out of the rational numbers ( frac{5}{-11}, frac{5}{-12}, frac{5}{-17}, ) which is the greatest? A ( cdot frac{-5}{11} ) в. ( frac{5}{-12} ) ( c cdot frac{-5}{17} ) D. Cannot be compared | 7 |

52 | 64. If a = b + c, b = c + a and c = a + b, then the value of 11 1 1+ a + 1+b + 1+c is (1) abc (2) ałbc2 (3) 1 (4) O | 8 |

53 | The product of any number with 0 will be ( mathbf{A} cdot mathbf{1} ) B. 0 c. number itself D. none of these | 7 |

54 | If a and x represent real numbers for which ( x^{2}=-a, ) which of the following statements could be true? I. ( a>0 ) II. ( boldsymbol{a}=mathbf{0} ) III. ( boldsymbol{a}<mathbf{0} ) A. None B. II only c. ॥ा only D. I and II only E. II and III only | 7 |

55 | If there are two possible positive integer values for ( boldsymbol{x} ) satisfying ( boldsymbol{y}=boldsymbol{x}(1+boldsymbol{x}) ) What is a possible value for ( y ? ) A . -30 B. – 1 c. 0 D. 15 E .20 | 7 |

56 | ( 4 frac{1}{3}+5 frac{2}{3}= ) A ( cdot frac{13}{3} ) B. 30 c. ( frac{14}{3} ) D. 10 | 7 |

57 | 2 24 48 Represent the the following on the number line. 6. | 8 |

58 | #NAME? | 8 |

59 | Which of the following pairs represent the same rational number? This question has multiple correct options A ( cdot frac{-7}{21} ) and ( frac{3}{9} ) B. ( frac{-16}{20} ) and ( frac{20}{-25} ) c. ( frac{-2}{-3} ) and ( frac{2}{3} ) D. ( frac{-3}{5} ) and ( frac{-12}{20} ) E ( frac{8}{-5} ) and ( frac{-24}{15} ) F. ( frac{1}{3} ) and ( frac{-1}{9} ) | 7 |

60 | Fill in the blanks with ( >,,(text { ii) }-<, text { (iii) }-= ) B. (i)-<, (ii)- ( c cdot(i)->,(text { ii) }- ) D. (i)-=, (ii)->, (iii)- | 7 |

61 | The fraction, ( frac{1}{3} ) A. equals 0.33333333 B. is less than 0.33333333 by ( frac{1}{3.10^{8}} ) c. is less than 0.33333333 by ( frac{1}{3.10^{9}} ) D ‘ is greater than 0.33333333 by ( frac{1}{3.10^{8}} ) E ( cdot ) is greater than 0.33333333 by ( frac{1}{3.10^{9}} ) | 7 |

62 | State whether True or False The square of ( sqrt{5}-2 ) is ( 9-4 sqrt{5} ) | 7 |

63 | Simplify: ( frac{8}{9}+frac{-11}{6} ) | 7 |

64 | Classify the numbers are rational or irrational ¡) ( 2-sqrt{3} ) ii) ( (3+sqrt{2})-sqrt{23} ) iii) ( frac{2 sqrt{2}}{7 sqrt{7}} ) | 8 |

65 | Multiplication distributes over substraction of rational numbers. If true then enter 1 and if false then enter 0 | 8 |

66 | Which of the following pairs represent the same rational numbers: ( frac{-2}{-3} ) and ( frac{2}{3} ) | 7 |

67 | How many rational numbers exist between any two distinct rational numbers? A .2 B. 3 c. 10 D. Infinite | 8 |

68 | 1. Express rational number with positive denominator -14 | 8 |

69 | You know that ( frac{1}{7}=0.142857 . ) Find the decimal expansions of ( frac{2}{7}, frac{3}{7}, frac{4}{7}, frac{5}{7}, frac{6}{7} ) are without actually doing the long division? | 7 |

70 | 7. © öte…. = 3 15 74 23 Write the additive inverse of each of the following rat | 8 |

71 | Out of the rational numbers ( frac{-5}{11}, frac{-5}{12}, frac{-5}{17} ) which is smallest. | 7 |

72 | 1. Match the following Column-I e law is satisfied by (B) Commutative law is satisfied by © Closure law is ) satisfied by (D) Distributive law of multiplication is satisfied by Column-II (p) Addition of rational numbers @ Subtraction of rational numbers (1) Multiplication of rational number (8) Division of rational number von | 8 |

73 | Add the following rational numbers: ( frac{6}{13} ) and ( frac{-9}{13} ) | 7 |

74 | The smallest rationalizing factor of ( sqrt[3]{63} ) is A ( cdot sqrt[3]{37} ) в. ( sqrt[3]{62} ) ( c cdot sqrt[3]{147} ) D. ( sqrt[3]{243} ) | 7 |

75 | Add the following rational numbers: ( frac{7}{-18} ) and ( frac{8}{27} ) | 7 |

76 | The reciprocal of a negative rational number is A. negative B. positive c. cannot be determined D. none | 8 |

77 | The sum of the fractions ( frac{1}{2}+frac{1}{6}+frac{1}{12}+ ) ( frac{1}{20}+frac{1}{30}+frac{1}{42}+frac{1}{56}+frac{1}{72}+frac{1}{90}+ ) ( frac{1}{110}+frac{1}{132} ) is ( A cdot frac{7}{8} ) в. ( frac{11}{12} ) ( c cdot frac{15}{16} ) D. ( frac{17}{18} ) | 7 |

78 | Add the following rational numbers: ( frac{-7}{27} ) and ( frac{11}{18} ) | 7 |

79 | Which of the following options is correct? (1) Every integer and fraction is a rational number. (2) A rational number ( frac{p}{q} ) is positive if ( p ) and ( q ) are either both positive or both negative. (3) A rational number ( frac{p}{q} ) is negative if one of ( p ) and ( q ) is positive and other is negative. (4) If there are two rational numbers with same denominator, then the one with the larger numerator is larger numerator is larger than the other. A. Both 1 and 4 are incorrect B. Both 2 and 3 are incorrect c. only 1 is correct D. All are correct | 7 |

80 | The multiplicative inverse of a positive rational number is A. always positive. B. may be positive. c. always negative. D. maybe negative. | 8 |

81 | Using above properties of addition of rational numbers, -5 2 +3+= express the following as a rational number: | 8 |

82 | 1. Assertion : Zero is a rational number. Reason: Each rational number is a quotient of any two integers, while its divisor should not be zero. Thus, a number of the form where p and q are integers and q O is a rational number. | 8 |

83 | The number with which when 82 is multiplied product remains the same. ( mathbf{A} cdot 82 ) B. 0 c. ( frac{1}{82} ) D. | 8 |

84 | The points ( P, Q, R, S, T, U, A ) and ( B ) on the number line are such that, ( boldsymbol{T} boldsymbol{R}= ) ( boldsymbol{R S}=boldsymbol{S U} ) and ( boldsymbol{A P}=boldsymbol{P Q}=boldsymbol{Q B} . ) Name the rational numbers represented by ( P, Q, R ) and ( S ) ( ^{mathbf{A}} cdot P=frac{8}{3}, Q=frac{7}{3}, R=frac{-4}{3}, S=frac{-5}{3} ) B. ( P=frac{7}{3}, Q=frac{7}{3}, R=frac{-5}{3}, S=frac{-4}{3} ) ( ^{mathrm{C}} P=frac{7}{3}, Q=frac{8}{3}, R=frac{-4}{3}, S=frac{-5}{3} ) D. ( quad P=frac{8}{3}, Q=frac{7}{3}, R=frac{-5}{3}, S=frac{-4}{3} ) | 7 |

85 | 6. By what number should we multiply 1, so that the product may be | 8 |

86 | What are the properties of ( R ) used in the following? ( boldsymbol{pi} times mathbf{1}=boldsymbol{pi} ) | 8 |

87 | Write the negative (additive inverse) of each of the following: -1 | 8 |

88 | Find the value of ( 0.006 div 0.06 ) A . 0.01 в. 1.0 c. ( 0 . ) D. 0.001 | 7 |

89 | 3. Every whole number is a rational number. ielas a whole | 8 |

90 | 6. A rational number between The denominato and | 8 |

91 | Fill in the blank: ( left(-frac{1}{3}right)+ ) ( left[left(frac{-4}{3}right)+frac{3}{7}right]=left[left(frac{-1}{3}right)+dots . .right]+frac{3}{7} ) ( A cdot frac{-1}{3} ) B. ( frac{-4}{3} ) ( c cdot frac{3}{7} ) D. ( frac{-3}{7} ) | 8 |

92 | If ( n ) is a positive integer, which of the following CANNOT be the units digit of ( mathbf{3}^{n} ? ) A . B. 3 ( c .5 ) D. | 7 |

93 | Sum of the numbers 0.5,12.56 and ( mathbf{0 . 0 0 3} ) is A . 13.063 в. 31.063 c. 12.063 D. none of these | 7 |

94 | Order from least to greatest: ( frac{8}{18} ) ii) 0.8 iii) ( 40 % ) of 1 | 7 |

95 | Which of the following indicates ascending order of the fractions? A. ( frac{4}{13}, frac{2}{7}, frac{3}{11}, frac{1}{5} ) B. ( frac{1}{5}, frac{2}{7}, frac{3}{11}, frac{4}{13} ) C. ( frac{1}{5}, frac{3}{11}, frac{2}{7}, frac{4}{13} ) D. ( frac{2}{7}, frac{1}{5}, frac{3}{11}, frac{4}{13} ) | 7 |

96 | Write the multiplicate inverse of ( frac{3}{2} ) | 8 |

97 | Find a rational number between and | 8 |

98 | 9. Write any three rational numbers between -2 and 0. | 8 |

99 | 11. Use the distributivity of multiplication of rational numbers over their addition to simplify: 3 (35 10 ola X + 5 (24 | 8 |

100 | ( frac{-8}{11}+frac{-4}{11}=frac{p}{11} ) then ( boldsymbol{p}=? ) | 7 |

101 | Find the multiplicative inverse of 3 and -7 | 8 |

102 | Prove that, if ( a, b, c ) and ( d ) be positive rationals such that, ( a+sqrt{b}=c+sqrt{d} ) then either ( a=c ) and ( b=d ) or ( b ) and ( d ) are squares of rationals. | 7 |

103 | Which is the smallest of the following fractions? A ( cdot frac{4}{9} ) B. ( frac{2}{5} ) ( c cdot frac{3}{7} ) D. ( frac{1}{4} ) | 7 |

104 | ( frac{-7}{5}+left(frac{2}{-11}+frac{-13}{25}right)= ) ( left(frac{-7}{5}+frac{2}{-11}right)+frac{-13}{25} ) This property is A . closure B. commutative c. associative D. identity | 8 |

105 | Subtraction of +43 from -26 gives A . -17 B. +17 ( c .-69 ) D. +69 | 7 |

106 | The sum of an integer and its additive inverse is always A . B. – – c. 0 ( D ) | 8 |

107 | Tell what property allows you to compute ( frac{1}{3} timesleft(6 times frac{4}{3}right) ) as ( left(frac{1}{3} times 6right) times ) 4 ( overline{mathbf{3}} ) | 8 |

108 | If ( P=left(frac{-3}{4}right)^{3}, Q=left(frac{-2}{5}right)^{2}, R= ) ( (0.3)^{2}, S=(-1.2)^{2} ) which of the following is true? A. ( P>Q>R>S ) в. ( S>P>Q>R ) c. ( S>Q>R>P ) ( mathbf{D} cdot S>R>P>Q ) | 7 |

109 | 3. Using appropriate properties, find. 35 31 35 256 1 3 1 2 –X-+– – 6 2 14 5 | 8 |

110 | If ( sqrt{3}(sqrt{7}-sqrt{3})=sqrt{a}+b, ) then find the values of a and b. | 8 |

111 | The multiplicative inverse of ( frac{1}{5} ) is | 8 |

112 | Two fractions are equivalent, if their cross multiplications are ( mathbf{A} cdot mathbf{0} ) B. c. equal D. not equal | 7 |

113 | & Write the additive inverse of each of the following rational numbers: Lon DIR li (iv) | 8 |

114 | After expressing the following as a rational number of the form ( frac{boldsymbol{p}}{boldsymbol{q}} ) ( frac{-mathbf{7}}{mathbf{4}}+frac{mathbf{5}}{mathbf{3}}+frac{-mathbf{1}}{mathbf{2}}+frac{-mathbf{5}}{mathbf{6}}+mathbf{2}, ) then the value equivalent to ( p ) is | 7 |

115 | AS2 and 10. Find ten rational numbers between | 8 |

116 | Find the sum of ( frac{5}{6} ) and ( frac{11}{13}, frac{4}{7} ) and ( frac{-3}{5} ) ( frac{-7}{4} ) and ( frac{-3}{7}: ) | 7 |

117 | The multiplicative inverse of -1 is ( p ) then ( -p ) is equal to | 8 |

118 | Which among the following is a rational number? A. ( sqrt{2} ) в. ( sqrt{pi} ) ( c cdot sqrt{7} ) D. ( sqrt{frac{5}{25}} ) E ( cdot sqrt{frac{64}{49}} ) | 8 |

119 | xand ( frac{8}{9} ) are the additive inverse of each other.Then the value of ( x ) is A ( cdot frac{-8}{9} ) в. ( frac{-4}{9} ) c. ( frac{-5}{9} ) D. ( frac{-7}{9} ) | 8 |

120 | 2. The product of two negative rational numbers is always….. | 8 |

121 | A rational number between ( sqrt{2} ) and ( sqrt{3} ) is : A ( cdot frac{3}{2} ) B. ( frac{2}{3} ) c. 1 D. 5 | 8 |

122 | Simplify using commutative and associative property: ( left[frac{2}{5}+frac{5}{7}+frac{-12}{5}right] ) A ( cdot-2 frac{5}{7} ) B. ( frac{9}{7} ) c. ( frac{-7}{9} ) D. ( frac{-9}{7} ) | 8 |

123 | Fill in the bank with ( langle,>,=operatorname{sign} ) a) ( (-3)+(-6)–(-3)-(-6) ) b)(-21)-(-10) c)45-(-11) d)(-25)-(-42) | 7 |

124 | ( left(frac{-9}{13} times frac{5}{6}right)-left(frac{-9}{13} times frac{4}{6}right)=frac{-9}{13} times ) ( left(frac{5}{6}-frac{4}{6}right) ) If true then enter 1 and if false then enter 0 | 8 |

125 | ( frac{7}{8} timesleft(frac{17}{13}+frac{14}{13}right)=left(frac{7}{8} times frac{14}{13}right)+ ) ( left(frac{7}{8} times frac{17}{13}right) ) If true then enter 1 and if false then enter 0 | 8 |

126 | Simplify using associative property : ( frac{-8}{9} timesleft(frac{27}{32} times frac{-8}{21}right) ) A ( cdot frac{2}{7} ) B. ( frac{-2}{7} ) ( c cdot frac{-8}{21} ) D. ( frac{-3}{4} ) | 8 |

127 | Rational number ( frac{-18}{5} ) lies between consecutive integers ( A cdot-2 ) and -3 B. -3 and -4 c. -4 and -5 D. -5 and -6 | 7 |

128 | The missing value in ( frac{2}{3} times frac{5}{6}=dots . . times frac{2}{3} ) is A ( cdot frac{2}{3} ) B. ( frac{3}{2} ) ( c cdot frac{5}{6} ) D. | 8 |

129 | The rational numbers whose absolute value is ( frac{4}{3}, ) is ( A cdot frac{8}{6} ) в. ( frac{16}{9} ) ( c .1 ) D. – | 7 |

130 | Difference of 99.999 and 100 is A. 1.11 B. 1.000 ( c .0 .00 ) D. 0.01 | 7 |

131 | The ( ldots ). whional number and its reciprocal is 1 A. sum B. difference c. product D. quotient | 8 |

132 | 2. 11 19 -90.-7 Evaluate: 14105 074 | 8 |

133 | Which set of rational numbers is arranged in ascending order? A ( cdot-frac{5}{14},-frac{25}{28},-frac{3}{7},-frac{1}{2} ) B. ( -frac{25}{28}, frac{-5}{14}, frac{-3}{7},-frac{1}{2} ) c. ( -frac{25}{28},-frac{1}{2},-frac{3}{7},-frac{5}{14} ) D. ( -frac{1}{2}, frac{-3}{7}, frac{-5}{14}, frac{-25}{28} ) | 7 |

134 | Which of the following pairs represent the same rational number? ( frac{-7}{21} ) and ( frac{3}{9} ) | 7 |

135 | An illustration of the associative law for multiplication is given by A ( cdotleft(frac{1}{3} times 5right) times 8=frac{1}{3} times(5 times 8) ) В ( cdot frac{1}{3} times 5 times 8=frac{1}{3} times 8 times 5 ) c. ( frac{1}{3} times 5+frac{1}{3} times 8=frac{1}{3} times 13 ) D ( cdot frac{1}{3} times 5 times 8=left(frac{1}{3} times 5right) timesleft(frac{1}{3} times 8right) ) E. none of these | 8 |

136 | Which pair of numbers are rationalising factors to one another This question has multiple correct options ( A cdot 2 sqrt{3} ) and ( sqrt{3} ) B ( cdot 3^{1 / 3}-3^{-1 / 3} ) and ( 3^{2 / 3}+1+3^{-2 / 3} ) ( x^{1 / x}-x^{-1 / n} ) and ( left(frac{n-1}{n}-x frac{n-2}{n}+ldots ldots . . x^{-}left(frac{n-1}{n}right)right) ) ( sqrt[3]{5}+frac{1}{sqrt[3]{5}} ) and ( sqrt[3]{5^{2}}+1-frac{1}{sqrt[3]{5^{2}}} ) | 8 |

137 | s = = -10-31 1 2-85 (1) 5’9’9 -2 -8 -5 -2 -8.5 | 8 |

138 | 3. Find four rational numbers between – and | 8 |

139 | Sum of the product of 1,234 and 78 with 5,678 and 89 is A. 60,594 B. 60,194 ( mathbf{c} cdot 6,05,194 ) D. 6,01,594 | 7 |

140 | The value of ( 4-frac{5}{1+frac{1}{3+frac{1}{2+frac{1}{4}}}} ) is A ( cdot frac{40}{31} ) B. ( frac{4}{9} ) ( c cdot frac{1}{8} ) D. ( frac{31}{40} ) | 7 |

141 | Write the additive inverse of each of the following rational numbers: ( frac{-2}{17} ) | 8 |

142 | . o 7. Find any ten rational numbers between and | 8 |

143 | Rational numbers are closed under substraction. A. True B. False c. Cannot be determined D. None | 8 |

144 | The value of ( frac{overline{mathbf{5}}}{mathbf{5}} ) is ( A cdot frac{2}{25} ) B. ( frac{10}{5} ) ( c cdot frac{2}{5} ) D. None of the above | 7 |

145 | The value of ( (625)^{0.16} times(625)^{0.09} ) is ( A cdot 4 ) B. 5 c. 25 D. 625 | 8 |

146 | 6. Represent 3 on the number line. | 8 |

147 | 5. Find three rational numbers between 0 and 0.2 | 8 |

148 | Evaluate each of the following: ( frac{-4}{13}-frac{-5}{26}=frac{x}{26} ) what is ‘x’? | 7 |

149 | Suppose a pool begins with a population of only 1 bacterium. What would be the mass of the population after 30 hours? | 7 |

150 | a. Write additive inverse of ( frac{2}{8} ) and ( frac{-6}{-5} ) b. Write multiplicative inverse of ( -13 a n d frac{-13}{19} ) | 8 |

151 | 5. Let a, b, c, be the three rational numbers wh à (1) a + (b + c) = (a + b) + c (Associative property of addition) (1) a (b * c) = (a * b) * c (Associatative property of multiplication) | 8 |

152 | Verify the following: ( frac{-13}{24} timesleft(frac{-12}{5} times frac{35}{36}right)= ) ( left(frac{-13}{24} times frac{-12}{5}right) times frac{35}{36} ) | 8 |

153 | One integer is greater than the other by ( +4 . ) If one number is ( -16, ) then the other will be A. +12 B. 0 c. -1 D. -12 | 7 |

154 | Find the difference between 3.477773 .47777 and 2.85888 | 8 |

155 | Which of the following is a negative rational number: A ( cdot frac{-15}{25} ) B. ( c cdot frac{3}{5} ) ( D cdot frac{-3}{-5} ) | 7 |

156 | 4. For * — and = verify that -(x+y)= (x) + (4) 4. For X = = and y = = verify that -(x+y)=(-x)+(y) | 8 |

157 | Fill in the blanks: ( frac{-9}{14}+ldots . .=-1 . ) Hence find the sum of the numerator and denominator so obtained. | 7 |

158 | The value of WIN (b) S 10 © (d) | 8 |

159 | 4. If – is a rational number, then y is always a whole number. | 8 |

160 | 5. Multiply by the reciprocal of 16 | 8 |

161 | is the additive inverse of ( frac{-3}{11} ) A ( cdot frac{-3}{11} ) в. ( frac{11}{3} ) c. -1 D. ( frac{3}{11} ) | 8 |

162 | Name the property indicated in the following: ( frac{22}{23} cdot frac{23}{22}=1 ) | 8 |

163 | Which number line correctly shows the rational number ( left(-frac{2}{9}+frac{1}{9}right) ? ) ( A ) B. ( c ) ( D ) | 7 |

164 | 5. If x= = then verify N xx(y−z)=(x xy)-(x ^z) | 8 |

165 | The rational number that is equal to its negative. | 8 |

166 | Find the value of ( frac{6}{sqrt{5}-sqrt{3}}, ) it being given that ( sqrt{3}=1.732 ) and ( sqrt{5}=2.236 ) A . 11.9304 B. 11.3904 c. 11.904 D. None of the above | 7 |

167 | Let O, P and Z represent the numbers 0, 3 and – 5 respectively on the number line. choose a point T between Z and O so that ZT = TO. Which rational number does T represent? | 8 |

168 | 9. For any rational number a (a0), a =(-a)=…… and -1 | 8 |

169 | Write the additive inverse of each of the following rational numbers: ( frac{-11}{-25} ) | 8 |

170 | ( [x] ) is defined as the greatest integer less than ( x ) ( {x} ) is defined as the least integer greater than ( x ) What is the value of ( [25.8]-{13.9} ? ) A . 13 B. 0.8 c. 11 D. 11.9 | 7 |

171 | Arrange ( -frac{5}{9}, frac{7}{12},-frac{2}{3} ) and ( frac{11}{18} ) in ascending order of their magnitudes, the difference between the largest and the smallest of these fractions is: | 7 |

172 | Multiplicative inverse of ( 2 frac{2}{7} ) is 2.2 A. True B. False c. cannot say D. None | 8 |

173 | 10. Which of the following is false? -5 – 7 (6) + (d) 8 9 7 11 7 11 8 9 | 8 |

174 | Fill in the blank: ( (-12)+left(4+frac{1}{8}right)= ) ( [(-12)+ldots . .]+frac{1}{8} ) A. (-12) B. 4 c. 1 D. | 8 |

175 | یہ ادا | 8 |

176 | – – + 5 ( | 8 |

177 | Find the multiplicative inverse of ( frac{mathbf{5}}{mathbf{3}} ) ( +frac{-17}{11} ) A ( cdot frac{33}{4} ) в. ( frac{33}{23} ) ( c cdot frac{3}{4} ) D. None of these | 8 |

178 | Which of the following pairs represent the same rational number? ( frac{-2}{-3} ) and ( frac{2}{3} ) | 7 |

179 | 60 7. Choose the rational number which does not lie between rational numbers-and- rational numbers (b) To (d) 20 28 | 8 |

180 | Write five rational numbers which are smaller than 2 | 8 |

181 | Fill the blank spaces: ( frac{4}{-9} times ldots . .=frac{7}{6} times ) A ( cdot frac{-4}{9}, frac{7}{6} ) в. ( frac{4}{-9}, frac{7}{6} ) c. ( frac{7}{6}, frac{4}{-9} ) D. ( frac{7}{6}, frac{7}{6} ) | 8 |

182 | Simplify ( (-90) times 52+(-52) times(-25) ) using a suitable frequency. | 8 |

183 | Subtract the first rational number from the second in each of the following: ( frac{1}{4}, frac{-3}{8} ) | 7 |

184 | Add the following rational numbers: ( frac{31}{-4} ) and ( frac{-5}{8} ) | 7 |

185 | 3. A rational number between (b) 0.29 (d) All of these | 8 |

186 | 3. can’t be expressed as rational number having denominator 5 beacuse 5 is not the multiple of – | 8 |

187 | Tuilplanon) 6. Identify the rational number which is different from the 2 4 11 other three : Explain your reasoning. | 8 |

188 | Write the rational numbers that are equal to their reciprocals. | 7 |

189 | is the only rational number which is equal to its additive inverse. A . B. – 1 c. 0 D. ( frac{1}{2} ) | 8 |

190 | What is the difference in the greatest and the least fractions out of ( frac{6}{7}, frac{7}{8}, frac{8}{9} ) and ( frac{mathbf{9}}{mathbf{1 0}} ) ? ( A cdot frac{3}{70} ) в. ( frac{1}{56} ) c. ( frac{1}{40} ) D. ( frac{1}{72} ) | 7 |

191 | se up 13 16 the multiplicative inverse of -1-? Why or why not? | 8 |

192 | Evaluate each of the following: ( frac{13}{15}-frac{12}{25} ) is ( frac{x}{75} ) find ‘x’ | 7 |

193 | The value of ( frac{2}{3} times frac{3}{frac{5}{6} div frac{2}{3} text { of } 1 frac{1}{4}} ) is : ( A cdot 2 ) B. ( c cdot frac{1}{2} ) D. | 7 |

194 | 1. Verify the distributive property xx (y +z)=xy + xz where -4 1 -7 and write the denominator of (x+y) xz. | 8 |

195 | Compare ( frac{mathbf{1 9}}{mathbf{2 0}} ) and ( frac{mathbf{1 4}}{mathbf{2 0}} ) A ( cdot frac{19}{20}=frac{14}{20} ) в ( cdot frac{19}{20}>frac{14}{20} ) c. ( frac{19}{20} geq frac{14}{20} ) D. ( frac{19}{20} leq frac{14}{20} ) | 7 |

196 | Write down ten positive rational numbers such that the sum of the numerator and the denominator of each is 11. Write them in decreasing order | 7 |

197 | ( frac{5}{13}+-=frac{5}{13} ) ( mathbf{A} cdot mathbf{0} ) B. c. ( frac{5}{13} ) D. ( frac{2}{13} ) | 8 |

198 | For any two real number, an operation defined by ( a * b=1+a b ) is. A. Commutative but not associative B. Associative but not commutative c. Neither Commutative nor associative D. Both commutative and associative | 8 |

199 | 5. Every integer is a rational number. | 8 |

200 | The missing value in ( ldots ldots ldots+frac{2}{7}=frac{2}{7}+ ) ( frac{-11}{13} ) is A ( cdot frac{2}{7} ) в. ( frac{-11}{13} ) c. ( frac{-2}{7} ) D. ( frac{11}{13} ) | 8 |

201 | 2. The rational numbers and on the number line. are on opposite sides of 0 | 8 |

202 | Which fraction on the number line below is in the wrong place? ( A cdot frac{1}{4} ) B. ( c cdot frac{1}{2} ) D. E. None of the above | 7 |

203 | The multiplicative inverse of ( frac{-4}{11} ) is A ( cdot frac{-11}{4} ) в. ( frac{-4}{11} ) c. ( frac{11}{4} ) D. ( frac{4}{11} ) | 8 |

204 | Find the unknown value ( boldsymbol{x}: frac{mathbf{5}}{mathbf{1 3}}+boldsymbol{x}= ) ( frac{5}{13} ) ( mathbf{A} cdot mathbf{0} ) B. c. ( frac{5}{13} ) D. ( frac{2}{13} ) | 7 |

205 | Prove that the associative property hold true for the addition ( left(frac{7}{8}+frac{2}{5}right)+frac{8}{3} ) | 8 |

206 | The value of ( sqrt{mathbf{9 0 0}}+sqrt{mathbf{0 . 0 9}}- ) ( sqrt{0.000009} ) is A . 30.297 в. 30.197 c. 30.097 D. 30.397 | 7 |

207 | Standard form of ( 900000000+3000+ ) 7 is equal to A .90,00,03,007 7 B. 9,00,03,007 ( mathrm{c} .90,00,03,000 ) D. none of these | 7 |

208 | Find ten rational numbers between ( frac{-2}{5} ) and ( frac{1}{2} ) A ( frac{-7}{20}, frac{-11}{20}, frac{-5}{20}, frac{-4}{20}, frac{-3}{20}, frac{-2}{20}, frac{-1}{20}, 0, frac{1}{20} ) and ( frac{2}{20} ) B. ( frac{-7}{20}, frac{-6}{20}, frac{-5}{20}, frac{-4}{20}, frac{-3}{20}, frac{-2}{20}, frac{-1}{20}, 0, frac{1}{20} ) and ( frac{2}{20} ) C. ( frac{-7}{20}, frac{-6}{20}, frac{-5}{20}, frac{-4}{20}, frac{-3}{20}, frac{-2}{20}, frac{-1}{20}, 0, frac{1}{20} ) and ( frac{13}{20} ) D. ( frac{-7}{20}, frac{-6}{20}, frac{-5}{20}, frac{-4}{20}, frac{-3}{20}, frac{-2}{20}, frac{-1}{20}, 0, frac{15}{20} ) and ( frac{2}{20} ) | 7 |

209 | What is the multiplicative inverse of -6 ( ? ) A. -6 B. 6 c. ( frac{-1}{6} ) D. ( frac{1}{6} ) | 8 |

210 | Find the multiplicative inverse of the following. ()-1 | 8 |

211 | Fill in the blanks: ( frac{-mathbf{7}}{mathbf{9}}+ldots ldots=3 . ) Hence find the sum of the numerator and denominator so obtained. | 7 |

212 | Check the commutative property of multiplication for ( frac{-mathbf{7}}{mathbf{1 3}}, frac{mathbf{2 5}}{mathbf{2 7}} ) | 8 |

213 | 8. If = then x = ………….. 5 X | 8 |

214 | 2. Fil in blank 2. — Fill in blank: | 8 |

215 | The additive identify of rational number is ( mathbf{A} cdot mathbf{0} ) B. ( c cdot-1 ) ( D ) | 8 |

216 | Which of these four numbers ( sqrt{boldsymbol{pi}^{2}}, sqrt[3]{boldsymbol{0 . 8}}, sqrt[4]{.00016}, sqrt[3]{-1} cdot sqrt{(.09)^{-1}} ) is (are) rational: A. none B. all c. the first and fourth D. only the fourth E. only the first | 7 |

217 | Write the additive inverse of each of the following rational numbers: ( frac{4}{9} ; frac{-13}{7} ; frac{5}{-11} ; frac{-11}{-14} ) A ( cdot frac{-4}{9} ; frac{13}{7} ; frac{5}{11} ; frac{-13}{14} ) В. ( frac{-4}{9} ; frac{1}{7} ; frac{5}{11} ; frac{-11}{14} ) c. ( frac{-4}{9} ; frac{13}{7} ; frac{5}{11} ; frac{-11}{14} ) D. ( frac{-5}{9} ; frac{13}{7} ; frac{5}{11} ; frac{-11}{14} ) | 8 |

218 | Which of the following is true about the number ( 0.66 overline{66} ? ) A. It is a rational number B. It is an irrational number c. It is correctly gridded as “.66” D. It is equivalent to ( frac{67}{100} ) E. None of the above | 8 |

219 | What per cent is the least rational number of the greatest rational number if ( frac{1}{2}, frac{2}{5}, frac{1}{3} ) and ( frac{5}{9} ) are arranged in ascending order? A . 60% B . 10% c. 20% D. 30% | 7 |

220 | How many one-fourths need to be 1 added to ( 2 frac{1}{4} ) to make ( 4 ? ) A . 3 B. 4 c. 5 D. | 7 |

221 | Which one of the following fractions is more than one-third? A ( cdot frac{23}{70} ) в. ( frac{205}{819} ) c. ( frac{26}{75} ) D. ( frac{118}{355} ) | 7 |

222 | 10. A rational number between | 8 |

223 | Find 10 rational numbers between | 8 |

224 | If . med from the collection of rational numbers, then they are closed under division. A .2 B. ( c cdot 0 ) D. – | 8 |

225 | 9. Verify the property :xx (y+z)=xxy+xx z by taking: 5 | 8 |

226 | 10. Use the distributivity of multiplication of rational numbers over addition to simplify 35 10 10 X 1 5 one cm [16 ] 3 -40 | 8 |

227 | Arrange the following decimal numbers in ascending order. 5.5,0.55,0.055,0.005 A. 5.5,0.055,0.005,0.55 В. 0.55,0.005,0.055,5.5 c. 5.5,0.55,0.055,0.005 D. 0.005,0.055,0.55,5.5 | 7 |

228 | 2. Using above properties of addition of rational numbers, 7 11 5 express the following as a rational number: -+–+- 3 2 3 ddition of rational numbers. | 8 |

229 | 1. The product of two rational numbers is 63. If one of the 40 number is , find the other number. | 8 |

230 | Write four more rational numbers in each of the following patterns: ( frac{-1}{6}, frac{2}{-12}, frac{3}{-18}, frac{4}{-24}, dots ) | 7 |

231 | Find the additive inverse of: ( sqrt{5} ) | 8 |

232 | If ( D ) be subset of the set of all rational numbers, then ( D ) is closed under the binary operations of A. addition, subtraction and division B. addition, multiplication and division c. addition, subtraction and multiplication. D. subtraction, multiplication and division | 8 |

233 | Number should be added top ( frac{-5}{7} ) to get ( frac{-2}{3} ) is ( frac{1}{x} . ) Find ‘x? | 7 |

234 | Solve ( frac{-3}{5}+frac{-12}{20} ) | 8 |

235 | USICUPIUCHULU, U UPI 5. The number 0 is ……… the reciprocal of any number. | 8 |

236 | Write the multiplicate inverse of: ( -mathbf{5} frac{mathbf{6}}{7} ) | 8 |

237 | Find the value of ( (-12) times(+21) ) A ( .-2412 ) B . -242 ( mathbf{c} .-252 ) D. +252 | 7 |

238 | The identity elements with respect to multiplication in integers is A . B. – – c. 0 D. none | 8 |

239 | 5. Name the property used above. (a) Commutativity of multiplication over addition (b) Communtativity of addition over multiplication (c) Distributivity of multiplication over addition (d) Distributivity of addition over multiplication | 8 |

240 | Write the following rational numbers in ascending order: ( frac{3}{4}, frac{7}{12}, frac{15}{11}, frac{22}{19}, frac{101}{100}, frac{-4}{5}, frac{-102}{81}, frac{-13}{7} ) | 7 |

241 | Write five rational numbers which are smaller than 2 A ( cdot_{1, frac{1}{2}, 0,-1,-frac{1}{2}} ) в. ( 0,1,1.414, sqrt{3},-1 ) D. ( 0,1,1.732, sqrt{2},-1 ) | 8 |

242 | ( left(1-frac{1}{3}right)left(1-frac{1}{4}right)left(1-frac{1}{5}right) dotsleft(1-frac{1}{n}right) ) equals A. B. ( frac{2}{n} ) c. ( frac{3}{n} ) D. | 7 |

243 | If ( a=3+sqrt{23}, ) then find ( frac{-14}{a} ) | 7 |

244 | 2. a X (b + c) = ab + ac Column-II (p) rational numbers Column-I Distributive property of multiplication over addition is A rational number which lies between any two rational numbers a and bis B. (9) For any three rational numbers a, b, and c; we have a(b+c= ab + ac (r) irrational C. All integers numbers are a + b D. Square root of all positive prime numbers are Very Short Answer Questions: | 8 |

245 | Identify the property in the following statements: ( mathbf{2}+(mathbf{3}+mathbf{4})=(mathbf{2}+mathbf{3})+mathbf{4} ) | 8 |

246 | Check the commutative property of multiplication for ( frac{mathbf{2 2}}{mathbf{4}}, frac{mathbf{3}}{mathbf{4}} ) | 8 |

247 | 2. Simplify: su (7-9-6-3-6-9 | 8 |

248 | Sum of two integers is ( +62 . ) If one of the integer is ( -48, ) then the other integer is A ( .+14 ) в. -14 c. -110 D. +110 | 7 |

249 | Arrange the following in an ascending order. ( -4,2,0,-frac{5}{4}, 2.17,-3.7, frac{22}{7}, 8 ) A ( cdot-4,-3.7,-frac{5}{4}, 0,2,2.17, frac{22}{7}, 8 ) в. ( _{-4,0,-frac{5}{4},-3.7,2,2.17, frac{22}{7}, 8} ) c. ( _{-4,-3.7,-frac{5}{4}, 2,0,2.17, frac{22}{7}, 8} ) D. ( -4,-3.7,-frac{5}{4}, 2.17,2,0, frac{22}{7}, 8 ) | 7 |

250 | Arrange the fractions ( frac{4}{5}, frac{9}{11}, frac{3}{5}, frac{7}{12} ) in descending order. A ( cdot frac{7}{12}, frac{9}{11}, frac{4}{5}, frac{3}{5} ) В. ( frac{7}{12}, frac{4}{5}, frac{3}{5}, frac{9}{11} ) c. ( frac{9}{11}, frac{4}{5}, frac{3}{5}, frac{7}{12} ) D. None of these | 7 |

251 | If all the fractions ( frac{3}{5}, frac{1}{8}, frac{8}{11}, frac{4}{9}, frac{2}{7}, frac{5}{7} ) and ( frac{5}{4} ) are arranged in descending order of ( overline{mathbf{1 2}} ) their values which one will be the third? A ( cdot frac{1}{8} ) B. ( frac{3}{5} ) c. ( frac{5}{12} ) D. ( frac{8}{11} ) | 7 |

252 | Fill in the blanks so as to make the statement true: Two rational numbers are said to be | 7 |

253 | The sum of two numbers is ( frac{-4}{3} . ) If one of the numbers is ( -5, ) find the other | 7 |

254 | Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number: ( frac{3}{7}+frac{-4}{9}+frac{-11}{7}+frac{7}{9} ) | 8 |

255 | Fill in the blanks. (i) Zero has (ii) The numbers and are their own reciprocals. (iii) The reciprocal of -5 is (iv) Reciprocal of ( frac{1}{x}, ) where ( x neq 0 ) is (v) The product of two rational numbers is always a (vi) The reciprocal of a positive rational number is | 8 |

256 | The resultant of: ( frac{20 times(0.3)^{2}}{0.018} div 0.5 ) of 0.2 is A . 10 в. 100 ( c cdot 20 ) D. 1000 | 7 |

257 | Which step in the following problem is wrong? ( boldsymbol{a}=boldsymbol{b}=mathbf{1} ) ( boldsymbol{a}=boldsymbol{b} ) step-1: ( a^{2}=a b ) step-2: ( a^{2}-b^{2}=a b-b^{2} ) step-3: ( (boldsymbol{a}+boldsymbol{b})(boldsymbol{a}-boldsymbol{b})=boldsymbol{b}(boldsymbol{a}-boldsymbol{b}) ) step- ( 4: a+b=frac{b(a-b)}{a-b} ) ( boldsymbol{a}+boldsymbol{b}=boldsymbol{b} ) ( mathbf{1}+mathbf{1}=mathbf{1} ) ( mathbf{2}=mathbf{1} ) A. Step-4 B. Step-3 c. step- – D. Step- – | 7 |

258 | Using appropriate properties, find 2 | 8 |

259 | Find the unknown number: ( _{—}+frac{3}{7}=frac{3}{7} ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot frac{3}{7} ) D. | 7 |

260 | Re-arrange suitably and find the sum in each of the following: ( frac{-6}{7}+frac{-5}{6}+frac{-4}{9}+frac{-15}{7} ) | 7 |

261 | Which of the following pairs represent the same rational number? This question has multiple correct options A ( cdot frac{-7}{21} ) and ( frac{3}{9} ) B. ( frac{-16}{20} ) and ( frac{20}{-25} ) c. ( frac{-2}{-3} ) and ( frac{2}{3} ) D. ( frac{-1}{3} ) and ( frac{2}{9} ) | 7 |

262 | Which of the following is not the reciprocal of ( left(frac{2}{3}right)^{4} ? ) ( ^{A} cdotleft(frac{3}{2}right)^{4} ) ( ^{text {B }}left(frac{2}{3}right)^{-4} ) ( ^{c}left(frac{3}{2}right)^{-4} ) D. ( frac{3^{4}}{4^{2}} ) | 8 |

263 | Every rational number is A. A natural number B. An integer C. A real number D. A whole number | 8 |

264 | 9. The sum of the additive inverse and multiplicative inverse of 2 is: (b) = NIT NIw Wh: 1 fmful | 8 |

265 | 1. The sum of two rational numbers is . If one of the numbers is -, find the other. 20 | 8 |

266 | Express 1.4191919 ….. in the form of ( frac{p}{q} ) where ( p ) and ( q ) are integer and ( q neq 0 ) | 8 |

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