Rational Numbers Questions

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
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
commutative.
A. True
B. False
c. Cannot be determined
D. None of these

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
equal, if they have the same form.

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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