Rational Numbers Questions

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Rational Numbers Questions

List of rational numbers Questions

Question NoQuestionsClass
1A 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
2The property satisfied by the division of whole numbers is
A. closure property
B. Commutative property
c. Associative property
D. None of these
8
33.
Which of the following rational numbers is in the standard
form?
fa tla
rse
8
47.
The denominator of a rational number cannot be ……
8
5The 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
69.
Find five rational numbers between.
8
7Arrange ( 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
8If the multiplicative inverse of ( frac{x+1}{x} ) is ( frac{2}{3}, ) then find ( x )8
9By what number should ( (2)^{-7} ) be
multiplied so that the product is 1
8
10Ifa is reciprocal of b, then the reciprocal of bis ….
prolofany number
8
11Check the distributive property for the
stated triples of rational numbers:
( frac{1}{8}, frac{1}{9}, frac{1}{10} )
8
12Subtraction 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
1357. (1-1)(-1)(-5)–(-5)=-
(3) 7
14 2-1
7
14Check the distributive property for the stated triples of rational numbers:
( frac{3}{8}, 0, frac{13}{7} )
8
15A rational number whose product with a
given rational number is equal to a rational number
A. True
B. False
8
16Simplify :
( [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
17There are ……. rational number which
when multiplied by ( 0, ) gives product as
1.
A . 0
B. 2
( c cdot 4 )
D. infinite
8
18Find the multiplicative inverse of each of the following numbers:
( 2, frac{6}{11}, frac{-8}{15}, frac{19}{18}, frac{1}{1000} )
8
19Write the negative (additive inverse) of each of the following:
( frac{-16}{13} )
8
20The multiplicative inverse of ( frac{-13}{19} ) is ( frac{-19}{q}, ) then the value of ( q ) is equal to ( ? )8
21The sum of two numbers is ( frac{-1}{3} . ) If one of the number is ( frac{-12}{3}, ) find the other7
22The value of ( (-32) div(-4) ) is equal to
( A cdot+8 )
B. -18
( c cdot+18 )
D. – 8
7
23Is 0.21 the multiplicative inverse of ( 4 frac{16}{21} )
( ? )
A. Yes
B. No
c. cannot say
D. None
8
241.
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
25Prove that ( 3+sqrt{5} ) is an rational
number.
7
26Prove that ( (-1) times(-1)=1 )8
27(1
4.
What should be added to
+
to get 3?
8
285.
Insert three rational numbers between
and
8
2971. The value of
3+ ਡ ‘
‘ – 1s
(1) 3+3
3) 1
(2) 3
(4) 0
8
30Choose 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
31Rational numbers are closed under
A. addition
B. subtraction
c. multiplication
D. all of the above
8
3228
33Find 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
34f ( 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
35Simplify 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
36Use 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
37For 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
38If ( 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
407.
The value of 4 —
3+
1
8
41The 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
426.
All rational numbers can be represented on a number line.
8
43Find 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
44For any real number a, prove that ( a times ) ( mathbf{0}=mathbf{0} )8
45PUU 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
471. Simplity – R
B D
8
48Multiply ( frac{6}{13} ) by the reciprocal of ( frac{-7}{16} ) is ( frac{-96}{q}, ) then ( q ) is equal to7
49The 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
503.
G-G)«(-7)
Sumpit
Simp
13
8
51Out 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
5264. 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
53The product of any number with 0 will
be
( mathbf{A} cdot mathbf{1} )
B. 0
c. number itself
D. none of these
7
54If 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
55If 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
572 24 48
Represent the the following on the number line.
6.
8
58#NAME?8
59Which 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
60Fill in the blanks with ( >,,(text { ii) }-<, text { (iii) }-= )
B. (i)-<, (ii)-
( c cdot(i)->,(text { ii) }- )
D. (i)-=, (ii)->, (iii)-
7
61The 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
62State whether True or False
The square of ( sqrt{5}-2 ) is ( 9-4 sqrt{5} )
7
63Simplify:
( frac{8}{9}+frac{-11}{6} )
7
64Classify the numbers are rational or irrational
¡) ( 2-sqrt{3} )
ii) ( (3+sqrt{2})-sqrt{23} )
iii) ( frac{2 sqrt{2}}{7 sqrt{7}} )
8
65Multiplication distributes over
substraction of rational numbers.
If true then enter 1 and if false then
enter 0
8
66Which of the following pairs represent the same rational numbers:
( frac{-2}{-3} ) and ( frac{2}{3} )
7
67How many rational numbers exist between any two distinct rational numbers?
A .2
B. 3
c. 10
D. Infinite
8
681.
Express
rational number with positive denominator
-14
8
69You 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
707.
©
öte…. = 3
15
74
23
Write the additive inverse of each of the following rat
8
71Out of the rational numbers
( frac{-5}{11}, frac{-5}{12}, frac{-5}{17} ) which is smallest.
7
721.
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
73Add the following rational numbers:
( frac{6}{13} ) and ( frac{-9}{13} )
7
74The 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
75Add the following rational numbers:
( frac{7}{-18} ) and ( frac{8}{27} )
7
76The reciprocal of a negative rational
number is
A. negative
B. positive
c. cannot be determined
D. none
8
77The 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
78Add the following rational numbers:
( frac{-7}{27} ) and ( frac{11}{18} )
7
79Which 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
80The multiplicative inverse of a positive rational number is
A. always positive.
B. may be positive.
c. always negative.
D. maybe negative.
8
81Using above properties of addition of rational numbers,
-5
2
+3+=
express the following as a rational number:
8
821.
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
83The number with which when 82 is
multiplied product remains the same.
( mathbf{A} cdot 82 )
B. 0
c. ( frac{1}{82} )
D.
8
84The 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
856.
By what number should we multiply
1, so that the
product may be
8
86What are the properties of ( R ) used in the
following? ( boldsymbol{pi} times mathbf{1}=boldsymbol{pi} )
8
87Write the negative (additive inverse) of
each of the following:
-1
8
88Find the value of ( 0.006 div 0.06 )
A . 0.01
в. 1.0
c. ( 0 . )
D. 0.001
7
893. Every whole number is a rational number.
ielas a whole
8
906.
A rational number between
The denominato
and
8
91Fill 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
92If ( 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
93Sum 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
94Order from least to greatest:
( frac{8}{18} )
ii) 0.8
iii) ( 40 % ) of 1
7
95Which 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
96Write the multiplicate inverse of ( frac{3}{2} )8
97Find a rational number between
and
8
989.
Write any three rational numbers between -2 and 0.
8
9911.
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
101Find the multiplicative inverse of 3 and
-7
8
102Prove 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
103Which 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
105Subtraction of +43 from -26 gives
A . -17
B. +17
( c .-69 )
D. +69
7
106The sum of an integer and its additive inverse is always
A .
B. – –
c. 0
( D )
8
107Tell 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
108If ( 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
1093.
Using appropriate properties, find.
35 31
35 256
1 3 1 2
–X-+– –
6 2 14 5
8
110If ( sqrt{3}(sqrt{7}-sqrt{3})=sqrt{a}+b, ) then find the
values of a and b.
8
111The multiplicative inverse of ( frac{1}{5} ) is8
112Two 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
114After 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
115AS2
and
10.
Find ten rational numbers between
8
116Find 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
117The multiplicative inverse of -1 is ( p )
then ( -p ) is equal to
8
118Which 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
119xand ( 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
1202.
The product of two negative rational numbers is
always…..
8
121A rational number between ( sqrt{2} ) and ( sqrt{3} )
is :
A ( cdot frac{3}{2} )
B. ( frac{2}{3} )
c. 1
D. 5
8
122Simplify 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
123Fill 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
126Simplify 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
127Rational 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
128The 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
129The rational numbers whose absolute value is ( frac{4}{3}, ) is
( A cdot frac{8}{6} )
в. ( frac{16}{9} )
( c .1 )
D. –
7
130Difference of 99.999 and 100 is
A. 1.11
B. 1.000
( c .0 .00 )
D. 0.01
7
131The ( ldots ). whional number and its
reciprocal is 1
A. sum
B. difference
c. product
D. quotient
8
1322.
11 19 -90.-7
Evaluate: 14105 074
8
133Which 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
134Which of the following pairs represent the same rational number? ( frac{-7}{21} ) and ( frac{3}{9} )7
135An 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
136Which 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
137s
= = -10-31
1
2-85
(1) 5’9’9
-2 -8 -5
-2 -8.5
8
1383.
Find four rational numbers between
– and
8
139Sum 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
140The 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
141Write 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
143Rational numbers are closed under
substraction.
A. True
B. False
c. Cannot be determined
D. None
8
144The 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
145The value of ( (625)^{0.16} times(625)^{0.09} ) is
( A cdot 4 )
B. 5
c. 25
D. 625
8
1466. Represent 3 on the number line.8
1475.
Find three rational numbers between 0 and 0.2
8
148Evaluate each of the following:
( frac{-4}{13}-frac{-5}{26}=frac{x}{26} ) what is ‘x’?
7
149Suppose a pool begins with a population of only 1 bacterium. What would be the mass of the population
after 30 hours?
7
150a. Write additive inverse of ( frac{2}{8} ) and ( frac{-6}{-5} )
b. Write multiplicative inverse of
( -13 a n d frac{-13}{19} )
8
1515.
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
152Verify 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
153One 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
154Find the difference
between 3.477773 .47777 and 2.85888
8
155Which 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
1564. For * — and = verify that -(x+y)= (x) + (4)
4.
For X = = and y = = verify that -(x+y)=(-x)+(y)
8
157Fill in the blanks:
( frac{-9}{14}+ldots . .=-1 . ) Hence find the sum of the numerator and denominator so
obtained.
7
158The value of
WIN
(b)
S
10
©
(d)
8
1594.
If – is a rational number, then y is always a whole
number.
8
1605. Multiply
by the reciprocal of 16
8
161is the additive inverse of ( frac{-3}{11} )
A ( cdot frac{-3}{11} )
в. ( frac{11}{3} )
c. -1
D. ( frac{3}{11} )
8
162Name the property indicated in the following:
( frac{22}{23} cdot frac{23}{22}=1 )
8
163Which number line correctly shows the
rational number ( left(-frac{2}{9}+frac{1}{9}right) ? )
( A )
B.
( c )
( D )
7
1645. If x= =
then verify
N
xx(y−z)=(x xy)-(x ^z)
8
165The rational number that is equal to its
negative.
8
166Find 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
167Let 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
1689.
For any rational number a (a0), a =(-a)=……
and -1
8
169Write 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
171Arrange ( -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
172Multiplicative inverse of ( 2 frac{2}{7} ) is 2.2
A. True
B. False
c. cannot say
D. None
8
17310. Which of the following is false?
-5
– 7
(6)
+
(d)
8
9
7
11
7
11
8
9
8
174Fill in the blank: ( (-12)+left(4+frac{1}{8}right)= ) ( [(-12)+ldots . .]+frac{1}{8} )
A. (-12)
B. 4
c. 1
D.
8
175یہ ادا8
176

+
5
(
8
177Find 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
178Which of the following pairs represent the same rational number?
( frac{-2}{-3} ) and ( frac{2}{3} )
7
17960
7.
Choose the rational number which does not lie between
rational numbers-and-
rational numbers
(b) To
(d)
20
28
8
180Write five rational numbers which are
smaller than 2
8
181Fill 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
182Simplify ( (-90) times 52+(-52) times(-25) )
using a suitable frequency.
8
183Subtract the first rational number from
the second in each of the following:
( frac{1}{4}, frac{-3}{8} )
7
184Add the following rational numbers:
( frac{31}{-4} ) and ( frac{-5}{8} )
7
1853.
A rational number between
(b) 0.29
(d) All of these
8
1863.
can’t be expressed as rational number having
denominator 5 beacuse 5 is not the multiple of –
8
187Tuilplanon)
6.
Identify the rational number which is different from the
2 4 11
other three :
Explain your reasoning.
8
188Write the rational numbers that are
equal to their reciprocals.
7
189is the only rational number which is equal to its additive inverse.
A .
B. – 1
c. 0
D. ( frac{1}{2} )
8
190What 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
191se
up 13
16
the multiplicative inverse of -1-? Why or why not?
8
192Evaluate each of the following:
( frac{13}{15}-frac{12}{25} ) is ( frac{x}{75} ) find ‘x’
7
193The 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
1941.
Verify the distributive property xx (y +z)=xy + xz where
-4 1 -7
and write the denominator of
(x+y) xz.
8
195Compare ( 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
196Write 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
198For 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
1995.
Every integer is a rational number.
8
200The 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
2012. The rational numbers and
on the number line.
are on opposite sides of 0
8
202Which 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
203The 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
204Find 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
205Prove that the associative property hold true for the addition ( left(frac{7}{8}+frac{2}{5}right)+frac{8}{3} )8
206The 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
207Standard 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
208Find 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
209What is the multiplicative inverse of -6
( ? )
A. -6
B. 6
c. ( frac{-1}{6} )
D. ( frac{1}{6} )
8
210Find the multiplicative inverse of the following.
()-1
8
211Fill in the blanks:
( frac{-mathbf{7}}{mathbf{9}}+ldots ldots=3 . ) Hence find the sum of
the numerator and denominator so
obtained.
7
212Check the commutative property of multiplication for ( frac{-mathbf{7}}{mathbf{1 3}}, frac{mathbf{2 5}}{mathbf{2 7}} )8
2138.
If
=
then x = …………..
5
X
8
2142. Fil in blank
2.

Fill in blank:
8
215The additive identify of rational number
is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
( D )
8
216Which 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
217Write 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
218Which 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
219What 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
220How many one-fourths need to be 1 added to ( 2 frac{1}{4} ) to make ( 4 ? )
A . 3
B. 4
c. 5
D.
7
221Which 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
22210. A rational number between8
223Find 10 rational numbers between8
224If . med from the collection
of rational numbers, then they are closed under division.
A .2
B.
( c cdot 0 )
D. –
8
2259.
Verify the property :xx (y+z)=xxy+xx z by taking:
5
8
22610. Use the distributivity of multiplication of rational numbers
over addition to simplify
35
10
10
X
1
5
one
cm [16 ]
3
-40
8
227Arrange 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
2282.
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
2291.
The product of two rational numbers is 63. If one of the
40
number is
, find the other number.
8
230Write four more rational numbers in
each of the following patterns:
( frac{-1}{6}, frac{2}{-12}, frac{3}{-18}, frac{4}{-24}, dots )
7
231Find the additive inverse of: ( sqrt{5} )8
232If ( 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
233Number should be added top ( frac{-5}{7} ) to get ( frac{-2}{3} ) is ( frac{1}{x} . ) Find ‘x?7
234Solve
( frac{-3}{5}+frac{-12}{20} )
8
235USICUPIUCHULU, U
UPI
5.
The number 0 is ……… the reciprocal of any number.
8
236Write the multiplicate inverse of:
( -mathbf{5} frac{mathbf{6}}{7} )
8
237Find the value of ( (-12) times(+21) )
A ( .-2412 )
B . -242
( mathbf{c} .-252 )
D. +252
7
238The identity elements with respect to multiplication in integers is
A .
B. – –
c. 0
D. none
8
2395.
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
240Write 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
241Write 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
243If ( a=3+sqrt{23}, ) then find ( frac{-14}{a} )7
2442.
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
245Identify the property in the following
statements:
( mathbf{2}+(mathbf{3}+mathbf{4})=(mathbf{2}+mathbf{3})+mathbf{4} )
8
246Check the commutative property of multiplication for ( frac{mathbf{2 2}}{mathbf{4}}, frac{mathbf{3}}{mathbf{4}} )8
2472.
Simplify:
su (7-9-6-3-6-9
8
248Sum 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
249Arrange 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
250Arrange 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
251If 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
252Fill 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
253The sum of two numbers is ( frac{-4}{3} . ) If one of
the numbers is ( -5, ) find the other
7
254Using 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
255Fill 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
256The 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
257Which 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
258Using appropriate properties, find
2
8
259Find the unknown number: ( _{—}+frac{3}{7}=frac{3}{7} )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot frac{3}{7} )
D.
7
260Re-arrange suitably and find the sum in
each of the following:
( frac{-6}{7}+frac{-5}{6}+frac{-4}{9}+frac{-15}{7} )
7
261Which 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
262Which 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
263Every rational number is
A. A natural number
B. An integer
C. A real number
D. A whole number
8
2649.
The sum of the additive inverse and multiplicative inverse
of 2 is:
(b) =
NIT NIw
Wh: 1 fmful
8
2651.
The sum of two rational numbers is
. If one of the numbers is
-, find the other.
20
8
266Express 1.4191919 ….. in the form of ( frac{p}{q} )
where ( p ) and ( q ) are integer and ( q neq 0 )
8

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