NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers are part of NCERT Exemplar Class 8 Maths. Here we have given NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers.

NCERT  Exemplar Class 8 Maths Chapter 1 Rational Numbers

Multiple Choice Questions
Question . 1 A number which can be expressed as \(\frac { p }{ q }\) , where p and q are integers and \( q\neq 0\) is
(a) natural number (b) whole number
(c) integer (d) rational number
Solution. (d) A number which can be expressed as \(\frac { p }{ q }\), where p and q are integers and \( q\neq 0\) is a rational number.

Question . 2 A number of the form \(\frac { p }{ q }\) is said to be a rational number, if
(a) p, q are integers (b) p, q are integers and \( q\neq 0\)
(c) p, q are integers and \( p\neq 0\) (d) p, q are integers and \( p\neq 0\), also \( q\neq 0\)
Solution. (b) A number of the form \(\frac { p }{ q }\) is said to be a rational number, if p and q are integers and

Question . 3 The numerical expression \( \frac { 3 }{ 8 } +\frac { (-5) }{ 7 } =\frac { -19 }{ 56 }\) shows that
(a)rational numbers are closed under addition
(b) rational numbers are not closed under addition
(c) rational numbers are closed under multiplication
(d) addition of rational numbers is not commutative
Solution. (b) We have \( \frac { 3 }{ 8 } +\frac { (-5) }{ 7 } =\frac { -19 }{ 56 }\)
Show that rational numbers are closed under addition.
[\(\frac { 3 }{ 8 }\) and\( \frac { -5 }{ 7 }\) are rational numbers and their addition is \(\frac { -19 }{ 56 }\) which is also a rational number]
Note The sum of any two rational numbers is always a rational number.

Question . 4 Which of the following is not true?
(a) rational numbers are closed under addition
(b) rational numbers are closed under subtraction
(c) rational numbers are closed under multiplication
(d) rational numbers are closed under division
Solution. (d) Rational numbers are not closed under division.
As, 1 and 0 are the rational numbers but \( \frac { 1 }{ 0 }\) is not defined.

Question . 5 \(-\frac { 3 }{ 8 } +\frac { 1 }{ 7 } =\frac { 1 }{ 7 } +[\frac { -3 }{ 8 } ]\) is an example to show that
(a) addition of rational numbers is commutative
(b) rational numbers are closed under addition
(c) addition of rational numbers is associative
(d) rational numbers are distributive under addition
Solution.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-1
Clearly, a + b = b + a
So, addition is communication for rational numbers
Question . 6 Which of the following expressions shows that rational numbers are associative under multiplication.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-2
Solution.
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-3
So, a x (b  x c) = (a x b) x c
Hence, the given expression shows that rational numbers are associative under multiplication.

Question . 7 Zero (0) is
(a) the identity for addition of rational numbers
(b) the identity for subtraction of rational numbers
(c) the identity for multiplication of rational numbers
(d) the identity for  division of rational numbers
Solution . (a) Zero (0) is the identity for addition of rational numbers.
That means,
If a is a rational number.
Then, a+0=0+a = a
Note Zero (0) is also the additive identity for integers and whole number as well.

Question . 8 One (1) is
(a) the identity for addition of rational numbers
(b) the identity for subtraction of rational numbers
(c) the identity for multiplication of rational numbers
(d) the identity for division of rational numbers
Solution . (c) One (1) is the identity for multiplication of rational numbers.
That means,
If a is  a rational number.
Then, a-1 = 1-a = a
Note One (1) is the multiplication identity for integers and whole number also.

Question . 9 The additive inverse  of \(\frac { -7 }{ 19 }\) is
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-4

Solution . (b) We know that, if a and b are the additive inverse of each other, then a + b = 0
Suppose, x is the additive inverse of \(\frac { -7 }{ 19 }\)
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-5

Question . 10 Multiplicative inverse of a negative rational number is
(a) a positive rational number (b) a negative rational number
(c) 0 (d) 1
Solution. (b) We know that, the product of two rational numbers is 1, taken they are multiplication inverse of each other, e.g.
Suppose, p is negative rational number, i.e.
\(\frac { 1 }{ p }\) is the  multiplicative inverse of-p, then, -p x \(\frac { 1 }{ -p }\) = 1
Hence, multiplicative inverse of a negative rational number is a negative rational number.

Question. 11 If x + 0 = 0 + x = x, which is rational number, then 0 is called
(a) identity for addition of rational numbers
(b) additive inverse of  x
(c) multiplicative inverse of x
(d) reciprocal of x
Solution . (a) We know that, the sum of any rational number and zero (0) is the rational number itself.
Now, x + 0 = 0+ x= x, which is a rational number, then 0 is called identity for addition of rational numbers.

Question . 12 To get the product 1,  we should multiply \( \frac { 8 }{ 21 }\) by
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-6

Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-7
Question . 13 – (-x) is same as
(a)-x (b)x (c)\(\frac { 1 }{ x }\) (d)\(\frac { -1 }{ x }\)
Solution . (b) -(-x) = x
Negative of negative rational number is equal to positive rational number.

Question . 14 The multiplicative inverse of \( -1\frac { 1 }{ 7 }\) is
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-8

Solution . (d) We know that, if the product of two rational numbers is 1, then they are multiplicative inverse of each other.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-9

Question . 15 If x is any rational number, then x + 0 is equal to
(a)x (b) 0 (c)-x (d) Not defined
Solution . (a) If x is any rational number, then x + 0 = x [0 is the additive identity]

Question . 16  The reciprocal of 1 is ;
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (a) The reciprocal of 1 is the number itself.

Question . 17  The reciprocal of -1 is
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (b) The reciprocal of -1 is the number itself.

Question . 18 The reciprocal of 0 is
(a) 1 (b) -1 (c) 0 (d) Not defined
Solution . (d) The reciprocal of 0 is not defined.

Question . 19 The reciprocal of any rational number \(\frac { p }{ q }\) , where p and q are integers and \( q\neq 0\) is
(a)\(\frac { p }{ q }\) (b)1 (c)0 (d)\(\frac { q }{ p }\)
Solution . (d) The reciprocal of any rational number \(\frac { p }{ q }\), where p and q are integers and \( q\neq 0\) is \(\frac { q }{ p }\)

Question . 20 If y is the reciprocal of rational number x, then the reciprocal of y will be
(a)x (b) y (c) \(\frac { x }{ y }\) (d) \(\frac { y }{ x }\)
Solution . (a) If y be the reciprocal of rational number x, i.e. y = \(\frac { 1 }{ x }\) or x = \(\frac { 1 }{ y }\).
Hence, the reciprocal of y will be x.

Question .21
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-10
Soiution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-11

Question . 22 Which of the following is an example of distributive property of multiplication over addition for rational numbers.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-12

Solution . We know that, the distributive property of multiplication over addition for rational numbers can be expressed as a x (b + c) = ab + ac, where a, b and c are rational numbers.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-13
is the example of distributive property of multiplication over addition for rational numbers.

Question . 23 Between two given rational numbers, we can find
(a) one and only one rational number
(b) only two rational numbers
(c) only ten rational numbers
(d) infinitely many rational numbers
Solution . (d) We can find infinite many rational numbers between two given rational numbers.

Question .24

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-14
(a) Between x and y
(b) Less than x and y both
(c) Greater than x and y both
(d) Less than x but greater than y
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-15

Question . 25 Which of the following statements is always true?NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-16

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-17

Fill in the Blanks
In questions 26 to 47, fill in the blanks to make the statements true.
Question . 26 The equivalent of \( \frac { 5 }{ 7 } \) whose numerator is 45, is —.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-18

Question . 27 The equivalent rational number of \( \frac { 7 }{ 9} \) , whose denominator is 45 is——————.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-19

Question . 28 Between the numbers \(\frac {15 }{ 20} \) and \(\frac { 35 }{ 40} \), the greater number is———————-.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-20
Question . 29 The reciprocal of a positive rational number is—————.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-21
Question . 30 The reciprocal of a negative rational number is——————–.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-22

Question. 31 Zero has————reciprocal.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-23

Question. 32 The numbers ————–and————–are their own reciprocal.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-24

Question . 33 If y is the reciprocal of x, then the reciprocal of \({ y }^{ 2 }\) in terms of x will be—————-.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-25
= x2

Question . 34
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-26
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-27

Question . 35

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-28

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-29

Question . 36 The negative of 1 is—————-.
Solution . -1 The negative of 1 is -1.

Question . 37
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-30

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-31

Question . 38 \(\frac { -5 }{ 7 }\) is———————than -3.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-32

Question . 39 There are rational numbers between any two rational numbers.
Solution . Infinite
There are infinite rational numbers between any two rational numbers.

Question . 40 The rational numbers \(\frac { 1 }{ 3 }\) and \(\frac { -1 }{ 3 }\) are on the sides of zero on the number line.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-33

Question . 41 The negative of a negative rational number is always a—————-rational
number.
Solution. positive
Let x be a positive rational number.
Then, – x be a negative rational number.
Now, negative of a negative rational number = – (- x)= x =positive rational number.

Question . 42 Rational numbers can be added or multiplied in any————-.
Solution . order
Rational numbers can be added or multiplied in any order and this concept is known as commutative property.

Question . 43 The reciprocal of \(\frac { -5 }{ 7 }\) is——————.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-34

Question . 44 The multiplicative inverse of \(\frac { 4 }{ 3 }\) is———–.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-35
Question . 45 The rational number 10.11 in the form \(\frac { p }{ q }\) is ——–.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-36

Question .46

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-37

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-38

Question . 47 The two rational numbers lying between -2 and -5 with denominator as 1 are———–and————.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-39

True/False
In questions 48 to 99, state whether the given statements are True or False.
Question . 48 If \(\frac { x }{ y }\)is a rational number, then y is always a whole number.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-40
Question . 49 If \(\frac { p }{ q }\) is a rational number, then p Cannot be equal to zero.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-41

Question . 50 If \(\frac { r }{ s }\) is a rational number, then s cannot be equal to zero.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-42

Question . 51 \(\frac { 5 }{ 6 }\) lies between \(\frac { 2 }{ 3 }\) and 1.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-43

Question . 52 \(\frac { 5 }{ 10 }\) lies between \(\frac { 1 }{ 2 }\) and 1.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-44
Question . 53 \(\frac { 5 }{ 10 }\) lies between -3 and 4.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-45

Question . 54 \(\frac { 9 }{ 6 }\) lies between 1 and 2.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-46

Question . 55 If \(a\neq 0\) the multiplicative inverse of \(\frac { a }{ b }\) is \(\frac { b }{ a }\) .
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-47

Question . 56 The multiplicative inverse of \(\frac { -3 }{ 5 }\) is \(\frac { 5 }{ 3 }\) .
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-48

Question . 57 The additive inverse of \(\frac { 1 }{ 2 }\) is -2.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-49

Question . 58

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-50

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-51

Question . 59 For every rational number x, x + 1 = x.
Solution . False
For every rational number , x + 0 = x

Question . 60
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-52
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-53

Question . 61 The reciprocal of a non-zero rational number \(\frac { q }{ p }\) is the rational number \(\frac { q }{ p }\).
Solution .False
The reciprocal of a non-zero rational number \(\frac { q }{ p }\) . is the rational number\(\frac { p }{ q }\)

Question . 62 If x + y = 0, then -y is known as the negative of x, where x and y are rational numbers.
Solution . False
If x and y are rational numbers and x+ y = 0.
Then, y is known as the negative of x.

Question . 63 The negative of the negative of any rational number is the number itself.
Solution . True
Let x be a positive rational number. Then, -x be a negative rational number.
Now, negative of negative rational number = -(-x)= x = Positive rational number

Question . 64 The negative of 0 does not exist.
Solution . True
Since, zero is neither a positive integer nor a negative integer.

Question . 65 The negative of 1 is 1 itself.
Solution . False
The negative of 1 is -1.

Question . 66 For all rational numbers x and y,x-y = y- x
Solution . False
For all rational numbers x and y,
x-y = -(y-x)

Question . 67 For all rational numbers x and y, x x y = y x x.
Solution . True
For all rational numbers x and y,
x x y= y x x

Question . 68 For every rational number x, x x 0 = x.
Solution . False
For every rational number x,
x x 0 = 0

Question . 69 For every rational numbers x, y and z, x + (y x z) = (x + y) x (x + z)
Solution . False
For all rational numbers a, b and c.
a(b + c) = ab+ ac

Question . 70 For all rational numbers a, b and c,a (b + c) = ab + bc.
Solution . False
As, addition is not distributive over multiplication.

Question . 71 1 is the only number which is its own reciprocal.
Solution . False
Reciprocal of 1 is 1 and reciprocal of -1 is -1.

Question . 72 -1 is not the reciprocal of any rational number.
Solution . False
-1 is the reciprocal of -1.

Question . 73 For any rational number x, x + (-1) = – x.
Solution . False
For every rational number x,
x x (-1) = – x

Question . 74 For rational numbers x and y, if x < y, then x – y is a positive rational number.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-54

Question . 75 If x and y are negative rational numbers, then so is x + y.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-55
= -1

Question . 76 Between any two rational numbers there are exactly ten rational . numbers.
Solution . False
There are infinite rational numbers between any two rational numbers.

Question . 77 Rational numbers are closed under addition and multiplication but not under subtraction.
Solution . False
Rational numbers are closed under addition, subtraction and multiplication.

Question . 78 Subtraction of rational number is commutative.
Solution . False
Subtraction of rational numbers is not commutative, i.e. \(a-b\neq b-a\)
where, a and b are rational numbers.

Question . 79 \(-\frac { 3 }{ 4 }\) is smaller than -2 .
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-56

Question . 80 0 is a rational number.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-57

Question . 81 All positive rational numbers lie between 0 and 1000.
Solution . False
Infinite positive rational numbers lie on the right side of 0 on the number line.

Question. 82 The population of India in 2004-05 is a rational number.
Solution. True
The population of India in 2004-05 is a rational number.

Question. 83 There are countless rational numbers between \(-\frac { 5 }{ 6 }\) and \(-\frac { 8 }{ 9 }\).
Solution.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-58

Question. 84

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-59
Solution.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-60

Question. 85 The rational number \(-\frac { 57 }{ 23 }\) lies to the left of zero on the number line.
Solution. False
Since,\(-\frac { 57 }{ 23 }\) is a positive rational number.
So, it lies on the right of zero on the number line.

Question .86 The rational number \(-\frac { 7 }{ -4 }\) lies to the right of zero on the number line.
Solution . False
Since, \(-\frac { 7 }{ -4 }\) is a negative rational number.
So, it lies on the left of zero on the number line.

Question .87 The rational number \(-\frac { -8 }{ -3 }\) lies neither to the right nor to the left of zero on the number line.
Solution . False
\(-\frac { -8 }{ -3 }\) = \(-\frac { 8 }{ 3 }\) is a positive rational number.
Hence, it lies on the right of zero on the number line.

Question . 88 The rational numbers \(-\frac { 1 }{ 2 }\) and -1 are on the opposite sides of zero on the number tine.
Solution . True
Since, positive rational number and negative rational number are on the opposite sides of zero on the number line.’
Hence, \(-\frac { 1 }{ 2 }\) and -1 are on the opposite sides of zero on the number line.

Question . 89 Every fraction is a rational number.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-61

Question . 90 Every integer is a rational number.
Solution . True
Every integer is a rational number whose denominator remain 1.

Question . 91 The rational numbers can be represented on the number line.
Solution . True
The rational numbers can be represented on the number line.

Question . 92 The negative of a negative rational number is a positive rational number.
Solution . True
Let be a positive rational number.
Then, – x be the negative rational number.
Hence, negative of negative rational number = – (- x)= x = Positive rational number

Question . 93 If x and y are two rational numbers such that x > y, then x – y is always a positive rational number.
Solution . True
If x and y are two rational numbers such that x > y.
Then, there are three possible cases, i.e.
Case I x and y both are positive. ‘
Case II x is positive and y is negative.
Case III x and y both are negative.
In all three cases, x – y is always a positive rational number.

Question . 94 0 is the smallest rational number.
Solution . False
As the smallest rational number does not exist.

Question .95 Every whole number is an integer.
Solution .True
W (whole numbers) = {0,1,2, 3 }
Z (integers) = {…- 3, – 2, -1, 0,1,2, 3,…}
Every whole number is an integer, but every integer is not a whole number.

Question .96 Every whole number is a rational number.
Solution .True
Every whole number can be written in the form of \(-\frac { p }{ q }\), where p, q are integers and \(q\neq 0\).
Hence, every whole number is a rational number.

Question . 97 0 is whole number but it is not a rational number.
Solution . False
0 is a whole number and also a rational number.

Question . 98 The rational numbers \(-\frac { 1 }{ 2 }\)and \(-\frac -{ 5 }{ 2}\) are on the opposite sides of zero on the number line.
Solution . True
Positive rational number and negative rational number remain on opposite sides of zero on the number line.

Question .99 Rational numbers can be added (or multiplied) in any order
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-62
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-63

Question . 100 Solve the following, select the rational numbers from the list which are also the integers.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-64
Solution . From the given rational numbers, the numbers whose denominator is 1 and the numbers whose numerator is the multiple of denominator are the integers.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-65

Question . 101 Select those which can be written as a rational number with denominator 4 in their lowest form
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-66

Solution . From the given rational numbers, the number with denominator 4 in their lowest form is \(-\frac { 5 }{ -4 }\)

Question . 102 Using suitable rearrangement and find the sum
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-67
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-68

Question . 103 Verify – (-x) = x for

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-69

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-70

Question . 104 Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.
Solution . We know that, rational numbers are closed under addition, subtraction and multiplication. We can understand this from the following examples.
Rational numbers are closed under addition

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-71

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-72
But rational are not closed under division. If zero is excluded from the collection of rational numbers, then we can say that rational numbers are closed under division.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-73

Question . 105 Verify the property x + y = y + x of rational numbers by taking

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-74

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-75

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-76

Question . 106 Simplify each of the following by using suitable property. Also, name the property.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-77

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-78

Question . 107

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-79

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-80

Question . 108 Verify the property x x y = y x x of rational numbers by using

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-81

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-82

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-83

Question . 109 Verify the property x x (y x z)=i.(x x y) x z of rational numbers by usingNCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-84
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-85

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-86

Question . 110 Verify the property x x (y + z) = x x y + x x z of rational numbers by taking

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-87
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-88

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-89

Question . 111 Use the distributivity of multiplication of rational numbers over addition to simplifyNCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-90

Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-91

Question. 112 Simplify
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-92
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-93

Question. 113 Identify the rational number that does not belong with the other three. Explain your reasoning

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-94
Solution . 
does not belong with the other three. Since,−73 as it is smaller than -1 whereas rest of the numbers are greater than -1.

Question. 114 The cost of \( \frac { 19 }{ 4 }\) m of wire is Rs \( \frac { 171 }{ 2 }\) Find the cost of one metre of the wire.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-95

Question. 115 A train travels \( \frac { 1445 }{ 2 }\) km in \( \frac { 17 }{ 2 }\) h. Find the speed of the train in km/h.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-96

Question. 116 If 16 shirts of equal size can be made out of 24m of cloth, how much cloth is needed for making one shirt?
Solution . If 16 shirts are to be made by cloth of 24 m
Then, 1 shirt is to be made by cloth of = \( \frac { 24 }{ 16 }\) m = \( \frac { 3 }{ 2 }\) m = 1.5 m
Hence, 1.5 m cloth is needed for making one shirt.
Question. 117 \( \frac { 7 }{ 11 }\) of all the money in Hamid’s bank account is Rs 77000. How much money does Hamid have in his bank account?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-97

Question. 118 A 117\( \frac { 1 }{ 3 }\) m long rope is cut into equal pieces measuring 7\( \frac { 1 }{ 3 }\) m each. How many such small pieces are these?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-98

Question. 119 \( \frac { 1 }{ 6 }\) of the class students are above average, \( \frac { 1 }{ 4 }\) are average and rest are below average. If there are 48 students in all, how many students are below average in the class?
Solution . Number of above average students = \( \frac { 1 }{ 6 }\) of the class students
Number of average students = \( \frac { 1 }{ 4 }\)of the class students
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-99

Question. 120 \( \frac { 2 }{ 5 }\)of total number of students of a school come by car while \( \frac { 1 }{ 4 }\) of students come by bus to school. All the other students walk to school of which \( \frac { 1 }{ 3 }\)walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in that school?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-100
Question. 121 Huma, Hubna and Seema received a total of Rs 2016 as monthly allowance from their mother such that Seema gets \( \frac { 1 }{ 2 }\) of what Hubna gets and Huma gets 1\( \frac { 2 }{ 3 }\) times Seema’s share. How much money do the three sisters get individually?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-101
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-102

Question. 122 A mother and her two daughters got a room constructed for Rs 62000. The elder daughter contributes \( \frac { 3 }{ 8 }\)of her mother’s contribution while the younger daughter contributes \( \frac { 1 }{ 2 }\)of her mother’s share. How much do the three contribute individually?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-103
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-104

Question. 123 Tell which property allows you to compare
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-105
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-106

Question. 124 Name the property used in each of the following:NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-107

Solution . (i) Commutative property over multiplication
(ii) Distributive property over addition
(iii) Associative property over addition
(iv) Existence of additive identity
(v) Existence of multiplicative identity

Question. 125 Find the multiplicative inverse of(i)-1\( \frac { 1 }{ 8 }\) (ii)3 \( \frac { 1 }{ 3 }\)
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-108

Question. 126 Arrange the numbers is \( \frac { 1 }{ 4 }\) , \( \frac { 13 }{ 16 }\) , \( \frac { 5 }{ 8 }\)in the descending order.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-109

Question. 127 The product of two rational numbers is \( \frac { -14 }{ 27 }\) If one of the numbers be \( \frac { 7 }{ 9 }\) find the other.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-110

Question. 128 By what numbers should we multiply \( \frac { -15 }{ 20 }\) so that the product may be \( \frac { -5 }{ 7 }\) ?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-111

Question. 129 By what number should we multiply \( \frac { -8 }{ 13 }\) so that the product may be 24?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-112

Question. 130 The product of two rational numbers is -7. If one of the number is -5, find the other?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-113

Question. 131 Can you find a rational number whose multiplicative inverse is -1?
Solution . No, we cannot find a rational number whose multiplicative inverse is -1.

Question. 132 Find five rational numbers between 0 and 1.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-114

Question. 133 Find the two rational numbers whose absolute value is \( \frac { 1 }{ 5 }\) .
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-115

Question. 134 From a rope 40 m long, pieces of equal size are cut. If the length of one piece is \( \frac { 10 }{ 3 }\) m, find the number of such pieces.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-116

Question. 135 5 \( \frac { 1 }{ 2 }\) m long rope is cut into 12 equal pieces. What is the length of each piece?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-117

Question. 136 Write the following rational numbers in the descending order.
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-118
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-119

Question. 137 Find
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-120
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-121

Question. 138 On a winter day the temperature at a place in Himachal Pradesh was -16°C. Convert it in degree Fahrenheit (°F) by using the formula
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-122
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-123

Question. 139 Find the sum of additive inverse and multiplicative inverse of 7.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-124

Question. 140 Find the product of additive inverse and multiplicative inverse of \( -\frac { 1 }{ 3 }\).
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-125

Question. 141 The diagram shows the wingspans of different species of birds. Use the diagram to answer the question given below

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-126
(a) How much longer is the wingspan of an Albatross than the wingspan of a Sea gull?
(b) How much longer is the wingspan of a Golden eagle than the wingspan of a Blue jay?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-127

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-128

Question. 142 Shalini has to cut out circles of diameter 1 \( -\frac { 1 }{ 4 }\) cm from an aluminium strip of dimensions 8\( -\frac { 3 }{ 4 }\) cm by 1 \( -\frac { 1 }{ 4 }\) cm. How many full circles can Shalini cut? Also, calculate the wastage of the aluminium strip.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-129
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-130

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-131

Question. 143 One fruit salad recipe requires \( -\frac { 1 }{ 2 }\) cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is 1 equivalent to \( -\frac { 1 }{ 16 }\) cup, how much more sugar does the first recipe require?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-132

Question. 144 Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-133
(a) How farther did Soni hop than Nancy?
(b) What is the total distance covered by Seema and Megha?
(c) Who walked farther, Nancy or Megha?
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-134

Question. 145 The table given below shows the distances, in kilo metres, between four villages of a state. To find the distance between two villages, locate the square, where the row for one village and the column for the other village intersect.

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-135
(a) Compare the distance between Himgaon and Rawalpur to Sonapur and Ramgarh?
(b) If you drove from Himgaon to Sonapur and then from Sonapur to Rawalpur, how far would you drive?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-136

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-137

Question. 146 The table shows the portion of some common materials that are recycled.NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-138

(a) Is the rational number expressing the amount of paper recycled more than \( -\frac { 1 }{ 2 }\) or less than \( -\frac { 1 }{ 2 }\) ?
(b) Which items have a Recycled amount less than \( -\frac { 1 }{ 2 }\) ?
(c) Is the quantity of aluminium fans recycled more (or less) than half of the quantity of aluminium cans?
(d) Arrange the rate of recycling the materials from the greatest to the smallest.
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-139

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-140

Question. 147 The overall width in cm of several wide-screen televisions are 97.28 cm,98\( -\frac { 4 }{ 9 }\) cm, 98\( -\frac { 1 }{ 25 }\) cm and 97.94 cm. Express these numbers as rational numbers in the form \( -\frac { p }{ q }\) and arrange the widths in ascending order.
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-141

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-142

Question. 148 Roller coaster at an amusement park is \( -\frac { 2 }{ 3 }\) m high. If a new roller coaster is built that is \( -\frac { 3 }{ 5 }\) times the height of the existing coaster, what will be the height of the new roller coaster?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-143

Question. 149 Here is a table which gives the information about the total rainfall for several months compared to the average monthly rains of a town. Write each decimal in the form of rational number \( -\frac { p }{ q }\) .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-144

Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-145

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-146

Question. 150 The average life expectancies of males for several states are shown in the table. Express each decimal in the form \( -\frac { p }{ q }\) and arrange the states from the least to the greatest male life expectancy.
State-wise data are included below; more indicators can be found in the “FACTFILE” section on the homepage for each state.
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-147
Source Registrar General of India (2003) SRS Based Abridged Lefe Tables. SRS Analytical Studies, Report No. 3 of 2003, New Delhi: Registrar General of India.
The data are for the 1995-99 period; states subsequently divided are therefore included in their pre-partition states (Chhatisgarh in MP, Uttaranchal in UP and Jharkhand in Bihar)
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-148
Arrangement of the states from the least to the greatest male life expectancy, Haryana, Tamil Nadu, West Bengal, Karnataka, Gujarat, AndhraPradesh, Bihar, Rajasthan, Uttar Pradesh, Orissa, Assam, Madhya Pradesh.

Question. 151 A skirt that is 35 \( \frac { 7 }{ 8 }\) cm long has a hem of 3\( \frac { 1 }{ 8 }\) cm. How tong will the skirt . be if the hem is let down?
Solution .
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-149

Question. 152 Manavi and Kuber each receives an equal allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If allowance of each is Rs 1260, find the amount left with each.
NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-150
Solution .

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-151

NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers-152

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