RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1E.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q1.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q1.2

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q2.3

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q3.4

Question 4.
Solution:
Product of two numbers = – 9
one number = – 12
Let second number = x
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q4.1

Question 5.
Solution:
Product of two rational numbers = \(\\ \frac { -16}{ 9 } \)
One number = \(\\ \frac { -4 }{ 3 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q5.1

Question 6.
Solution:
Let x be multiplied
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q6.1

Question 7.
Solution:
Let x be multiplied
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q7.1

Question 8.
Solution:
Let required number = x
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q8.1

Question 9.
Solution:
sum of \(\\ \frac { 13 }{ 5 } \) and \(\\ \frac { -12 }{ 7 } \)
= \(\\ \frac { 13 }{ 5 } \) + \(\\ \frac { -12 }{ 7 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q9.1

Question 10.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q10.1

Question 11.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1E Q11.3

Question 12.
Solution:
(i) No, not always closed under division.
(ii) No, not always commutative.
(iii) No, not always associative.
(iv) No. It is not possible to divide any number by zero.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1E are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1D.

Other Exercises

Question 1.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 1.4

Question 2.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 2.3

Question 3.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.4
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 3.5

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 4.1

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 5.1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 5.2

Question 6.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 6.1

Question 7.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.4
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 7.5

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 8.2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1D 8.3

Question 9.
Solution:
(i) The product of a rational number and its reciprocal is 1.
(ii) Zero has no reciprocal.
(iii) The numbers 1 and -1 are their own reciprocal.
(iv) Zero is not the reciprocal of any number.
(v) The reciprocal of a, where a≠0, is \(\\ \frac { 1 }{ a } \)
(vi) The reciprocal of \(\\ \frac { 1 }{ a } \) where a≠0 is a
(vii) The reciprocal of a positive rational number is positive.
(viii) The reciprocal of a negative rational number is negative.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1D are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1C.

Other Exercises

Question 1.
Solution:
(i) \(\\ \frac { -2 }{ 5 } \) + \(\\ \frac { 4 }{ 5 } \)
= \(\\ \frac { -2+4 }{ 5 } \) = \(\\ \frac { 2 }{ 5 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 1

Question 2.
Solution:
(i) \(\frac { 3 }{ 4 } +\left( \frac { -3 }{ 5 } \right) \)
\(\frac { 15+\left( -12 \right) }{ 20 } =\frac { 15-12 }{ 20 } =\frac { 3 }{ 20 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 4

Question 3.
Solution:
(i) L.H.S = \(\\ \frac { -12 }{ 5 } \) + \(\\ \frac { 2 }{ 7 } \)
= \(\\ \frac { -84+10 }{ 35 } \) = \(\\ \frac { -74 }{ 35 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 5
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 6
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 7

Question 4.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 8
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 9
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 10
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 11
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 12

Question 5.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 13
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 14

Question 6.
Solution:
We know that additive inverse of \(\\ \frac { a }{ b } \) is \(\\ \frac { -a }{ b } \) and of \(\\ \frac { -a }{ b } \) is \(\\ \frac { a }{ b } \).
Therefore Additive inverse of
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 15
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 16

Question 7.
Solution:
(i) \(\\ \frac { 3 }{ 4 } \) from \(\\ \frac { 1 }{ 3 } \) or \(\\ \frac { 1 }{ 3 } \) – \(\\ \frac { 3 }{ 4 } \)
= \(\\ \frac { 4-9 }{ 12 } \) = \(\\ \frac { -5 }{ 12 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 17
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 18
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 19
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 20

Question 8.
Solution:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 21
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 22
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 23

Question 9.
Solution:
Sum of two numbers = – 2
one number = \(\\ \frac { -14 }{ 5 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 24

Question 10.
Solution:
Sum of two numbers = \(\\ \frac { -1 }{ 2 } \)
One number = \(\\ \frac { 5 }{ 6 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 25

Question 11.
Solution:
Sum of two numbers = \(\\ \frac { -3 }{ 2 } \)
one number = \(\\ \frac { -5 }{ 8 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 26

Question 12.
Solution:
Sum of two numbers = \(\\ \frac { 5 }{ 7 } \)
One number = – 1
Second number = \(\\ \frac { 5 }{ 7 } \) – ( – 1)
= \(\\ \frac { 5 }{ 7 } \) + \(\\ \frac { 1 }{ 1 } \)
\(\\ \frac { 5+7 }{ 7 } \) = \(\\ \frac { 12 }{ 7 } \)

Question 13.
Solution:
Difference of two numbers = \(\\ \frac { -1 }{ 6 } \)
One number = \(\\ \frac { -2 }{ 3 } \)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1C 27

Question 14.
Solution:
(i) 0 is the rational number.
(ii) Yes, the difference of two rational numbers is also rational.
(iii) Yes, addition is commutative.
(iv) Yes, addition associative.
(v) No, subtraction is not commutative.
(vi) No, subtraction is not associative.
(vii) The number itself.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1C are helpful to complete your math homework.

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RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1B.

Other Exercises

Question 1.
Solution:
(i) \(\\ \frac { 1 }{ 3 } \)
Draw a line and take a point O on it.
Let it represent 0.
From O, set off unit OA, AB to right side of O, representing integers 1, 2 respectively.
Now, divide OA into 3 equal parts and take one part OR Which is \(\\ \frac { 1 }{ 3 } \) as shown below on the line.
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 2
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 3
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 4
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 5
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 6
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 7

Question 2.
Solution:
(i) \(\\ \frac { -1 }{ 3 } \)
Draw a line and take a point O on it.
Let it represent O.
Now, from O, take OA, AB to the left of O, representing integers – 1, – 2 respectively. Divide OA into three equal parts and take one part.
Then OP = \(\\ \frac { -1 }{ 3 } \) which is shown on the number line as given below :
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 8
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 9
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 10
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 11
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 12
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 13
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1B 14

Question 3.
Solution:
(i) True, as the numbers left of O are negative.
(ii) False, as the numbers right of O are positive and \(\\ \frac { -12 }{ 7 } \) is negative.
(iii) True, as \(\\ \frac { 1 }{ 3 } \) is positive and \(\\ \frac { -5 }{ 2 } \) is negative.
(iv) False \(\\ \frac { -18 }{ -13 } \) = \(\\ \frac { 18 }{ 13 } \) which is positive and positive numbers lie on the right of O.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A

RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1A.

Other Exercises

Question 1.
Solution:
(i) 20 = 5 x 4
\(\\ \frac { -3 }{ 5 } \) = \(\\ \frac { -3X4 }{ 5X4 } \)
(multiplying numerator and denominator by 4)
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 1
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 2

You can also Download NCERT Solutions for Class 8 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Question 2.
Solution:
98 = 7 x 14
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 3

Question 3.
Solution:
60 = 5 x 12
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 4

Question 4.
Solution:
(i) \(\\ \frac { -12 }{ 30 } \)
H.C.F of 12 and 30 = 6
Dividing the numerator and denominator
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 5
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 6

Question 5.
Solution:
(i) \(\\ \frac { 3 }{ 8 } \) or 0
We know that every positive rational number is greater than 0.
∴\(\\ \frac { 3 }{ 8 } \) is greater
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 7
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 8
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 9
and clearly \(\frac{-1}{2} \) is greater. Ans.

Question 6.
Solution:
(i) \(\\ \frac { -4 }{ 3 } \) or \(\\ \frac { 8 }{ 7 } \)
Her,denominator are not same
LCM of 3 and 7 = 21
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 10
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 11
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 12
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 13
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 14

Question 7.
Solution:
(i) Between \(\\ \frac { -3 }{ 7 } \) and \(\\ \frac { 6 }{ -13 } \)
or \(\\ \frac { -3 }{ 7 } \) and \(\\ \frac { -6 }{ 13 } \)
LCM of 7 and 13 = 91
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 15
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 16
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 17
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 18
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 19

Question 8.
Solution:
Among, \(\\ \frac { 4 }{ -9 } \),\(\\ \frac { -5 }{ 12 } \),\(\\ \frac { 7 }{ -18 } \),\(\\ \frac { -2 }{ 3 } \) making their denominator positive,we get:
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 20
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 21
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 22
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 23
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 24
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 25

Question 9.
Solution:
(i)Among – 2,\(\\ \frac { -13 }{ 6 } \),\(\\ \frac { 8 }{ -3 } \),\(\\ \frac { 1 }{ 3 } \)
Making the denominator of \(\\ \frac { 8 }{ -3 } \) as
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 26
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 27
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 28
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 29
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 30
RS Aggarwal Class 8 Solutions Chapter 1 Rational Numbers Ex 1A 31

Question 10.
Solution:
(i) True, as the set of whole numbers is a subset of the set of rational numbers
(ii) True, as the set of integers is a subset of the set of rational numbers.
(iii) False, as 0 is a whole number and set of the whole number is a subset of rational numbers
∴ 0 is also a rational number.

Hope given RS Aggarwal Solutions Class 8 Chapter 1 Rational Numbers Ex 1A are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.