NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1.

BoardCBSE
TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 1
Chapter NameRational Numbers
ExerciseEx 1.1
Number of Questions Solved11
CategoryNCERT Solutions

NCERT Solutions for Class 8 Maths will help you to score more marks in your CBSE board Examination.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1

Question 1.
Using appropriate properties find:
(i) \(-\frac { 2 }{ 5 } \times \frac { 3 }{ 5 } +\frac { 5 }{ 2 } -\frac { 3 }{ 5 } \times \frac { 1 }{ 6 } \)
(ii) \(\frac { 2 }{ 5 } \times \left( -\frac { 3 }{ 7 } \right) -\frac { 1 }{ 6 } \times \frac { 3 }{ 2 } +\frac { 1 }{ 14 } \times \frac { 2 }{ 5 } \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 1
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 2
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 3

Question 2.
Write the additive inverse of each of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 4
Solution.
(i) \(\frac { 2 }{ 8 } \)
Additive inverse of \(\frac { 2 }{ 8 } \) is \(\frac { 2 }{ 8 } \)

(ii) \(-\frac { 5 }{ 9 } \)
\(\frac { -6 }{ -5 } =\frac { 6 }{ 5 } \)
Additive inverse of \(\frac { -6 }{ -5 } \) is \(\frac { -6 }{ 5 } \)

(iii) \(\frac { -6 }{ -5 } \)
\(\frac { -6 }{ -5 } \)=\(\frac { 6 }{ 5 } \)
Additive inverse of \(\frac { -6 }{ -5 } \) is \(\frac { -6 }{ 5 } \)

(iv) \(\frac { 2 }{ -9 } \)
Additive inverse of \(\frac { 2 }{ -9 } \) is \(\frac { 2 }{ 9 }\)

(v) \(\frac { 19 }{ -6 } \)
Additive inverse of  \(\frac { 19 }{ -6 } \) is \(\frac { 19 }{ 6 }\)

Question 3.
Verify that – (-x) = x for :
(i) \(x=\frac { 11 }{ 15 } \)
(ii) \(x=-\frac { 13 }{ 17 } \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 5

Question 4.
Find the multiplicative inverse of the following:
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 6
Solution.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 7

Question 5.
Name the property under multiplication used in each of the following:
(i) \(\frac { -4 }{ 5 } \times \left( 1 \right) =1\times \frac { -4 }{ 5 } =-\frac { 4 }{ 5 } \)
(ii) \(-\frac { 13 }{ 17 } \times \frac { -2 }{ 7 } =\frac { -2 }{ 7 } \times \frac { -13 }{ 17 } \)
(iii) \(\frac { -19 }{ 29 } \times \frac { 29 }{ -19 } =1\)
Solution.
(i) 1 is the multiplicative identity
(ii) Commutativity of multiplication
(iii) Multiplicative inverse.

Question 6.
Multiply \(\frac { 6 }{ 13 } \) by the reciprocal of \(\frac { -7 }{ 16 } \)
Solution.
Reciprocal of \(\frac { -7 }{ 16 } \) is \(\frac { -16 }{ 7 } \)
Now,
\(\frac { 6 }{ 13 } \times \frac { -16 }{ 7 } =\frac { 6\times \left( -16 \right) }{ 13\times 7 } =\frac { -96 }{ 91 } \)

Question 7.
Tell what property allows you to compute : \(\frac { 1 }{ 3 } \times \left( 6\times \frac { 4 }{ 3 } \right) \) as \(\left( \frac { 1 }{ 3 } \times 6 \right) \times \frac { 4 }{ 3 } \)
Solution.
Associativity.

Question 8.
Is the \(\frac { 8 }{ 9 } \) multiplicative inverse of \(-1\frac { 1 }{ 8 } \) ? Why or why not?
Solution.
\(-1\frac { 1 }{ 8 } =-\frac { 9 }{ 8 } \)
Now, \(\frac { 8 }{ 9 } \times \frac { -9 }{ 8 } =-1\neq 1\)
So, No ; \(\frac { 8 }{ 9 } \) is not the multiplicative inverse of \(-1\frac { 1 }{ 8 } \left( =-\frac { 9 }{ 8 } \right) \) because the product of \(\frac { 8 }{ 9 } \) and -13(-) and \(-1\frac { 1 }{ 8 } \left( =-\frac { 9 }{ 8 } \right) \) is not 1.

Question 9.
Is 0.3 the multiplicative inverse of \(3\frac { 1 }{ 3 }\) ? Why or why not?
Solution.
Yes ; 0.3 is the multiplicative inverse of \(\frac { 10 }{ 3 } \) because
\(\frac { 3 }{ 10 } \times \frac { 10 }{ 3 } =\frac { 3\times 10 }{ 10\times 3 } =\frac { 30 }{ 30 } =1\)

Question 10.
Write :
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution.
(i) The rational number ‘0′ does not have a reciprocal.
(ii) The rational numbers 1 and (-1) are equal to their own reciprocals.
(iii) The rational number 0 is equal to its negative.

Question 11.
Fill in the blanks :
(i) Zero has……….reciprocal.
(ii) The numbers……….and………are their own reciprocals.
(iii) The reciprocal of – 5 is.………….
(iv) Reciprocal of \(\frac { 1 }{ x } \), where \(x\neq 0\)
(v) The product of two rational numbers is always a.………
(vi) The reciprocal of a positive rational number is……….
Solution.
(i) Zero has no reciprocal.
(ii) The numbers 1 and -1 are their own reciprocals.
(iii) The reciprocal of – 5 is \(-\frac { 1 }{ 5 } \)
(iv) Reciprocal of \(\frac { 1 }{ x } \), where \(x\neq 0\) is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive.

We hope the NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2.

BoardCBSE
TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 16
Chapter NamePlaying with Numbers
ExerciseEx 16.2
Number of Questions Solved4
CategoryNCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2

Question 1.
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
Solution.
Since 21y5 is a multiple of 9, its sum of digits 2 + 1+ y + 5 = 8+ y isa multiple of 9; so 8 + y is one of these numbers: 0, 9, 18, 27, 36, 45,… .
But since y is a digit, it can only be possible that 8 + y = 9. Therefore, y = 1.

Question 2.
If 31z5 is a multiple of 9, where z is a digit, what is the value of z?
You will find that there are two answers to the last problem. Why is this so?
Solution.
Since 31z5 is a multiple of 9, its sum of digits 3 + 1 + z + 5 = 9 + z isa multiple of 9; so 9 + z is one of these numbers: 0, 9, 18, 27, 36, 45, … .
But since z is a digit, it can only be possible that 9 + z = 9 or 18. Therefore, z = 0 or 9.

Question 3.
If 24x is a multiple of 3, where x is a digit, what is the value of x?
(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … .
But since xis a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)
Solution.
The solution is given with question.

Question 4.
If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
Solution.
Since 31z5 is a multiple of 3, its sum of digits 3 + 1 + z + 5 = 9 + z is a multiple of 3; so 9 + z is one of these numbers: 0, 3, 6, 9, 12, 15, 18, … .
But since z is a digit, it can only be possible that 9 + z = 9 or 12 or 15 or 18. Therefore, z = 0 or 3 or 6 or 9.

We hope the NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers Ex 16.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3.

BoardCBSE
TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 15
Chapter NameIntroduction to Graphs
ExerciseEx 15.3
Number of Questions Solved2
CategoryNCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3

Question 1.
Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 1
(b) Distance travelled by a car
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 2
(i) How much distance the car cover during the period 7.30 a.m. to 8 a.m.?
(ii) What was the time when the car had covered a distance of 100 km since it starts?

(c) Interest on deposits for a year.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 3
(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on? 2500 for a year.
(iii) To get an interest of ? 280 per year, how much money should be deposited?
Solution.
(a)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 4
Scale:
On horizontal axis:         2 units = 1 apple
On vertical axis:              1 unit = ₹ 5
Mark number of apples on the horizontal axis.
Mark cost (in ?) on the vertical axis.
Plot the points: (1, 5), (2, 10), (3, 15), (4, 20) and (5, 25)
Join the points.
We get a linear graph.

(b)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 5
Scale:
On horizontal axis:      2 units = 1 hour
On vertical axis:           2 units = 40 km
Mark time (in hours) on the horizontal axis.
Mark distances (in km) on the vertical axis.
Plot the points (6 a.m., 40), (7 a.m., 80) (8 a.m., 120) and (9 a.m., 160).
Join the points.
We get a linear graph.
(i) Distance covered during 7.30 a.m. to 8 a.m.
= 120 km – 100 km = 20 km
(ii) The time when the car had covered a distance of 100 km since its start was 7.30 a.m.

(c)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 6Scale:
On horizontal axis:       2 units = ₹ 1000
On vertical axis:            2 units = ₹ 80
Mark deposit (in ₹ on the horizontal axis.
Mark simple interest (in ₹) on the vertical axis.
Plot the points (1000, 80), (2000, 160), (3000, 240) (4000, 320) and (5000, 400).
Join the points.
We get a linear graph.
(i) Yes! The graph passes through the origin.
(ii) Interest on ₹ 2500 for a year = ₹ 200
(iii) To get an interest of ₹ 280 per year, ₹ 3500 should be deposited.

Question 2.
Draw a graph for the following:
(i)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 7
Is it a linear graph?
(ii)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 8
Is it a linear graph?
Solution.
(i)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 9
Scale:
On horizontal axis:     1 unit = 1 cm
On vertical axis:          1 unit = 4 cm
Mark side of the square (in cm) on the horizontal axis.
Mark perimeter (in cm) on the vertical axis.
Plot the points (2, 8), (3, 12), (3.5. 14) (5, 20) and (6, 24).
Join the points.
Yes ; it is a linear graph.

(ii)
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.3 10
• Scale:
On horizontal axis: 2 units = 2 cm
On vertical axis: 1 unit = 2 cm
Mark side of the square (in cm) on the horizontal axis.
Mark area (in cm ) on the vertical axis.
Plot the points (2, 4) (3, 9), (4, 16), (5, 25) and (6, 36).
Join the points.
The graph we get is not linear.

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2.

BoardCBSE
TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 15
Chapter NameIntroduction to Graphs
ExerciseEx 15.2
Number of Questions Solved4
CategoryNCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2

Question 1.
Plot the following points on a graph sheet. Verify if they lie on a line.
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(l, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 1
(a) The points lie on a line.
(b) The points lie on a line.
(c) The points do not lie on a line.

Question 2.
Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Solution.
The coordinates of the points at which this line meets the x-axis and y-axis are (5, 0) and (0, 5) respectively. See the graph given above.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 2

Question 3.
Write the coordinates of the vertices of each of these adjoining figures.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 15.2 3
Solution.
O → (0, 0)
A → (2,0)
B → (2, 3)
C → (0,3)

P → (4, 3)
Q → (6, 1)
R → (6, 5)
S → (4, 7)

K → (10, 5)
L → (7, 7)
M → (10, 8)

Question 4.
State whether True or False. Correct that is false.
(i) A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
(ii) A point whose y-coordinate is zero ‘ and x-coordinate is 5 will lie on y-axis.
(iii) The coordinates of the origin are (0, 0).
Solution.
(i) True
(ii) False; A point whose y-coordinate is zero and x-coordinate is 5 will lie on x-axis.
(iii) True

 

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4.

BoardCBSE
TextbookNCERT
ClassClass 8
SubjectMaths
ChapterChapter 14
Chapter NameFactorisation
ExerciseEx 14.4
Number of Questions Solved21
CategoryNCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4

Find and correct the errors in the following mathematical statements.
Question 1.
4(x – 5) = 4x – 5
Solution.
4(x – 5) = 4x – 20

Question 2.
x(3x + 2) = \({ 3x }^{ 2 }+2\)
Solution.
x(3x + 2) = \({ 3x }^{ 2 }+2x\)

Question 3.
2x + 3y = 5xy
Solution.
2x + 3y = 2x + 3y

Question 4.
x + 2x + 3x = 5x
Solution.
x + 2x + 3x = 6x

Question 5.
5y + 2y + y – 7y = 0
Solution.
5y + 2y + y – 7y – y

Question 6.
3x + 2x = \({ 5x }^{ 2 }\)
Solution..
3x + 2x = 5x

Question 7.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 2x }^{ 2 } + 8x + 7 \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 4x }^{ 2 } + 8x + 7 \)

Question 8.
\({ \left( 2x \right) }^{ 2 } + 5x = 4x + 5x = 9x \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 5x = { 4x }^{ 2 } + 5x \)

Question 9.
\({ \left( 3x+2 \right) }^{ 2 } = { 3x }^{ 2 } + 6x + 4. \)
Solution.
\({ \left( 3x+2 \right) }^{ 2 } = { 9x }^{ 2 }+ 12x + 4. \)

Question 10.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 1
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 2

Question 11.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 9 \)
Solution.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 2(y)(3) + { 3 }^{ 2 }\)
= \({ y }^{ 2 } – 6y + 9 \)
and not equal to \({ y }^{ 2 } – 9 \)

Question 12.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 25 \)
Solution.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 2(z) (5) + { 5}^{ 2 }\)
= \({ z }^{ 2 } + 10z + 25 \)
and not equal to \({ z }^{ 2 } + 25 \)

Question 13.
\(\left( 2a+36 \right) \left( a-b \right) = { 2a }^{ 2 }-{ 3b }^{ 2 }\)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 3
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 4

Question 14.
\(\left( a+4 \right) \left( a+2 \right) = { a}^{ 2 } + 8 \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 5

Question 15.
\(\left( a-4 \right) \left( a-2 \right) = { a}^{ 2 }-8 \)
Solution.
NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 6

Question 16.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =0\)
Solution.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =1\) and not equal to 0

Question 17.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =1+1=2\)
Solution.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } +\frac { 1 }{ { 3x }^{ 2 } } \)
=\(1+\frac { 1 }{ { 3x }^{ 2 } }\) and not equal to 1 + 1 = 2

Question 18.
\(\frac { 3x }{ 3x+2 } =\frac { 1 }{ 2 } \)
Solution.
\(\frac { 3x }{ 3x+2 } =\frac { 3x }{ 3x+2 } \) and not equal to \(\frac { 1 }{ 2 }\)

Question 19.
\(\frac { 3 }{ 4x+3 } =\frac { 1 }{ 4x } \)
Solution.
\(\frac { 3 }{ 4x+3 } =\frac { 3 }{ 4x+3 } \) and not equal to \(\frac { 1 }{ 4x }\)

Question 20.
\(\frac { 4x+5 }{ 4x } =5\)
Solution.
\(\frac { 4x+5 }{ 4x } =\frac { 4x }{ 4x } +\frac { 5 }{ 4x } =1+\frac { 5 }{ 4x } \) and not equal to 5

Question 21.
\(\frac { 7x+5 }{ 5 } =7x\)
Solution.
\(\frac { 7x+5 }{ 5 } =\frac { 7x }{ 5 } +\frac { 5 }{ 5 } =\frac { 7x }{ 5 } +1\) and not equal to 7x

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4, drop a comment below and we will get back to you at the earliest.