NCERT Solutions For Class 8 Maths Chapter 1

NCERT Solutions Class 8 Maths Rational Numbers

NCERT solutions for class 8 maths chapter 1 Rational numbers is provided here. Class 8 is an important phase of a students life, the topic which are taught in class 8 are essential to understand the topics of class 9. To score good marks in class 8 mathematics examination it is advised to solve questions provided at the end of each chapter in the NCERT book. Solving NCERT questions will help you to know about the different types of questions with their difficulty level. Students can download NCERT solutions for class 8 maths chapter 1 pdf from the table below.

NCERT Solutions Class 8 Maths Chapter 1 Exercises

Exercise – 1.1

  1. Using appropriate properties find the value of 23×35+5235×16

Sol.   23×35+5235×1623×3535×16+52

=35(23+16)+52

=35(4+16)+52

=35(56)+52

=1530+52

=12+52

=42

=2

 therefore23×35+5235×16 =2

 

  1. Using appropriate properties find the value of 25×3716×32+114×25

Sol. 25×3716×32+114×25

= 25×3712×12+17×15

=63514+135

=53514

=1714

=1128

=25×3716×32+114×25

=1128

 

  1. Solving the additive inverse of 28

Sol.  Additive inverse of 28is28

 

  1. Solving the additive inverse of 59

Sol.  Additive inverse of 59is59

 

  1. Solving the additive inverse of 65

Sol. 6565

Additive inverse of 65is65

Additive inverse of 6565

 

  1. Solving the additive inverse of 29

Sol.  Additive inverse of 29is29

 

  1. Verify that –(-x )=x for x=1115

Sol. x=1115

x=1115 (x)=(1115)

=1115=x

 therefore(x)=x

 

  1. Verify that –(-x )=x for x=1317

Sol. x=1317

x=(1317)=1317 (x)=(1317)

=1317=x

 therefore(x)=x

 

  1. Solve that multiplicative inverse of -13

Sol. Given multiplicative inverse -13 is113

 

  1. Solve that multiplicative inverse of 1319

Sol. Given multiplicative inverse 1319is1913

 

  1. Solve that multiplicative inverse of 58×37

Sol. Given multiplicative inverse 58×37is 85×73 or 85×73

 

  1. What is the multiplicative inverse of -1.

Sol.  The multiplicative inverse of -1 is -1.

 

  1. Name the property under multiplicative used in each of the following.

 (i) 45×1=1×45=45

(ii) 1317×27=27×1317

(iii) 1929×2919=1

Sol. (i) ROLE OF 1

(ii) COMMUTATIVITY

(iii) MULTIPLICATIVE  INVERSE

 

  1. Multiply 613 by the reciprocal of 76

Sol. Reciprocal of 76 is 67

 therefore613×67

=3691

 

  1. what property allows you to compute 13×(6×43)(13×6)×45

Sol.  Associativity

 

  1. Is 89 the multiplicative inverse of 118 ? why or why not.

Sol.

118=98

=89×98

=11

 therefore89 is  not the multiplicative inverse of 118

 

  1. Is 0.3 the multiplicative inverse of 313 ? why or why not.

Sol.        313=103=3.3

                          3.3×0.3=0.991

 therefore0.3isnotthemultiplicativeinverseof313

 

Exercise 1.2:

Question 1:

Solve the following using appropriate properties:

  1. ii)25371632+11425

Answers:

  1. ii) Use commutativity of rational numbers
25371632+11425

Using distributive property

25[37+114]14

= 2532+11414

=2551414

=4728=1128

 

Question 2:

(i) 57

(ii) 47

(iii)25

(iv)59

Solution:

(i) 57

additive inverse = 57

(ii)  4747

Additive inverse = 47

(iii)  25

Additive inverse = 25

(iv)  59

Additive inverse = 59
Question 3:

(i)  x = 1115

(ii) x= 1317

Solution:

x = 1115

The additive inverse of  is   x = 1115

This equality

x = 1115+frac1115=0

=(x)=x

x= 1317

The additive inverse of  x= 1317 =  x= 1317

This equaliity

x = 1317+frac1317=0

=(x)=x

 

Question 4:

(i)  -12

(ii) 1913

(iii) 13

(iv)  3838

(v)  135

Solutions:

  1. The multiplicative inverse of  -12 is 112
  2. The multiplicative inverse of 1913 is1319
  3. The multiplicative inverse of 13  is 31 = 3
  4. The multiplicative inverse of  135 is 53

 

Question 5:

Find out the multiplication property that is used in the following sums:

(i) 371=137=37

(ii) 141734=341417

(iii) 17373717=1

Solutions:

  1. This use the multiplicative identity property and the multiplicative identity is 1
  2. This uses the commutativity property
  3. This uses the multiplicative inverse property

Question 6:

Find the product of  715 and the reciprocal of 417

Solution:

Reciprocal of  4171714

7151714=11960

 

Question 7:

  1. Which rational number does not have a reciprocal
  2. Which rational number is equal to its own reciprocal
  3. Which rational number is equal to its own negative

Solution:

  1. Zero is the rational number that has no reciprocal
  2. One and negative one are rational numbers that are equal to their own reciprocal
  3. Zero is a rational number that is also equal to its own negative.

 

Question 8: Answer or complete the following sentences:

  1. Does zero have a reciprocal?
  2. The two numbers _____ and _________ are their own reciprocals.
  3. What is the reciprocal of -6?
  4. What is the reciprocal of ?
  5. The product of two rational numbers is always a __________.
  6. The reciprocal of a positive rational number is ___________.

 

Solutions:

  1. No it doesn’t
  2. 1, -1
  3. -1/6
  4. X
  5. Rational number
  6. Positive rational number

 

Question 9:

Find the multiplicative inverse of the following:

  1. -12
  2. 1218
  3. 27
  4. -1
  5. 3857
  6. 227

Solutions:

  1. 112
  2. 1218
  3. 72
  4. -1
  5. 5615
  6. 72

 

Question 10:

Is 0.3 the multiplicative inverse of   313? Why or why not?

Answer:

313=103 0.3313=0.3103=310103=1

As proved above the product is one.

Therefore, 0.3 is the multiplicative inverse of  313