#### Chapters

Chapter 2: Powers

Chapter 3: Squares and Square Roots

Chapter 4: Cubes and Cube Roots

Chapter 5: Playing with Numbers

Chapter 6: Algebraic Expressions and Identities

Chapter 7: Factorization

Chapter 8: Division of Algebraic Expressions

Chapter 9: Linear Equation in One Variable

Chapter 10: Direct and Inverse Variations

Chapter 11: Time and Work

Chapter 12: Percentage

Chapter 13: Proft, Loss, Discount and Value Added Tax (VAT)

Chapter 14: Compound Interest

Chapter 15: Understanding Shapes-I (Polygons)

Chapter 16: Understanding Shapes-II (Quadrilaterals)

Chapter 17: Understanding Shapes-III (Special Types of Quadrilaterals)

Chapter 18: Practical Geometry (Constructions)

Chapter 19: Visualising Shapes

Chapter 20: Mensuration - I (Area of a Trapezium and a Polygon)

Chapter 21: Mensuration - II (Volumes and Surface Areas of a Cuboid and a Cube)

Chapter 22: Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)

Chapter 23: Data Handling-I (Classification and Tabulation of Data)

Chapter 24: Data Handling-II (Graphical Representation of Data as Histograms)

Chapter 25: Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

Chapter 26: Data Handling-IV (Probability)

Chapter 27: Introduction to Graphs

## Chapter 1: Rational Numbers

#### 1.1 [Pages 5 - 6]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.1 [Pages 5 - 6]

Add the following rational numbers.

Add the following rational numbers.

Add the following rational numbers.

\[\frac{- 8}{11} and \frac{- 4}{11}\]

Add the following rational numbers.

Add the following rational numbers.

Add the following rational numbers:

\[\frac{3}{4} and \frac{- 5}{8}\]

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

#### 1.2 [Page 14]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.2 [Page 14]

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:

Verify associativity of addition of rational numbers i.e., (*x* + *y*) + *z* = *x* + (*y* + *z*), when:

Verify associativity of addition of rational numbers i.e., (*x* + *y*) + *z* = *x* + (*y* + *z*), when:

Verify associativity of addition of rational numbers i.e., (*x* + *y*) + *z* = *x* + (*y* + *z*), when:

Verify associativity of addition of rational numbers i.e., (*x* + *y*) + *z* = *x* + (*y* + *z*), when:

Write the additive inverse of each of the following rational numbers:

Write the additive inverse of each of the following rational numbers:

Write the additive inverse of each of the following rational numbers:

Write the additive inverse of each of the following rational numbers:

Write the negative (additive inverse) of each of the following:

Write the negative (additive inverse) of each of the following:

Write the negative (additive inverse) of each of the following:

Write the negative (additive inverse) of each of the following:

Write the negative (additive inverse) of each of the following:

Write the negative (additive inverse) of each of the following:

1

Write the negative (additive inverse) of each of the following:

−1

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

Re-arrange suitably and find the sum in each of the following:

Re-arrange suitably and find the sum in each of the following:

Re-arrange suitably and find the sum in each of the following:

Re-arrange suitably and find the sum in each of the following:

Re-arrange suitably and find the sum in each of the following:

Re-arrange suitably and find the sum in each of the following:

#### 1.3 [Pages 18 - 19]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.3 [Pages 18 - 19]

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Subtract the first rational number from the second in each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

The sum of the two numbers is \[\frac{5}{9} .\] If one of the numbers is \[\frac{1}{3},\] find the other.

The sum of two numbers is \[\frac{- 1}{3} .\] If one of the numbers is \[\frac{- 12}{3},\] find the other.

The sum of two numbers is \[\frac{- 4}{3} .\] If one of the numbers is −5, find the other.

The sum of two rational numbers is −8. If one of the numbers is\[\frac{- 15}{7},\] find the other.

What should be added to \[\frac{- 7}{8}\] so as to get \[\frac{5}{9}?\]

What number should be added to \[\frac{- 5}{11}\] so as to get\[\frac{26}{33}?\]

What number should be added to \[\frac{- 5}{7}\] to get\[\frac{- 2}{3}?\]

What number should be subtracted from \[\frac{- 5}{3}\] to get\[\frac{5}{6}?\]

What number should be subtracted from \[\frac{3}{7}\] to get\[\frac{5}{4}?\]

What should be added to \[\left( \frac{2}{3} + \frac{3}{5} \right)\] to get\[\frac{- 2}{15}?\]

What should be added to \[\left( \frac{1}{2} + \frac{1}{3} + \frac{1}{5} \right)\] to get 3?

What should be subtracted from \[\left( \frac{3}{4} - \frac{2}{3} \right)\] to get\[\frac{- 1}{6}?\]

Fill in the branks:

Fill in the branks:

Fill in the branks:

#### 1.4 [Pages 22 - 23]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.4 [Pages 22 - 23]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]\[\frac{- 11}{2} + \frac{7}{6} + \frac{- 5}{8}\]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]

Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]

Express each of the following as a rational number of the form \[\frac{p}{q}:\]

Express each of the following as a rational number of the form \[\frac{p}{q}:\]

Express each of the following as a rational number of the form \[\frac{p}{q}:\]

Express each of the following as a rational number of the form \[\frac{p}{q}:\]

Express each of the following as a rational number of the form \[\frac{p}{q}:\]

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

#### 1.5 [Pages 25 - 26]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.5 [Pages 25 - 26]

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify each of the following and express the result as a rational number in standard form:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

#### 1.6 [Pages 31 - 33]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.6 [Pages 31 - 33]

Verify the property: *x* × *y* = *y* × *x* by taking:

Verify the property: *x* × *y* = *y* × *x* by taking:

Verify the property: *x* × *y* = *y* × *x* by taking:

Verify the property: *x* × *y* = *y* × *x* by taking:

Verify the property: *x* × (*y* × *z*) = (*x* × *y*) × *z* by taking:

Verify the property: *x* × (*y* × *z*) = (*x* × *y*) × *z* by taking:

Verify the property: *x* × (*y* × *z*) = (*x* × *y*) × *z* by taking:

Verify the property: *x* × (*y* × *z*) = (*x* × *y*) × *z* by taking:

Verify the property: *x* × (*y* + *z*) = *x* × *y* + *x* × *z* by taking:

Verify the property: *x* × (*y* + *z*) = *x* × *y* + *x* × *z* by taking:

Verify the property: *x* × (*y* + *z*) = *x* × *y* + *x* × *z* by taking:

Verify the property: *x* × (*y* + *z*) = *x* × *y* + *x* × *z* by taking:

Use the distributivity of multiplication of rational numbers over their addition to simplify:

Use the distributivity of multiplication of rational numbers over their addition to simplify:

Use the distributivity of multiplication of rational numbers over their addition to simplify:

Use the distributivity of multiplication of rational numbers over their addition to simplify:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

9

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

−7

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Name the property of multiplication of rational numbers illustrated by the following statements:

Fill in the blanks:

The product of two positive rational numbers is always .....

Fill in the blanks:

The product of a positive rational number and a negative rational number is always .....

Fill in the blanks:

The product of two negative rational numbers is always .....

Fill in the blanks:

The reciprocal of a positive rational number is .....

Fill in the blanks:

The reciprocal of a negative rational number is .....

Fill in the blanks:

Zero has ..... reciprocal.

Fill in the blanks:

The product of a rational number and its reciprocal is .....

Fill in the blanks:

The numbers ..... and ..... are their own reciprocals.

Fill in the blanks:

If *a* is reciprocal of *b*, then the reciprocal of *b* is .....

Fill in the blanks:

The number 0 is ..... the reciprocal of any number.

Fill in the blanks:

Reciprocal of\[\frac{1}{a}, a \neq 0\]

Fill in the blanks:

(17 × 12)^{−1} = 17^{−1} × .....

Fill in the blanks:

Fill in the blanks:

Fill in the blanks:

Fill in the blanks:

#### 1.7 [Pages 35 - 36]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.7 [Pages 35 - 36]

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Find the value and express as a rational number in standard form:

Find the value and express as a rational number in standard form:

Find the value and express as a rational number in standard form:

Find the value and express as a rational number in standard form:

Find the value and express as a rational number in standard form:

Find the value and express as a rational number in standard form:

The product of two rational numbers is 15. If one of the numbers is −10, find the other.

The product of two rational numbers is\[\frac{- 8}{9} .\] If one of the numbers is \[\frac{- 4}{15},\] find the other.

By what number should we multiply \[\frac{- 1}{6}\] so that the product may be \[\frac{- 23}{9}?\]

By what number should we multiply \[\frac{- 15}{28}\] so that the product may be\[\frac{- 5}{7}?\]

By what number should we multiply \[\frac{- 8}{13}\]

so that the product may be 24?

By what number should \[\frac{- 3}{4}\] be multiplied in order to produce \[\frac{2}{3}?\]

Find (*x* + *y*) ÷ (*x* − *y*), if

Find (*x* + *y*) ÷ (*x* − *y*), if

Find (*x* + *y*) ÷ (*x* − *y*), if

Find (*x* + *y*) ÷ (*x* − *y*), if

Find (*x* + *y*) ÷ (*x* − *y*), if

The cost of \[7\frac{2}{3}\] metres of rope is Rs \[12\frac{3}{4} .\]

Find its cost per metre.

The cost of \[2\frac{1}{3}\] metres of cloth is Rs. \[75\frac{1}{4} .\]Find the cost of cloth per metre.

By what number should \[\frac{- 33}{16}\] be divided to get\[\frac{- 11}{4}?\]

Divide the sum of \[\frac{- 13}{5}\] and \[\frac{12}{7}\] by the product of\[\frac{- 31}{7} \text{and} \frac{- 1}{2} .\]

Divide the sum of \[\frac{65}{12} \text{and}\ \frac{12}{7}\] by their difference.

If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?

#### 1.8 [Page 43]

### RD Sharma solutions for Class 8 Maths Chapter 1 Rational Numbers 1.8 [Page 43]

Find a rational number between −3 and 1.

Find any five rational numbers less than 2.

Find two rational numbers between \[\frac{- 2}{9} \text{and} \frac{5}{9} .\]

Find two rational numbers between\[\frac{1}{5} \text{and} \frac{1}{2} .\]

Find ten rational numbers between \[\frac{1}{4} \text{and} \frac{1}{2} .\]

Find ten rational numbers between\[\frac{- 2}{5} \text{and} \frac{1}{2} .\]

Find ten rational numbers between\[\frac{3}{5} \text{and} \frac{3}{4} .\]

## Chapter 1: Rational Numbers

## RD Sharma solutions for Class 8 Maths chapter 1 - Rational Numbers

RD Sharma solutions for Class 8 Maths chapter 1 (Rational Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 1 Rational Numbers are Introduction of Rational Numbers, Closure, Commutativity, The Role of 1, Representation of Rational Numbers on the Number Line, Associativity, The Role of Zero (0), Negative of a Number, Reciprocal, Distributivity of Multiplication Over Addition for Rational, Rational Numbers Between Two Rational Numbers.

Using RD Sharma Class 8 solutions Rational Numbers exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer RD Sharma Textbook Solutions to score more in exam.

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