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# RD Sharma solutions for Class 8 Maths chapter 1 - Rational Numbers [Latest edition]

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#### Chapters ## Chapter 1: Rational Numbers

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5Exercise 1.6Exercise 1.7Exercise 1.8
Exercise 1.1 [Pages 5 - 6]

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

Exercise 1.1 | Q 1.1 | Page 5

Add the following rational numbers.

$\frac{- 5}{7} and \frac{3}{7}$

Exercise 1.1 | Q 1.2 | Page 5

Add the following rational numbers.

$\frac{- 15}{4} and \frac{7}{4}$

Exercise 1.1 | Q 1.3 | Page 5

Add the following rational numbers.
$\frac{- 8}{11} and \frac{- 4}{11}$

Exercise 1.1 | Q 1.4 | Page 5

Add the following rational numbers.

$\frac{- 8}{11} and \frac{- 4}{11}$

Exercise 1.1 | Q 1.5 | Page 5

Add the following rational numbers.

$\frac{6}{13} and \frac{- 9}{13}$

Exercise 1.1 | Q 2.1 | Page 6

Add the following rational numbers:
$\frac{3}{4} and \frac{- 5}{8}$

Exercise 1.1 | Q 2.2 | Page 6

Add the following rational numbers:

$\frac{5}{- 9} and \frac{7}{3}$
Exercise 1.1 | Q 2.3 | Page 6

Add the following rational numbers:

$- 3 and \frac{3}{5}$
Exercise 1.1 | Q 2.4 | Page 6

Add the following rational numbers:

$\frac{- 7}{27} and \frac{11}{18}$
Exercise 1.1 | Q 2.5 | Page 6

Add the following rational numbers:

$\frac{31}{- 4} and \frac{- 5}{8}$
Exercise 1.1 | Q 2.6 | Page 6

Add the following rational numbers:

$\frac{5}{36} and \frac{- 7}{12}$
Exercise 1.1 | Q 2.7 | Page 6

Add the following rational numbers:

$\frac{- 5}{16} and \frac{7}{24}$
Exercise 1.1 | Q 2.8 | Page 6

Add the following rational numbers:

$\frac{7}{- 18} and \frac{8}{27}$
Exercise 1.1 | Q 3.01 | Page 6

Simplify:

$\frac{8}{9} + \frac{- 11}{6}$

Exercise 1.1 | Q 3.02 | Page 6

Simplify:

$3 + \frac{5}{- 7}$
Exercise 1.1 | Q 3.03 | Page 6

Simplify:

$\frac{1}{- 12} + \frac{2}{- 15}$
Exercise 1.1 | Q 3.04 | Page 6

Simplify:

$\frac{- 8}{19} + \frac{- 4}{57}$
Exercise 1.1 | Q 3.05 | Page 6

Simplify:

$\frac{7}{9} + \frac{3}{- 4}$
Exercise 1.1 | Q 3.06 | Page 6

Simplify:

$\frac{5}{26} + \frac{11}{- 39}$
Exercise 1.1 | Q 3.07 | Page 6

Simplify:

$\frac{- 16}{9} + \frac{- 5}{12}$
Exercise 1.1 | Q 3.08 | Page 6

Simplify:

$\frac{- 13}{8} + \frac{5}{36}$
Exercise 1.1 | Q 3.09 | Page 6

Simplify:

$0 + \frac{- 3}{5}$
Exercise 1.1 | Q 3.1 | Page 6

Simplify:

$1 + \frac{- 4}{5}$
Exercise 1.1 | Q 4.1 | Page 6

Add and express the sum as a mixed fraction:

$\frac{- 12}{5} \text{and} \frac{43}{10}$
Exercise 1.1 | Q 4.2 | Page 6

Add and express the sum as a mixed fraction:

$\frac{24}{7} \text{and} \frac{- 11}{4}$
Exercise 1.1 | Q 4.3 | Page 6

Add and express the sum as a mixed fraction:

$\frac{- 31}{6} \text{and} \frac{- 27}{8}$
Exercise 1.1 | Q 4.4 | Page 6

Add and express the sum as a mixed fraction:

$\frac{101}{6} \text{and} \frac{7}{8}$
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Exercise 1.2 [Page 14]

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

Exercise 1.2 | Q 1.1 | Page 14

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

$\frac{- 11}{5} \text{and} \frac{4}{7}$
Exercise 1.2 | Q 1.2 | Page 14

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

$\frac{4}{9} \text{and} \frac{7}{- 12}$
Exercise 1.2 | Q 1.3 | Page 14

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

$\frac{- 3}{5} \text{and} \frac{- 2}{- 15}$
Exercise 1.2 | Q 1.4 | Page 14

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

$\frac{2}{- 7} \text{and} \frac{12}{- 35}$
Exercise 1.2 | Q 1.5 | Page 14

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

$4\ \text{and} \frac{- 3}{5}$
Exercise 1.2 | Q 1.6 | Page 14

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

$- 4\ \text{and} \frac{4}{- 7}$
Exercise 1.2 | Q 2.1 | Page 14

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

$x = \frac{1}{2}, y = \frac{2}{3}, z = - \frac{1}{5}$
Exercise 1.2 | Q 2.2 | Page 14

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

$x = \frac{- 2}{5}, y = \frac{4}{3}, z = \frac{- 7}{10}$
Exercise 1.2 | Q 2.3 | Page 14

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

$x = \frac{- 7}{11}, y = \frac{2}{- 5}, z = \frac{- 3}{22}$
Exercise 1.2 | Q 2.4 | Page 14

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

$x = - 2, y = \frac{3}{5}, z = \frac{- 4}{3}$
Exercise 1.2 | Q 3.1 | Page 14

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

$\frac{- 2}{17}$
Exercise 1.2 | Q 3.2 | Page 14

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

$\frac{3}{- 11}$
Exercise 1.2 | Q 3.3 | Page 14

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

$\frac{- 17}{5}$
Exercise 1.2 | Q 3.4 | Page 14

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

$\frac{- 11}{- 25}$
Exercise 1.2 | Q 4.1 | Page 14

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

$\frac{- 2}{5}$
Exercise 1.2 | Q 4.2 | Page 14

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

$\frac{7}{- 9}$
Exercise 1.2 | Q 4.3 | Page 14

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

$\frac{- 16}{13}$
Exercise 1.2 | Q 4.4 | Page 14

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

$\frac{- 5}{1}$
Exercise 1.2 | Q 4.5 | Page 14

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

0
Exercise 1.2 | Q 4.6 | Page 14

Write the negative (additive inverse) of each of the following:
1

Exercise 1.2 | Q 4.7 | Page 14

Write the negative (additive inverse) of each of the following:
−1

Exercise 1.2 | Q 5.1 | Page 14

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

$\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$
Exercise 1.2 | Q 5.2 | Page 14

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

$\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$
Exercise 1.2 | Q 5.3 | Page 14

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

$\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$
Exercise 1.2 | Q 5.4 | Page 14

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

$\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$
Exercise 1.2 | Q 6.1 | Page 14

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

$\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$
Exercise 1.2 | Q 6.2 | Page 14

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

$\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$
Exercise 1.2 | Q 6.3 | Page 14

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

$\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$
Exercise 1.2 | Q 6.4 | Page 14

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

$\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$
Exercise 1.2 | Q 6.5 | Page 14

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

$\frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5}$
Exercise 1.2 | Q 6.6 | Page 14

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

$\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$
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Exercise 1.3 [Pages 18 - 19]

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

Exercise 1.3 | Q 1.1 | Page 18

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

$\frac{3}{8}, \frac{5}{8}$
Exercise 1.3 | Q 1.2 | Page 18

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

$\frac{- 7}{9}, \frac{4}{9}$
Exercise 1.3 | Q 1.3 | Page 18

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

$\frac{- 2}{11}, \frac{- 9}{11}$
Exercise 1.3 | Q 1.4 | Page 18

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

$\frac{11}{13}, \frac{- 4}{13}$
Exercise 1.3 | Q 1.5 | Page 18

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

$\frac{1}{4}, \frac{- 3}{8}$
Exercise 1.3 | Q 1.6 | Page 18

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

$\frac{- 2}{3}, \frac{5}{6}$
Exercise 1.3 | Q 1.7 | Page 18

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

$\frac{- 6}{7}, \frac{- 13}{14}$
Exercise 1.3 | Q 1.8 | Page 18

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

$\frac{- 8}{33}, \frac{- 7}{22}$
Exercise 1.3 | Q 2.01 | Page 18

Evaluate each of the following:

$\frac{2}{3} - \frac{3}{5}$
Exercise 1.3 | Q 2.02 | Page 18

Evaluate each of the following:

$- \frac{4}{7} - \frac{2}{- 3}$
Exercise 1.3 | Q 2.03 | Page 18

Evaluate each of the following:

$\frac{4}{7} - \frac{- 5}{- 7}$
Exercise 1.3 | Q 2.04 | Page 18

Evaluate each of the following:

$- 2 - \frac{5}{9}$
Exercise 1.3 | Q 2.05 | Page 18

Evaluate each of the following:

$\frac{- 3}{- 8} - \frac{- 2}{7}$
Exercise 1.3 | Q 2.06 | Page 18

Evaluate each of the following:

$\frac{- 4}{13} - \frac{- 5}{26}$
Exercise 1.3 | Q 2.07 | Page 18

Evaluate each of the following:

$\frac{- 5}{14} - \frac{- 2}{7}$
Exercise 1.3 | Q 2.08 | Page 18

Evaluate each of the following:

$\frac{13}{15} - \frac{12}{25}$
Exercise 1.3 | Q 2.09 | Page 18

Evaluate each of the following:

$\frac{- 6}{13} - \frac{- 7}{13}$
Exercise 1.3 | Q 2.1 | Page 18

Evaluate each of the following:

$\frac{7}{24} - \frac{19}{36}$
Exercise 1.3 | Q 2.11 | Page 18

Evaluate each of the following:

$\frac{5}{63} - \frac{- 8}{21}$
Exercise 1.3 | Q 3 | Page 18

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

Exercise 1.3 | Q 4 | Page 18

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

Exercise 1.3 | Q 5 | Page 18

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

Exercise 1.3 | Q 6 | Page 18

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

Exercise 1.3 | Q 7 | Page 18

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

Exercise 1.3 | Q 8 | Page 18

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

Exercise 1.3 | Q 9 | Page 18

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

Exercise 1.3 | Q 10 | Page 18

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

Exercise 1.3 | Q 11 | Page 19

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

Exercise 1.3 | Q 12 | Page 19

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

Exercise 1.3 | Q 13 | Page 19

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

Exercise 1.3 | Q 14 | Page 19

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

Exercise 1.3 | Q 15.1 | Page 19

Fill in the branks:

$\frac{- 4}{13} - \frac{- 3}{26} = . . .$
Exercise 1.3 | Q 15.2 | Page 19

Fill in the branks:

$\frac{- 9}{14} + . . . = - 1$
Exercise 1.3 | Q 15.3 | Page 19

Fill in the branks:

$\frac{- 7}{9} + . . . = 3$
Exercise 1.3 | Q 15.4 | Page 19
Fill in the branks:
$. . . + \frac{15}{23} = 4$
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Exercise 1.4 [Pages 22 - 23]

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

Exercise 1.4 | Q 1.1 | Page 22

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

$\frac{3}{4} + \frac{5}{6} + \frac{- 7}{8}$
Exercise 1.4 | Q 1.2 | Page 22

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

$\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$
Exercise 1.4 | Q 1.3 | Page 22

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}$

Exercise 1.4 | Q 1.4 | Page 22

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

$\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}$

Exercise 1.4 | Q 1.5 | Page 22

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

$\frac{- 9}{10} + \frac{22}{15} + \frac{13}{- 20}$

Exercise 1.4 | Q 1.6 | Page 22

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

$\frac{5}{3} + \frac{3}{- 2} + \frac{- 7}{3} + 3$

Exercise 1.4 | Q 2.1 | Page 23

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

$\frac{- 8}{3} + \frac{- 1}{4} + \frac{- 11}{6} + \frac{3}{8} - 3$
Exercise 1.4 | Q 2.2 | Page 23

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

$\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}$
Exercise 1.4 | Q 2.3 | Page 23

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

$\frac{15}{2} + \frac{9}{8} + \frac{- 11}{3} + 6 + \frac{- 7}{6}$
Exercise 1.4 | Q 2.4 | Page 23

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

$\frac{- 7}{4} + 0 + \frac{- 9}{5} + \frac{19}{10} + \frac{11}{14}$
Exercise 1.4 | Q 2.5 | Page 23

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

$\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2$
Exercise 1.4 | Q 3.1 | Page 23

Simplify:

$\frac{- 3}{2} + \frac{5}{4} - \frac{7}{4}$
Exercise 1.4 | Q 3.2 | Page 23

Simplify:

$\frac{5}{3} - \frac{7}{6} + \frac{- 2}{3}$
Exercise 1.4 | Q 3.3 | Page 23

Simplify:

$\frac{5}{4} - \frac{7}{6} - \frac{- 2}{3}$
Exercise 1.4 | Q 3.4 | Page 23

Simplify:

$\frac{- 2}{5} - \frac{- 3}{10} - \frac{- 4}{7}$
Exercise 1.4 | Q 3.5 | Page 23

Simplify:

$\frac{5}{6} + \frac{- 2}{5} - \frac{- 2}{15}$
Exercise 1.4 | Q 3.6 | Page 23

Simplify:

$\frac{3}{8} - \frac{- 2}{9} + \frac{- 5}{36}$
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Exercise 1.5 [Pages 25 - 26]

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

Exercise 1.5 | Q 1.1 | Page 25

Multiply:

$\frac{7}{11} \text{by} \frac{5}{4}$
Exercise 1.5 | Q 1.2 | Page 25

Multiply:

$\frac{5}{7} \text{by} \frac{- 3}{4}$
Exercise 1.5 | Q 1.3 | Page 25

Multiply:

$\frac{- 2}{9} \text{by} \frac{5}{11}$
Exercise 1.5 | Q 1.4 | Page 25

Multiply:

$\frac{- 3}{17} \text{by} \frac{- 5}{- 4}$
Exercise 1.5 | Q 1.5 | Page 25

Multiply:

$\frac{9}{- 7} \text{by} \frac{36}{- 11}$
Exercise 1.5 | Q 1.6 | Page 25

Multiply:

$\frac{- 11}{13} \text{by} \frac{- 21}{7}$
Exercise 1.5 | Q 1.7 | Page 25

Multiply:

$- \frac{3}{5} \text{by} - \frac{4}{7}$
Exercise 1.5 | Q 1.8 | Page 25

Multiply:

$- \frac{15}{11} \text{by} 7$
Exercise 1.5 | Q 2.1 | Page 25

Multiply:

$\frac{- 5}{17} \text{by} \frac{51}{- 60}$
Exercise 1.5 | Q 2.2 | Page 25

Multiply:

$\frac{- 6}{11} \text{by} \frac{- 55}{36}$
Exercise 1.5 | Q 2.3 | Page 25

Multiply:

$\frac{- 8}{25} \text{by} \frac{- 5}{16}$
Exercise 1.5 | Q 2.4 | Page 25

Multiply:

$\frac{6}{7} \text{by} \frac{- 49}{36}$
Exercise 1.5 | Q 2.5 | Page 25

Multiply:

$\frac{8}{- 9} \text{by} \frac{- 7}{- 16}$
Exercise 1.5 | Q 2.6 | Page 25

Multiply:

$\frac{- 8}{9} \text{by} \frac{3}{64}$
Exercise 1.5 | Q 3.1 | Page 26

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

$\frac{- 16}{21} \times \frac{14}{5}$
Exercise 1.5 | Q 3.2 | Page 26

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

$\frac{7}{6} \times \frac{- 3}{28}$
Exercise 1.5 | Q 3.3 | Page 26

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

$\frac{- 19}{36} \times 16$
Exercise 1.5 | Q 3.4 | Page 26

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

$\frac{- 13}{9} \times \frac{27}{- 26}$
Exercise 1.5 | Q 3.5 | Page 26

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

$\frac{- 9}{16} \times \frac{- 64}{- 27}$
Exercise 1.5 | Q 3.6 | Page 26

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

$\frac{- 50}{7} \times \frac{14}{3}$
Exercise 1.5 | Q 3.7 | Page 26

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

$\frac{- 11}{9} \times \frac{- 81}{- 88}$
Exercise 1.5 | Q 3.8 | Page 26

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

$\frac{- 5}{9} \times \frac{72}{- 25}$
Exercise 1.5 | Q 4.1 | Page 26

Simplify:

$\left( \frac{25}{8} \times \frac{2}{5} \right) - \left( \frac{3}{5} \times \frac{- 10}{9} \right)$
Exercise 1.5 | Q 4.2 | Page 26

Simplify:

$\left( \frac{1}{2} \times \frac{1}{4} \right) + \left( \frac{1}{2} \times 6 \right)$
Exercise 1.5 | Q 4.3 | Page 26

Simplify:

$\left( - 5 \times \frac{2}{15} \right) - \left( - 6 \times \frac{2}{9} \right)$
Exercise 1.5 | Q 4.4 | Page 26

Simplify:

$\left( \frac{- 9}{4} \times \frac{5}{3} \right) + \left( \frac{13}{2} \times \frac{5}{6} \right)$
Exercise 1.5 | Q 4.5 | Page 26

Simplify:

$\left( \frac{- 4}{3} \times \frac{12}{- 5} \right) + \left( \frac{3}{7} \times \frac{21}{15} \right)$
Exercise 1.5 | Q 4.6 | Page 26

Simplify:

$\left( \frac{13}{5} \times \frac{8}{3} \right) - \left( \frac{- 5}{2} \times \frac{11}{3} \right)$
Exercise 1.5 | Q 4.7 | Page 26

Simplify:

$\left( \frac{13}{7} \times \frac{11}{26} \right) - \left( \frac{- 4}{3} \times \frac{5}{6} \right)$
Exercise 1.5 | Q 4.8 | Page 26

Simplify:

$\left( \frac{8}{5} \times \frac{- 3}{2} \right) + \left( \frac{- 3}{10} \times \frac{11}{16} \right)$
Exercise 1.5 | Q 5.1 | Page 26

Simplify:

$\left( \frac{3}{2} \times \frac{1}{6} \right) + \left( \frac{5}{3} \times \frac{7}{2} \right) - \left( \frac{13}{8} \times \frac{4}{3} \right)$
Exercise 1.5 | Q 5.2 | Page 26

Simplify:

$\left( \frac{1}{4} \times \frac{2}{7} \right) - \left( \frac{5}{14} \times \frac{- 2}{3} \right) + \left( \frac{3}{7} \times \frac{9}{2} \right)$
Exercise 1.5 | Q 5.3 | Page 26

Simplify:

$\left( \frac{13}{9} \times \frac{- 15}{2} \right) + \left( \frac{7}{3} \times \frac{8}{5} \right) + \left( \frac{3}{5} \times \frac{1}{2} \right)$
Exercise 1.5 | Q 5.4 | Page 26

Simplify:

$\left( \frac{3}{11} \times \frac{5}{6} \right) - \left( \frac{9}{12} \times \frac{4}{3} \right) + \left( \frac{5}{13} \times \frac{6}{15} \right)$
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Exercise 1.6 [Pages 31 - 33]

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

Exercise 1.6 | Q 1.1 | Page 31

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

$x = - \frac{1}{3}, y = \frac{2}{7}$
Exercise 1.6 | Q 1.2 | Page 31

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

$x = \frac{- 3}{5}, y = \frac{- 11}{13}$
Exercise 1.6 | Q 1.3 | Page 31

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

$x = 2, y = \frac{7}{- 8}$
Exercise 1.6 | Q 1.4 | Page 31

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

$x = 0, y = \frac{- 15}{8}$
Exercise 1.6 | Q 2.1 | Page 31

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

$x = \frac{- 7}{3}, y = \frac{12}{5}, z = \frac{4}{9}$
Exercise 1.6 | Q 2.2 | Page 31

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

$x = 0, y = \frac{- 3}{5}, z = \frac{- 9}{4}$
Exercise 1.6 | Q 2.3 | Page 31

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

$x = \frac{1}{2}, y = \frac{5}{- 4}, z = \frac{- 7}{5}$
Exercise 1.6 | Q 2.4 | Page 31

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

$x = \frac{5}{7}, y = \frac{- 12}{13}, z = \frac{- 7}{18}$
Exercise 1.6 | Q 3.1 | Page 32

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

$x = \frac{- 3}{7}, y = \frac{12}{13}, z = \frac{- 5}{6}$
Exercise 1.6 | Q 3.2 | Page 32

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

$x = \frac{- 12}{5}, y = \frac{- 15}{4}, z = \frac{8}{3}$
Exercise 1.6 | Q 3.3 | Page 32

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

$x = \frac{- 8}{3}, y = \frac{5}{6}, z = \frac{- 13}{12}$
Exercise 1.6 | Q 3.4 | Page 32

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

$x = \frac{- 3}{4}, y = \frac{- 5}{2}, z = \frac{7}{6}$
Exercise 1.6 | Q 4.1 | Page 32

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

$\frac{3}{5} \times \left( \frac{35}{24} + \frac{10}{1} \right)$
Exercise 1.6 | Q 4.2 | Page 32

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

$\frac{- 5}{4} \times \left( \frac{8}{5} + \frac{16}{5} \right)$
Exercise 1.6 | Q 4.3 | Page 32

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

$\frac{2}{7} \times \left( \frac{7}{16} - \frac{21}{4} \right)$
Exercise 1.6 | Q 4.4 | Page 32

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

$\frac{3}{4} \times \left( \frac{8}{9} - 40 \right)$
Exercise 1.6 | Q 5.01 | Page 32

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

9

Exercise 1.6 | Q 5.02 | Page 32

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

−7

Exercise 1.6 | Q 5.03 | Page 32

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

$\frac{12}{5}$
Exercise 1.6 | Q 5.04 | Page 32

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

$\frac{- 7}{9}$
Exercise 1.6 | Q 5.05 | Page 32

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

$\frac{- 3}{- 5}$
Exercise 1.6 | Q 5.06 | Page 32

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

$\frac{2}{3} \times \frac{9}{4}$
Exercise 1.6 | Q 5.07 | Page 32

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

$\frac{- 5}{8} \times \frac{16}{15}$
Exercise 1.6 | Q 5.08 | Page 32

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

$- 2 \times \frac{- 3}{5}$
Exercise 1.6 | Q 5.09 | Page 32

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

−1
Exercise 1.6 | Q 5.1 | Page 32

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

$\frac{0}{3}$
Exercise 1.6 | Q 5.11 | Page 32

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

1
Exercise 1.6 | Q 6.1 | Page 32

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

$\frac{- 5}{16} \times \frac{8}{15} = \frac{8}{15} \times \frac{- 5}{16}$
Exercise 1.6 | Q 6.2 | Page 32

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

$\frac{- 17}{5} \times 9 = 9 \times \frac{- 17}{5}$
Exercise 1.6 | Q 6.3 | Page 32

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

$\frac{7}{4} \times \left( \frac{- 8}{3} + \frac{- 13}{12} \right) = \frac{7}{4} \times \frac{- 8}{3} + \frac{7}{4} \times \frac{- 13}{12}$
Exercise 1.6 | Q 6.4 | Page 32

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

$\frac{- 5}{9} \times \left( \frac{4}{15} \times \frac{- 9}{8} \right) = \left( \frac{- 5}{9} \times \frac{4}{15} \right) \times \frac{- 9}{8}$
Exercise 1.6 | Q 6.5 | Page 32

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

$\frac{13}{- 17} \times 1 = \frac{13}{- 17} = 1 \times \frac{13}{- 17}$
Exercise 1.6 | Q 6.6 | Page 32

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

$\frac{- 11}{16} \times \frac{16}{- 11} = 1$
Exercise 1.6 | Q 6.7 | Page 32

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

$\frac{2}{13} \times 0 = 0 = 0 \times \frac{2}{13}$
Exercise 1.6 | Q 6.8 | Page 32

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

$\frac{- 3}{2} \times \frac{5}{4} + \frac{- 3}{2} \times \frac{- 7}{6} = \frac{- 3}{2} \times \left( \frac{5}{4} + \frac{- 7}{6} \right)$
Exercise 1.6 | Q 7.01 | Page 32

Fill in the blanks:
The product of two positive rational numbers is always .....

Exercise 1.6 | Q 7.02 | Page 32

Fill in the blanks:
The product of a positive rational number and a negative rational number is always .....

Exercise 1.6 | Q 7.03 | Page 32

Fill in the blanks:
The product of two negative rational numbers is always .....

Exercise 1.6 | Q 7.04 | Page 32

Fill in the blanks:
The reciprocal of a positive rational number is .....

Exercise 1.6 | Q 7.05 | Page 32

Fill in the blanks:
The reciprocal of a negative rational number is .....

Exercise 1.6 | Q 7.06 | Page 32

Fill in the blanks:
Zero has ..... reciprocal.

Exercise 1.6 | Q 7.07 | Page 32

Fill in the blanks:

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

Exercise 1.6 | Q 7.08 | Page 32

Fill in the blanks:

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

Exercise 1.6 | Q 7.09 | Page 32

Fill in the blanks:

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

Exercise 1.6 | Q 7.1 | Page 32

Fill in the blanks:
The number 0 is ..... the reciprocal of any number.

Exercise 1.6 | Q 7.11 | Page 32

Fill in the blanks:

Reciprocal of$\frac{1}{a}, a \neq 0$

Exercise 1.6 | Q 7.12 | Page 32

Fill in the blanks:

(17 × 12)−1 = 17−1 × .....

Exercise 1.6 | Q 8.1 | Page 33

Fill in the blanks:

$- 4 \times \frac{7}{9} = \frac{7}{9} \times . . . . . .$
Exercise 1.6 | Q 8.2 | Page 33

Fill in the blanks:

$\frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times . . . . . .$
Exercise 1.6 | Q 8.3 | Page 33

Fill in the blanks:

$\frac{1}{2} \times \left( \frac{3}{4} + \frac{- 5}{12} \right) = \frac{1}{2} \times . . . . . . + . . . . . . \times \frac{- 5}{12}$
Exercise 1.6 | Q 8.4 | Page 33

Fill in the blanks:

$\frac{- 4}{5} \times \left( \frac{5}{7} + \frac{- 8}{9} \right) = \left( \frac{- 4}{5} \times . . . . . \right) \times \frac{- 8}{9}$
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Exercise 1.7 [Pages 35 - 36]

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

Exercise 1.7 | Q 1.01 | Page 35

Divide:

$1 \text{by} \frac{1}{2}$
Exercise 1.7 | Q 1.02 | Page 35

Divide:

$5 \text{by} \frac{- 5}{7}$
Exercise 1.7 | Q 1.03 | Page 35

Divide:

$\frac{- 3}{4} \text{by} \frac{9}{- 16}$
Exercise 1.7 | Q 1.04 | Page 35

Divide:

$\frac{- 7}{8} \text{by} \frac{- 21}{16}$
Exercise 1.7 | Q 1.05 | Page 35

Divide:

$\frac{7}{- 4} \text{by} \frac{63}{64}$
Exercise 1.7 | Q 1.06 | Page 35

Divide:

$0 \text{by} \frac{- 7}{5}$
Exercise 1.7 | Q 1.07 | Page 35

Divide:

$\frac{- 3}{4} \text{by} - 6$
Exercise 1.7 | Q 1.08 | Page 35

Divide:

$\frac{2}{3} \text{by} \frac{- 7}{12}$
Exercise 1.7 | Q 1.09 | Page 35

Divide:

$- 4\ \text{by} \frac{- 3}{5}$
Exercise 1.7 | Q 1.1 | Page 35

Divide:

$\frac{- 3}{13}\ \text{by} \frac{- 4}{65}$
Exercise 1.7 | Q 2.1 | Page 36

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

$\frac{2}{5} \div \frac{26}{15}$
Exercise 1.7 | Q 2.2 | Page 36

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

$\frac{10}{3} \div \frac{- 35}{12}$
Exercise 1.7 | Q 2.3 | Page 36

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

$- 6 \div \left( \frac{- 8}{17} \right)$
Exercise 1.7 | Q 2.4 | Page 36

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

$\frac{- 40}{99} \div ( - 20)$
Exercise 1.7 | Q 2.5 | Page 36

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

$\frac{- 22}{27} \div \frac{- 110}{18}$
Exercise 1.7 | Q 2.6 | Page 36

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

$\frac{- 36}{125} \div \frac{- 3}{75}$
Exercise 1.7 | Q 3 | Page 36

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

Exercise 1.7 | Q 4 | Page 36

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

Exercise 1.7 | Q 5 | Page 36

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

Exercise 1.7 | Q 6 | Page 36

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

Exercise 1.7 | Q 7 | Page 36

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

so that the product may be 24?

Exercise 1.7 | Q 8 | Page 36

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

Exercise 1.7 | Q 9.1 | Page 36

Find (x + y) ÷ (x − y), if

$x = \frac{2}{3}, y = \frac{3}{2}$
Exercise 1.7 | Q 9.2 | Page 36

Find (x + y) ÷ (x − y), if

$x = \frac{2}{5}, y = \frac{1}{2}$
Exercise 1.7 | Q 9.3 | Page 36

Find (x + y) ÷ (x − y), if

$x = \frac{5}{4}, y = \frac{- 1}{3}$
Exercise 1.7 | Q 9.4 | Page 36

Find (x + y) ÷ (x − y), if

$x = \frac{2}{7}, y = \frac{4}{3}$
Exercise 1.7 | Q 9.5 | Page 36

Find (x + y) ÷ (x − y), if

$x = \frac{1}{4}, y = \frac{3}{2}$
Exercise 1.7 | Q 10 | Page 36

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

Find its cost per metre.

Exercise 1.7 | Q 11 | Page 36

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

Exercise 1.7 | Q 12 | Page 36

By what number should (- 33)/16 be divided to get (-11)/4?

Exercise 1.7 | Q 13 | Page 36

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

Exercise 1.7 | Q 14 | Page 36

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

Exercise 1.7 | Q 15 | Page 36

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

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Exercise 1.8 [Page 43]

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

Exercise 1.8 | Q 1 | Page 43

Find a rational number between −3 and 1.

Exercise 1.8 | Q 2 | Page 43

Find any five rational numbers less than 2.

Exercise 1.8 | Q 3 | Page 43

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

Exercise 1.8 | Q 4 | Page 43

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

Exercise 1.8 | Q 5 | Page 43

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

Exercise 1.8 | Q 6 | Page 43

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

Exercise 1.8 | Q 7 | Page 43

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

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## Chapter 1: Rational Numbers

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5Exercise 1.6Exercise 1.7Exercise 1.8 ## 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 Closure Property of Rational Numbers, Commutativity Property of Rational Numbers, Identity of Addition and Multiplication, Associativity of Rational Numbers, Distributivity of Multiplication Over Addition for Rational, Rational Numbers Between Two Rational Numbers, Concept of Rational Numbers, Negative of a Number, Additive Inverse of Rational Number, Rational Numbers on a Number Line.

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.

Get the free view of chapter 1 Rational Numbers Class 8 extra questions for Class 8 Maths and can use Shaalaa.com to keep it handy for your exam preparation

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