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

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## Chapter 1: Rational Numbers

Ex. 1.1Ex. 1.2Ex. 1.3Ex. 1.4Ex. 1.5Ex. 1.6Ex. 1.7Ex. 1.8

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

Ex. 1.1 | Q 1.1 | Page 5

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

Ex. 1.1 | Q 1.2 | Page 5

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

Ex. 1.1 | Q 1.3 | Page 5

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

Ex. 1.1 | Q 1.4 | Page 5

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

Ex. 1.1 | Q 1.5 | Page 5

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

Ex. 1.1 | Q 2.1 | Page 6

$\frac{3}{4} and \frac{- 5}{8}$

Ex. 1.1 | Q 2.2 | Page 6

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

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

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

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

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

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

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

Simplify:

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

Ex. 1.1 | Q 3.02 | Page 6

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Add and express the sum as a mixed fraction:

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

Add and express the sum as a mixed fraction:

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

Add and express the sum as a mixed fraction:

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

Add and express the sum as a mixed fraction:

$\frac{101}{6} \text{and} \frac{7}{8}$

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

Ex. 1.2 | Q 1.1 | Page 14

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

0
Ex. 1.2 | Q 4.6 | Page 14

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

Ex. 1.2 | Q 4.7 | Page 14

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

Ex. 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:

$\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$
Ex. 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:

$\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$
Ex. 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:

$\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$
Ex. 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:

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

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

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

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

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

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

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

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

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

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

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

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

$\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

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

Ex. 1.3 | Q 1.1 | Page 18

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

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

Evaluate each of the following:

$\frac{5}{63} - \frac{- 8}{21}$
Ex. 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.

Ex. 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.

Ex. 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.

Ex. 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.

Ex. 1.3 | Q 7 | Page 18

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

Ex. 1.3 | Q 8 | Page 18

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

Ex. 1.3 | Q 9 | Page 18

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

Ex. 1.3 | Q 10 | Page 18

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

Ex. 1.3 | Q 11 | Page 19

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

Ex. 1.3 | Q 12 | Page 19

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

Ex. 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?

Ex. 1.3 | Q 14 | Page 19

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

Ex. 1.3 | Q 15.1 | Page 19

Fill in the branks:

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

Fill in the branks:

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

Fill in the branks:

$\frac{- 7}{9} + . . . = 3$
Ex. 1.3 | Q 15.4 | Page 19
Fill in the branks:
$. . . + \frac{15}{23} = 4$

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

Ex. 1.4 | Q 1.1 | Page 22

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

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

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

$\frac{2}{3} + \frac{- 5}{6} + \frac{- 7}{9}$
Ex. 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}$

Ex. 1.4 | Q 1.4 | Page 22

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

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

Ex. 1.4 | Q 1.5 | Page 22

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

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

Ex. 1.4 | Q 1.6 | Page 22

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

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

Ex. 1.4 | Q 2.1 | Page 23

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

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

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

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

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

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

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

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

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

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

$\frac{3}{8} - \frac{- 2}{9} + \frac{- 5}{36}$

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

Ex. 1.5 | Q 1.1 | Page 25

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

Multiply:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

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

Simplify:

$\left( \frac{3}{11} \times \frac{5}{6} \right) - \left( \frac{9}{12} \times \frac{4}{3} \right) + \left( \frac{5}{13} \times \frac{6}{15} \right)$

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

Ex. 1.6 | Q 1.1 | Page 31

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

9

Ex. 1.6 | Q 5.02 | Page 32

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

−7

Ex. 1.6 | Q 5.03 | Page 32

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

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

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

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

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

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

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

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

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

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

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

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

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

−1
Ex. 1.6 | Q 5.1 | Page 32

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

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

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

1
Ex. 1.6 | Q 6.1 | Page 32

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ex. 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 .....

Ex. 1.6 | Q 7.03 | Page 32

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

Ex. 1.6 | Q 7.04 | Page 32

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

Ex. 1.6 | Q 7.05 | Page 32

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

Ex. 1.6 | Q 7.06 | Page 32

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

Ex. 1.6 | Q 7.07 | Page 32

Fill in the blanks:

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

Ex. 1.6 | Q 7.08 | Page 32

Fill in the blanks:

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

Ex. 1.6 | Q 7.09 | Page 32

Fill in the blanks:

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

Ex. 1.6 | Q 7.1 | Page 32

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

Ex. 1.6 | Q 7.11 | Page 32

Fill in the blanks:

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

Ex. 1.6 | Q 7.12 | Page 32

Fill in the blanks:

(17 × 12)−1 = 17−1 × .....

Ex. 1.6 | Q 8.1 | Page 33

Fill in the blanks:

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

Fill in the blanks:

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

Fill in the blanks:

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

Fill in the blanks:

$\frac{- 4}{5} \times \left( \frac{5}{7} + \frac{- 8}{9} \right) = \left( \frac{- 4}{5} \times . . . . . \right) \times \frac{- 8}{9}$

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

Ex. 1.7 | Q 1.01 | Page 35

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

Divide:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ex. 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.

Ex. 1.7 | Q 5 | Page 36

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

Ex. 1.7 | Q 6 | Page 36

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

Ex. 1.7 | Q 7 | Page 36

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

so that the product may be 24?

Ex. 1.7 | Q 8 | Page 36

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

Ex. 1.7 | Q 9.1 | Page 36

Find (x + y) ÷ (x − y), if

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

Find (x + y) ÷ (x − y), if

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

Find (x + y) ÷ (x − y), if

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

Find (x + y) ÷ (x − y), if

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

Find (x + y) ÷ (x − y), if

$x = \frac{1}{4}, y = \frac{3}{2}$
Ex. 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.

Ex. 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.

Ex. 1.7 | Q 12 | Page 36

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

Ex. 1.7 | Q 13 | Page 36

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

Ex. 1.7 | Q 14 | Page 36

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

Ex. 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?

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

Ex. 1.8 | Q 1 | Page 43

Find a rational number between −3 and 1.

Ex. 1.8 | Q 2 | Page 43

Find any five rational numbers less than 2.

Ex. 1.8 | Q 3 | Page 43

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

Ex. 1.8 | Q 4 | Page 43

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

Ex. 1.8 | Q 5 | Page 43

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

Ex. 1.8 | Q 6 | Page 43

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

Ex. 1.8 | Q 7 | Page 43

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

## Chapter 1: Rational Numbers

Ex. 1.1Ex. 1.2Ex. 1.3Ex. 1.4Ex. 1.5Ex. 1.6Ex. 1.7Ex. 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.

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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.

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