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RD Sharma solutions for Class 8 Mathematics chapter 1 - Rational Numbers

Mathematics for Class 8 by R D Sharma (2019-2020 Session)

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RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

Chapter 1: Rational Numbers

Ex. 1.10Ex. 1.20Ex. 1.30Ex. 1.40Ex. 1.50Ex. 1.60Ex. 1.70Ex. 1.80

Chapter 1: Rational Numbers Exercise 1.10 solutions [Pages 5 - 6]

Ex. 1.10 | Q 1.1 | Page 5

Add the following rational numbers.

\[\frac{- 5}{7} and \frac{3}{7}\]

 

Ex. 1.10 | Q 1.2 | Page 5

Add the following rational numbers.

\[\frac{- 15}{4} and \frac{7}{4}\]

 

Ex. 1.10 | Q 1.3 | Page 5

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

Ex. 1.10 | Q 1.4 | Page 5

Add the following rational numbers.

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

 

Ex. 1.10 | Q 1.5 | Page 5

Add the following rational numbers.

\[\frac{6}{13} and \frac{- 9}{13}\]

 

Ex. 1.10 | Q 2.1 | Page 6

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

Ex. 1.10 | Q 2.2 | Page 6

Add the following rational numbers:

\[\frac{5}{- 9} and \frac{7}{3}\]
Ex. 1.10 | Q 2.3 | Page 6

Add the following rational numbers:

\[- 3 and \frac{3}{5}\]
Ex. 1.10 | Q 2.4 | Page 6

Add the following rational numbers:

\[\frac{- 7}{27} and \frac{11}{18}\]
Ex. 1.10 | Q 2.5 | Page 6

Add the following rational numbers:

\[\frac{31}{- 4} and \frac{- 5}{8}\]
Ex. 1.10 | Q 2.6 | Page 6

Add the following rational numbers:

\[\frac{5}{36} and \frac{- 7}{12}\]
Ex. 1.10 | Q 2.7 | Page 6

Add the following rational numbers:

\[\frac{- 5}{16} and \frac{7}{24}\]
Ex. 1.10 | Q 2.8 | Page 6

Add the following rational numbers:

\[\frac{7}{- 18} and \frac{8}{27}\]
Ex. 1.10 | Q 3.01 | Page 6

Simplify:

\[\frac{8}{9} + \frac{- 11}{6}\]

 

Ex. 1.10 | Q 3.02 | Page 6

Simplify:

\[3 + \frac{5}{- 7}\]
Ex. 1.10 | Q 3.03 | Page 6

Simplify:

\[\frac{1}{- 12} + \frac{2}{- 15}\]
Ex. 1.10 | Q 3.04 | Page 6

Simplify:

\[\frac{- 8}{19} + \frac{- 4}{57}\]
Ex. 1.10 | Q 3.05 | Page 6

Simplify:

\[\frac{7}{9} + \frac{3}{- 4}\]
Ex. 1.10 | Q 3.06 | Page 6

Simplify:

\[\frac{5}{26} + \frac{11}{- 39}\]
Ex. 1.10 | Q 3.07 | Page 6

Simplify:

\[\frac{- 16}{9} + \frac{- 5}{12}\]
Ex. 1.10 | Q 3.08 | Page 6

Simplify:

\[\frac{- 13}{8} + \frac{5}{36}\]
Ex. 1.10 | Q 3.09 | Page 6

Simplify:

\[0 + \frac{- 3}{5}\]
Ex. 1.10 | Q 3.1 | Page 6

Simplify:

\[1 + \frac{- 4}{5}\]
Ex. 1.10 | Q 4.1 | Page 6

Add and express the sum as a mixed fraction:

\[\frac{- 12}{5} \text{and} \frac{43}{10}\]
Ex. 1.10 | Q 4.2 | Page 6

Add and express the sum as a mixed fraction:

\[\frac{24}{7} \text{and} \frac{- 11}{4}\]
Ex. 1.10 | Q 4.3 | Page 6

Add and express the sum as a mixed fraction:

\[\frac{- 31}{6} \text{and} \frac{- 27}{8}\]
Ex. 1.10 | Q 4.4 | Page 6

Add and express the sum as a mixed fraction:

\[\frac{101}{6} \text{and} \frac{7}{8}\]

Chapter 1: Rational Numbers Exercise 1.20 solutions [Page 14]

Ex. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | Q 3.1 | Page 14

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

\[\frac{- 2}{17}\]
Ex. 1.20 | Q 3.2 | Page 14

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

\[\frac{3}{- 11}\]
Ex. 1.20 | Q 3.3 | Page 14

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

\[\frac{- 17}{5}\]
Ex. 1.20 | Q 3.4 | Page 14

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

\[\frac{- 11}{- 25}\]
Ex. 1.20 | Q 4.1 | Page 14

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

\[\frac{- 2}{5}\]
Ex. 1.20 | Q 4.2 | Page 14

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

\[\frac{7}{- 9}\]
Ex. 1.20 | Q 4.3 | Page 14

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

\[\frac{- 16}{13}\]
Ex. 1.20 | Q 4.4 | Page 14

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

\[\frac{- 5}{1}\]
Ex. 1.20 | Q 4.5 | Page 14

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

 0
Ex. 1.20 | Q 4.6 | Page 14

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

Ex. 1.20 | Q 4.7 | Page 14

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

Ex. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | 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. 1.20 | Q 6.6 | Page 14

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

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

Chapter 1: Rational Numbers Exercise 1.30 solutions [Pages 18 - 19]

Ex. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | 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. 1.30 | Q 2.01 | Page 18

Evaluate each of the following:

\[\frac{2}{3} - \frac{3}{5}\]
Ex. 1.30 | Q 2.02 | Page 18

Evaluate each of the following:

\[- \frac{4}{7} - \frac{2}{- 3}\]
Ex. 1.30 | Q 2.03 | Page 18

Evaluate each of the following:

\[\frac{4}{7} - \frac{- 5}{- 7}\]
Ex. 1.30 | Q 2.04 | Page 18

Evaluate each of the following:

\[- 2 - \frac{5}{9}\]
Ex. 1.30 | Q 2.05 | Page 18

Evaluate each of the following:

\[\frac{- 3}{- 8} - \frac{- 2}{7}\]
Ex. 1.30 | Q 2.06 | Page 18

Evaluate each of the following:

\[\frac{- 4}{13} - \frac{- 5}{26}\]
Ex. 1.30 | Q 2.07 | Page 18

Evaluate each of the following:

\[\frac{- 5}{14} - \frac{- 2}{7}\]
Ex. 1.30 | Q 2.08 | Page 18

Evaluate each of the following:

\[\frac{13}{15} - \frac{12}{25}\]
Ex. 1.30 | Q 2.09 | Page 18

Evaluate each of the following:

\[\frac{- 6}{13} - \frac{- 7}{13}\]
Ex. 1.30 | Q 2.1 | Page 18

Evaluate each of the following:

\[\frac{7}{24} - \frac{19}{36}\]
Ex. 1.30 | Q 2.11 | Page 18

Evaluate each of the following:

\[\frac{5}{63} - \frac{- 8}{21}\]
Ex. 1.30 | 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. 1.30 | 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. 1.30 | Q 5 | Page 18

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

Ex. 1.30 | 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. 1.30 | Q 7 | Page 18

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

Ex. 1.30 | Q 8 | Page 18

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

Ex. 1.30 | Q 9 | Page 18

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

Ex. 1.30 | Q 10 | Page 18

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

Ex. 1.30 | Q 11 | Page 19

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

Ex. 1.30 | Q 12 | Page 19

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

Ex. 1.30 | Q 13 | Page 19

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

Ex. 1.30 | Q 14 | Page 19

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

Ex. 1.30 | Q 15.1 | Page 19

Fill in the branks:

\[\frac{- 4}{13} - \frac{- 3}{26} = . . .\]
Ex. 1.30 | Q 15.2 | Page 19

Fill in the branks:

\[\frac{- 9}{14} + . . . = - 1\]
Ex. 1.30 | Q 15.3 | Page 19

Fill in the branks:

\[\frac{- 7}{9} + . . . = 3\]
Ex. 1.30 | Q 15.4 | Page 19
Fill in the branks:
\[. . . + \frac{15}{23} = 4\]

Chapter 1: Rational Numbers Exercise 1.40 solutions [Pages 22 - 23]

Ex. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | 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. 1.40 | Q 3.1 | Page 23

Simplify:

\[\frac{- 3}{2} + \frac{5}{4} - \frac{7}{4}\]
Ex. 1.40 | Q 3.2 | Page 23

Simplify:

\[\frac{5}{3} - \frac{7}{6} + \frac{- 2}{3}\]
Ex. 1.40 | Q 3.3 | Page 23

Simplify:

\[\frac{5}{4} - \frac{7}{6} - \frac{- 2}{3}\]
Ex. 1.40 | Q 3.4 | Page 23

Simplify:

\[\frac{- 2}{5} - \frac{- 3}{10} - \frac{- 4}{7}\]
Ex. 1.40 | Q 3.5 | Page 23

Simplify:

\[\frac{5}{6} + \frac{- 2}{5} - \frac{- 2}{15}\]
Ex. 1.40 | Q 3.6 | Page 23

Simplify:

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

Chapter 1: Rational Numbers Exercise 1.50 solutions [Pages 25 - 26]

Ex. 1.50 | Q 1.1 | Page 25

Multiply:

\[\frac{7}{11} \text{by} \frac{5}{4}\]
Ex. 1.50 | Q 1.2 | Page 25

Multiply:

\[\frac{5}{7} \text{by} \frac{- 3}{4}\]
Ex. 1.50 | Q 1.3 | Page 25

Multiply:

\[\frac{- 2}{9} \text{by} \frac{5}{11}\]
Ex. 1.50 | Q 1.4 | Page 25

Multiply:

\[\frac{- 3}{17} \text{by} \frac{- 5}{- 4}\]
Ex. 1.50 | Q 1.5 | Page 25

Multiply:

\[\frac{9}{- 7} \text{by} \frac{36}{- 11}\]
Ex. 1.50 | Q 1.6 | Page 25

Multiply:

\[\frac{- 11}{13} \text{by} \frac{- 21}{7}\]
Ex. 1.50 | Q 1.7 | Page 25

Multiply:

\[- \frac{3}{5} \text{by} - \frac{4}{7}\]
Ex. 1.50 | Q 1.8 | Page 25

Multiply:

\[- \frac{15}{11} \text{by} 7\]
Ex. 1.50 | Q 2.1 | Page 25

Multiply:

\[\frac{- 5}{17} \text{by} \frac{51}{- 60}\]
Ex. 1.50 | Q 2.2 | Page 25

Multiply:

\[\frac{- 6}{11} \text{by} \frac{- 55}{36}\]
Ex. 1.50 | Q 2.3 | Page 25

Multiply:

\[\frac{- 8}{25} \text{by} \frac{- 5}{16}\]
Ex. 1.50 | Q 2.4 | Page 25

Multiply:

\[\frac{6}{7} \text{by} \frac{- 49}{36}\]
Ex. 1.50 | Q 2.5 | Page 25

Multiply:

\[\frac{8}{- 9} \text{by} \frac{- 7}{- 16}\]
Ex. 1.50 | Q 2.6 | Page 25

Multiply:

\[\frac{- 8}{9} \text{by} \frac{3}{64}\]
Ex. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | Q 4.2 | Page 26

Simplify:

\[\left( \frac{1}{2} \times \frac{1}{4} \right) + \left( \frac{1}{2} \times 6 \right)\]
Ex. 1.50 | Q 4.3 | Page 26

Simplify:

\[\left( - 5 \times \frac{2}{15} \right) - \left( - 6 \times \frac{2}{9} \right)\]
Ex. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | 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. 1.50 | Q 5.4 | Page 26

Simplify:

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

Chapter 1: Rational Numbers Exercise 1.60 solutions [Pages 31 - 33]

Ex. 1.60 | Q 1.1 | Page 31

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

\[x = - \frac{1}{3}, y = \frac{2}{7}\]
Ex. 1.60 | Q 1.2 | Page 31

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

\[x = \frac{- 3}{5}, y = \frac{- 11}{13}\]
Ex. 1.60 | Q 1.3 | Page 31

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

\[x = 2, y = \frac{7}{- 8}\]
Ex. 1.60 | Q 1.4 | Page 31

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

\[x = 0, y = \frac{- 15}{8}\]
Ex. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | Q 5.01 | Page 32

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

9

Ex. 1.60 | Q 5.02 | Page 32

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

−7

Ex. 1.60 | Q 5.03 | Page 32

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

\[\frac{12}{5}\]
Ex. 1.60 | Q 5.04 | Page 32

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

\[\frac{- 7}{9}\]
Ex. 1.60 | Q 5.05 | Page 32

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

\[\frac{- 3}{- 5}\]
Ex. 1.60 | 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. 1.60 | 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. 1.60 | Q 5.08 | Page 32

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

\[- 2 \times \frac{- 3}{5}\]
Ex. 1.60 | Q 5.09 | Page 32

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

 −1
Ex. 1.60 | Q 5.1 | Page 32

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

\[\frac{0}{3}\]
Ex. 1.60 | Q 5.11 | Page 32

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

1
Ex. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | 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. 1.60 | Q 7.01 | Page 32

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

Ex. 1.60 | Q 7.02 | Page 32

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

Ex. 1.60 | Q 7.03 | Page 32

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

Ex. 1.60 | Q 7.04 | Page 32

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

Ex. 1.60 | Q 7.05 | Page 32

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

Ex. 1.60 | Q 7.06 | Page 32

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

Ex. 1.60 | Q 7.07 | Page 32

Fill in the blanks:

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

Ex. 1.60 | Q 7.08 | Page 32

Fill in the blanks:

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

 

Ex. 1.60 | Q 7.09 | Page 32

Fill in the blanks:

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

 

Ex. 1.60 | Q 7.1 | Page 32

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

Ex. 1.60 | Q 7.11 | Page 32

Fill in the blanks:

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

Ex. 1.60 | Q 7.12 | Page 32

Fill in the blanks:

(17 × 12)−1 = 17−1 × .....

Ex. 1.60 | Q 8.1 | Page 33

Fill in the blanks:

\[- 4 \times \frac{7}{9} = \frac{7}{9} \times . . . . . .\]
Ex. 1.60 | Q 8.2 | Page 33

Fill in the blanks:

\[\frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times . . . . . .\]
Ex. 1.60 | 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. 1.60 | Q 8.4 | Page 33

Fill in the blanks:

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

Chapter 1: Rational Numbers Exercise 1.70 solutions [Pages 35 - 36]

Ex. 1.70 | Q 1.01 | Page 35

Divide:

\[1 \text{by} \frac{1}{2}\]
Ex. 1.70 | Q 1.02 | Page 35

Divide:

\[5 \text{by} \frac{- 5}{7}\]
Ex. 1.70 | Q 1.03 | Page 35

Divide:

\[\frac{- 3}{4} \text{by} \frac{9}{- 16}\]
Ex. 1.70 | Q 1.04 | Page 35

Divide:

\[\frac{- 7}{8} \text{by} \frac{- 21}{16}\]
Ex. 1.70 | Q 1.05 | Page 35

Divide:

\[\frac{7}{- 4} \text{by} \frac{63}{64}\]
Ex. 1.70 | Q 1.06 | Page 35

Divide:

\[0 \text{by} \frac{- 7}{5}\]
Ex. 1.70 | Q 1.07 | Page 35

Divide:

\[\frac{- 3}{4} \text{by} - 6\]
Ex. 1.70 | Q 1.08 | Page 35

Divide:

\[\frac{2}{3} \text{by} \frac{- 7}{12}\]
Ex. 1.70 | Q 1.09 | Page 35

Divide:

\[- 4\ \text{by} \frac{- 3}{5}\]
Ex. 1.70 | Q 1.1 | Page 35

Divide:

\[\frac{- 3}{13}\ \text{by} \frac{- 4}{65}\]
Ex. 1.70 | 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. 1.70 | 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. 1.70 | 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. 1.70 | Q 2.4 | Page 36

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

\[\frac{- 40}{99} \div ( - 20)\]
Ex. 1.70 | 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. 1.70 | 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. 1.70 | Q 3 | Page 36

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

Ex. 1.70 | 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. 1.70 | Q 5 | Page 36

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

Ex. 1.70 | Q 6 | Page 36

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

Ex. 1.70 | Q 7 | Page 36

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

 so that the product may be 24?

Ex. 1.70 | Q 8 | Page 36

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

Ex. 1.70 | Q 9.1 | Page 36

Find (x + y) ÷ (x − y), if

\[x = \frac{2}{3}, y = \frac{3}{2}\]
Ex. 1.70 | Q 9.2 | Page 36

Find (x + y) ÷ (x − y), if

\[x = \frac{2}{5}, y = \frac{1}{2}\]
Ex. 1.70 | Q 9.3 | Page 36

Find (x + y) ÷ (x − y), if

\[x = \frac{5}{4}, y = \frac{- 1}{3}\]
Ex. 1.70 | Q 9.4 | Page 36

Find (x + y) ÷ (x − y), if

\[x = \frac{2}{7}, y = \frac{4}{3}\]
Ex. 1.70 | Q 9.5 | Page 36

Find (x + y) ÷ (x − y), if

\[x = \frac{1}{4}, y = \frac{3}{2}\]
Ex. 1.70 | 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. 1.70 | 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. 1.70 | Q 12 | Page 36

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

Ex. 1.70 | 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. 1.70 | Q 14 | Page 36

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

Ex. 1.70 | 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?

Chapter 1: Rational Numbers Exercise 1.80 solutions [Page 43]

Ex. 1.80 | Q 1 | Page 43

Find a rational number between −3 and 1.

Ex. 1.80 | Q 2 | Page 43

 Find any five rational numbers less than 2.

Ex. 1.80 | Q 3 | Page 43

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

Ex. 1.80 | Q 4 | Page 43

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

Ex. 1.80 | Q 5 | Page 43

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

Ex. 1.80 | Q 6 | Page 43

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

Ex. 1.80 | Q 7 | Page 43

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

Chapter 1: Rational Numbers

Ex. 1.10Ex. 1.20Ex. 1.30Ex. 1.40Ex. 1.50Ex. 1.60Ex. 1.70Ex. 1.80

RD Sharma Mathematics Class 8 by R D Sharma (2019-2020 Session)

Mathematics for Class 8 by R D Sharma (2019-2020 Session) - Shaalaa.com

RD Sharma solutions for Class 8 Mathematics 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 Mathematics for Class 8 by R D Sharma (2019-2020 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 8 Mathematics 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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