RD Sharma solutions for Mathematics [English] Class 8 chapter 1 - Rational Numbers [Latest edition]

Add the following rational numbers.

Add the following rational numbers.

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

Add the following rational numbers.

Add the following rational numbers.

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

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Add the following rational numbers:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

Add and express the sum as a mixed fraction:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

Evaluate each of the following:

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

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

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

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

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

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

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

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

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

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

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

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

Fill in the branks:

Fill in the branks:

Fill in the branks:

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

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

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

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

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

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

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

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

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

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

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

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

Multiply:

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

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

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

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

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

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

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

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

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

Simplify:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

9

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

−7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Zero has ______ reciprocal.

Fill in the blanks:

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

Fill in the blanks:

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

Fill in the blanks:

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

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

Fill in the blanks:

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

Fill in the blanks:

(17 × 12)⁻¹ = 17⁻¹ × .....

Fill in the blanks:

Fill in the blanks:

Fill in the blanks:

Fill in the blanks:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

Divide:

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

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

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

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

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

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

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

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

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

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

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

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

Find (x + y) ÷ (x − y), if

Find (x + y) ÷ (x − y), if

Find (x + y) ÷ (x − y), if

Find (x + y) ÷ (x − y), if

Find (x + y) ÷ (x − y), if

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

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

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

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

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

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

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

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

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

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