Solution of Chapter 1. Rational Numbers (RD Sharma - Mathematics Book)

Exercise 1.1

1

(i) and

(ii) and

(iii) and

(iv) and

2

(i) and

(ii) and

(iii) and

(iv) and

(v) and

(vi) and

(vii) and

(viii) and

3

Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

4

Add and express the sum as a mixed fraction:

(i) and

(ii) and

(iii) and

(iv) and

Exercise 1.2

1

Verify commutativity of addition of rational numbers for each of the following pairson of rational numbers:

(i) and

(ii) and

(iii) and

(iv) and

(v) 4 and

(vi) -4and

2

Verify associativity of addition of rational numbers i.e., when:

(i)

(ii)

(iii)

(iv)

3

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

(i)

(ii)

(iii)

(iv)

4

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

(i)

(ii)

(iii)

(iv)

(v) 0

(vi) 1

(vii) -1

5

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

(i)

(ii)

(iii)

(iv)

6

Re-arrange sutably and find the sum in each of the following.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Exercise 1.3

1

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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

2

Evalute each of the following:

(i) +

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi) -

3

The sum of the two numbers is . If one of the numbers is , find the other

4

The sum of two numbers is . If one of the numbers is , find the other

5

The sum of two numbers is . If one of the numbers is -5, find the other

6

The sum of two ratinal numbers is -8. If one of the numbers is , find the other

7

What should be added to so as to get ?

8

What number should be added to so as to get ?

9

What number should be addede to to get?

10

What number should be subtracted from to get ?

11

What number should be subtracted from to get?

12

What should be added to ( + ) to get?

13

What should be subtracted from ( + + ) to get 3?

14

What should be subtracted from ( - ) to get ?

15

Fill in the blanks:

(i) (ii)

(iii) (iv)

Exercise 1.4

1

Simplify each of the following and write as rational number of the form:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

2

Express each of the following as a rational number of the form :

(i)

(ii)

(iii)

(iv)

(v)

3

Simplify:

(i)

(ii)

(iii) - -

(iv)

(v)

(vi)

Exercise 1.5

1

Multiply:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

2

Multiply:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

3

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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

4

Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

5

Simplify:

(i) ( * ) + ( * ) – ( * )

(ii)

(iii)

(iv)

Exercise 1.6

1

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

2

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

3

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

4

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

(i)

(ii)

(iii)

(iv)

5

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

(i) 9

(ii) -7

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix) -1

(x)

(xi)1

6

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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

7

Fill in the blanks:

(i) The product of two positive rational numbers is always………..

(ii) The product of a positive rational number and a negative rational number is always ……..

(iii) The product of two negative rational numbers is always………..

(iv)The reciprocal of a positive rational numbers is ………..

(v) The reciprocal of a negative rational number is………..

(vi) The product of a rational number and its reciprocal is……..

(vii) Zero has……. reciprocal

(viii) The numbers……. and….. are their own reciprocals.

(ix)If a is reciprocal of b, then the reciprocal of b is ………

(x) The number 0 is ……… the reciprocal of any number.

(xi) Reciprocal of is

(xii)

8

Fill in the blanks:

(i) (ii)

(iii)

(iv)

Exercise 1.7

1

Divide:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

2

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

(i)

(ii)

(iii)

(iv)

(v)

(vi)

3

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

4

The product of two rational numbers is . If one of thenumbers is , find the other.

5

By what number should we multiply so that the product may be?

6

By what number should we multiply so that the product may be?

7

By what number should we multiply so theat the product may be 24?

8

By what number should be multiplied in order to produce ?

9

Find if

(i)

(ii)

(iii)

(iv)

(v)

10

The cost of metres of rope is Rs .Find its cost per metre.

11

The cost of metres of cloth is Rs. Find the cost of cloth per metre

12

By what number should be divided to get?

13

Divide the sum of and by the product of and

14

Divide the sum of and by their difference.

15

If 24 trousers of equal size can be prepared in 54 metres of cloth. What length of cloth is required for

each trouser?

Exercise 1.8

1

Find a rational number between -3 and 1

2

Find any five rational numbers less than 2.

3

Find two rational numbers between and

4

Find two rational numbers between and

5

Find ten rational numbers between and