## Example.1

4568 x 75
- 12345 = ? + 5555

### Solution

799400 - 12345 = ? + 5555

&⇒ ? = 799400 - 12345 - 5555

&⇒ ? = 781500

## example.2

= ?

### Solution

=

= ? =

## example.3

Simplify:

### Solution

Hence the expression when simplified becomes

## example.4

Simplify :

### Solution

By substitution let 5.71 = a and 3.21 = b. .

The expression when simplified gives

which is equal to (a - b)

As a = 5.71 and b = 3.21 .

a - b = 2.5 .

## example.5

Simplify:

(2.25)^{3 }+ 6.75 x (2.75)^{2}
- 8.25 x (2.25)^{2} - 2.75^{3} .

### Solution

By
substituting 2.25 = a and 2.75 = b, the expression when simplified gives .

a^{3} + 3ab^{2} - 3a^{2}b
- b^{3} = (a - b)^{3}

As a = 2.25 and b = 2.75 .

(a - b)^{3} = (-0.5)^{3} =
-0.125 .

## example.6

Arrange the following fractions in descending
order. and

### Solution

Take the LCM of the denominators and then
compare the numerators. .

LCM of 9, 7 and 2 = 126

Comparing the numerators, 72 > 70 > 63

Hence > >

## example.7

Arrange and in ascending order.

### Solution

Let us make each of the denominators equal,
to the LCM of the denominators of the fractions

LCM (48, 4, 96) = 96

As the denominators are equal, comparing the
numerators 24 < 25 < 26

Hence < <

## example.8

Simplify:

### Solution

Applying BODMAS
rule,

of

Hence the expressions when simplified gives

= [15 + 31] = 46

## example.9

(3+ 4)(5+ ) - 24 = ?

### Solution

7x 6– 24 = ?

= ? = 84 - 24 = 60

## Example.10

### Solution

108 x 78 - 3025 = + 5329

&⇒ = 8424 - 3025 - 5329

&⇒ = 70 \ ? = (70)^{2 }=
4900