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 - 2.753 .
Solution
By
substituting 2.25 = a and 2.75 = b, the expression when simplified gives .
a3 + 3ab2 - 3a2b
- b3 = (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
