Example.1
4568 x 75
- 12345 = ? + 5555
Solution
799400 - 12345 = ? + 5555
&⇒ ? = 799400 - 12345 - 5555
&⇒ ? = 781500
example.2
= ?
Solution
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image002.gif)
= ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image003.gif)
= ? = ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image004.gif)
example.3
Simplify: ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image005.gif)
Solution
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image006.gif)
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image007.gif)
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image008.gif)
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image009.gif)
Hence the expression when simplified becomes ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image010.gif)
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 ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image014.gif)
Solution
Take the LCM of the denominators and then
compare the numerators. .
LCM of 9, 7 and 2 = 126
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image015.gif)
Comparing the numerators, 72 > 70 > 63
Hence
>
> ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image014.gif)
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
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image022.gif)
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image023.gif)
As the denominators are equal, comparing the
numerators 24 < 25 < 26
Hence
<
< ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image025.gif)
example.8
Simplify:
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image026.gif)
Solution
Applying BODMAS
rule,
of ![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image028.gif)
Hence the expressions when simplified gives
= [15 + 31] = 46
example.9
(3
+ 4
)(5
+
) - 24 = ?
Solution
7
x 6
– 24 = ?
= ? = 84 - 24 = 60
Example.10
![](http://www.quizsolver.com/radix/dth/notif/Worked%20out%20examples%20LCM%20HCF%202%20_files/image031.gif)
Solution
108 x 78 - 3025 =
+ 5329
&⇒
= 8424 - 3025 - 5329
&⇒
= 70 \ ? = (70)2 =
4900