Simplification of Complex Fraction
Method of Simplification -
1) An expression involving fraction is simplified by following the rules of BODMAS, brackets are removed in the order, line bracket, first brackets, second brackets then third brackets. Simplification of a complex fraction is like carrying out a division.
2) Then change 'OF' into 'X' and multiply
3) Carry out the operation of multiplication and division, in that order
4) Finally carry out the operations of addition and subtraction
Example.1)
3 6 4
Simplify 3 ------ of ------- + 5 ÷ [ 5 X { 4 – ( 4 - ----- )}]
5 5 5
Given expression is
3 6 4
3 ------ of ------ + 5 ÷ [ 5 X { 4 – ( 4 - ------ )}]
5 5 5
18 6 20 - 4
= -------- of -------- + 5 ÷ [ 5 X { 4 – ( ----------- )}]
5 5 5
18 6 20 - 4
= -------- of ------- + 5 ÷ [ 5 X { 4 – ---------- }]
5 5 5
18 6 20 - 16
= -------- of -------- + 5 ÷ [ 5 X { ---------- }]
5 5 5
18 6 4
= --------- of -------- + 5 ÷ [ 5 X --------- ]
5 5 5
18 6
= -------- of -------- + 5 ÷ 4
5 5
18 6 5 1
= ---------- of --------- + --------- X ---------
5 5 1 4
18 5 5 1
= ---------- X --------- + ---------- X --------
5 6 1 4
5 5
= 3 + -------- = 3 -------- (Ans.)
4 4
Example.2)
3 5 3
Simplify the following ------- of ( 2 ------- X 3 ------- )
4 7 5
3 5 3
Simplify the following -------- of ( 2 ------- X 3 ------- )
4 7 5
Ans.)
3 5 3
-------- of ( 2 ------- X 3 -------- )
4 7 5
3 19 18
= --------- of ( -------- X -------- )
4 7 5
3 342
= --------- of ( --------- )
4 35
3 35 35 35
= ------- X -------- = --------- = --------- (Ans.)
4 342 4 X 114 456
Example.3)
3 8 5 7
Simplify the equation ( ------ X ------ - ------- ) + -------
4 9 12 12
3 8 5 7
= ( ------- X ------- - ------- ) + ---------
4 9 12 12
2 5 7
= ( -------- - -------- ) + ---------
3 12 12
8 - 5 7
= ( ------------- ) + ---------
12 12
3 7 3 + 7 10 5
= ------- + ------- = --------- = ------- = -------- (Ans.)
12 12 12 12 6
Example.4)
4 5 5 8
Simplify the equation 8 ----- ÷ 9 ------ X ( 2 ------ X 4 ----- )
5 7 7 5
4 5 5 8
= 8 ------ ÷ 9 ------- X ( 2 ------ X 4 ------ )
5 7 7 5
44 68 76
= ---------- ÷ ---------- X -----------
5 7 5
44 68 X 76
= ---------- ÷ --------------
5 7 X 5
11 X 7 77
= --------------- = ---------- (Ans.)
17 X 76 1292
Example.5)
4 4 8 4 5
Simplify the equations ----- ÷ 7----- X {(----- + -----) - ----- }
15 10 18 9 12
4 4 8 4 5
= ----- ÷ 7----- X {(------ + ------) - ------ }
15 10 18 9 12
4 4 8 + 8 5
= ------ ÷ 7------ X { --------- - ------- }
15 10 18 12
4 4 16 5
= ------ ÷ 7------ X {------- - ------- }
15 10 18 12
4 4 16 5
= ------ ÷ 7 ------ X { ------ - ------- }
15 10 18 12
4 4 32 - 15
= ------ ÷ 7------- X { ----------- }
15 10 36
4 4 17
= --------- ÷ 7 -------- X ---------
15 10 36
4 629
= ------- ÷ -------
15 180
4 180 720
= ------- X --------- = ----------- (Ans.)
15 629 9435
Example.6 –
8 5 11 7 6
Simply the equations ------ of [----- X {----- - (----- + ----)}]
15 25 10 20 15
8 5 11 21 + 24
= ------ of [------ X {------ - ( ------------ )}]
15 25 10 60
8 5 11 3
= ------ of [------- X { ------- - ------- }]
15 25 10 4
8 5 22 - 15
= ------- of [------- X { ------------- }]
15 25 20
8 7
= ---------- of ----------
15 100
8 X 20 160 13
= ------------- = ---------- = 7 --------- (Ans.)
3 X 7 21 21