SIMPLIFICATION OF FRACTION
We are already familiar with the four fundamental operations such as Addition, Subtraction, Multiplication, Division on fractions –
As, We know -
x w
-------- + --------
y z
[x X { (LCM of y,z) ÷ y }] + [w X { (LCM of y, z) ÷ z }]
= --------------------------------------------------------------------------
LCM of y, z
x w
We know, -------- - ---------
y z
[x X { (LCM of y,z) ÷ y }] - [w X { (LCM of y, z) ÷ z }]
= -----------------------------------------------------
LCM of y, z
x w x X w xw
We know, ------ X ------- = ----------- = --------
y z y X z yz
x w x z x X z xz
We know, ----- ÷ ----- = ----- X ----- = --------- = ------
y z y w y X w yw
like directed numbers or integers we have positive (+) fraction as well as negative (-) fraction. 1, 2, 3, 4, etc…,are positive integers. The corresponding negative integers are -1, -2, -3, -4, etc., such that 1 + (-1) = 0, 2 + (-2) = 0, 3 + (-3) = 0, 4 + (-4) = 0
2 7 9
If we consider fraction then, -------, -------, -------, etc. are
5 12 26
called positive fraction.
- 2 - 7 - 9
And the corresponding negative fractions are, ------, ------, ------
5 12 26
, etc.are called negative integers.
Such that,
2 - 2 7 - 7 9 - 9
------ + (-----) = 0, ------ + (-----) = 0, ------ + (-----) = 0,
5 5 12 12 26 26
An expression involving fractions is simplified by following the rule of BODMAS, brackets are removed in order, such as Line Bracket, First Bracket, Second Brackets, Third Brackets.
For better understanding, we would like to show you some example which will help you to make a better understand –
Simplify the equation-
1 5 7 4 25 7
------ X [{ ------ ÷ ------ - ( ------ X ------ )} + ------ ]
5 12 16 15 10 20
1 5 7 4 25 7
Answer) ----- X [{ ----- ÷ ----- - ( ----- X ------)} + ------ ]
5 12 16 15 10 20
1 5 7 2 7
= ------ X [ { ------- ÷ ------- - ------ } + ------- ]
5 12 16 3 20
1 5 16 2 7
= ------- X [ { ------- X ------- - ------- } + ------- ]
5 12 7 3 20
1 20 2 7
= ------- X [ { ------- - ------- } + ------- ]
5 21 3 20
1 20 - 14 7
= ------- X [ { ------------ } + --------- ]
5 21 20
1 6 7
= --------- X [ --------- + --------- ]
5 21 20
1 2 7
= ---------- X [ --------- + --------- ]
5 7 20
1 ( 2 X 20 ) + ( 7 X 7 )
= ---------- X [ ------------------------ ]
5 140
1 40 + 49
= ---------- X [ --------------- ]
5 140
1 89
= ---------- X ----------
5 140
1 89
= --------- X ---------
5 140
89
= ---------- (Ans.)
700
Simplify The Equations -
1 3 8 3 6 2
------ ÷ ------ of ------- ------ ÷ ------ X ------
5 10 15 22 11 3
---------------------------- + --------------------------
1 5 1 1 1 2
------- ÷ ------- X ------- ------ of ------ ÷ ------
6 12 3 6 9 27
1 3 8 3 6 2
------- ÷ ------ of ------ ------- ÷ ------ X ------
5 10 15 22 11 3
= --------------------------- + --------------------------
1 5 1 1 1 2
------- ÷ ------- X ------- ------- of ------- ÷ -------
6 12 3 6 9 27
1 3 8 3 6 2
------ ÷ ( ------ X ------ ) ------- ÷ ------- X ------
5 10 15 22 11 3
= --------------------------- + --------------------------
1 5 1 1 1 2
------- ÷ ------- X ------- ( ------ X ------ ) ÷ -------
6 12 3 6 9 27
1 12 3 11 2
------- ÷ ------- ------- X ------- X -------
5 75 22 6 3
= ------------------------ + ----------------------------
1 5 1 1 2
----- X ----- X ------ ( ------- ÷ ------- )
6 12 3 54 27
1 75 1
------ X -------- -------
5 12 6
= ---------------------- + ----------------------
5 1 27
--------------- ------- X --------
18 X 12 54 2
15 1
--------- --------
12 6
= --------------------- + -----------------------
5 1
------------ -------------
18 X 12 4
15 5 1 1
= ( -------- ÷ --------- ) + ( -------- ÷ -------- )
12 18 X 12 6 4
15 18 X 12 1 4
= ( -------- X ------------ ) + ( -------- X -------- )
12 5 6 1
2
= ( 18 X 3 ) + ---------
3
( 54 X 3 ) + 2
= ---------------------
3
162 + 2
= -------------
3
164 2
= --------- = 54 ------- (Ans.)
3 3