Page 43 - WCS - Electrical

28+
7
+
=
28+
7
+
4 =
56 4
+ +
14
=
56
+
14
4 =
-
−
72 4
--
=
−8
72
-
−8
9 =
+
− 96 9
+
=
+16
− 96
+16
5y − 6
20
= 20
5y
5
5 =
5
x 5
x
4
5x 4
5x
= 25
5
5 =
5
5
10a
10a
2a
2a
8ac
− 8ac
2bc
−
− 2bc
5m −×
6n −
7p
6n −
−
5m −×
28mn
−
5a +−
20 28mn
5a +
20
28
7a +
7
m 28a +
a
m
a
a
=
m−
a
n =
a
n
3 a

2
3
3
2 −
2 =
=
2 =
2
1
3
2
2 =
2 =
2 =
2 −
2 + − 6 = 25 − m− n n 7p 1 2
2
2
2× 2× 2 8
2× 2× 2 = 8 = 2
2
2
4 =
=
2×
2
n 4
n 2×
WORKSHOP CALCULATION & SCIENCE - CITS
a

a  n
 a
a n =   
b n =    b  
n
b 
2
2 b 3  2  2 2× 2 4
3
(2 x 2) x (2 x 2) x (2 x 2) = (2 x 2 x 2) (2 x 2 x 2)
= 2×
 2
2
= 4
2
= 
 
3 2 =   3   = 3× 3 = 9
2
3 

4 x 4 x 4 = 64 3× 3 9
1
3
−
n
a − n = 1
=
n
a
8 x 8 = 64
a
n
1 a
−
2
2
= 1
A mixed number raised to a power is first converted into an improper fraction and then the result is evaluated.
2
−
2
2
=
2
2 2
2
 3  2 2  7  2
 7
 3 =   
1  

 1  4   =   4  
4
7  × 7 = 49 4
49 
7 

7
4 × 4 = 16
4 4 16
Indices
• The indices are added in multiplication
m x a = a m+ n 2 3 2
n
a
n
m x a = a m+ n = 3x 2 y 3 = y 2
a
m+
a
m m
n n
m+
y
n n
a
a = =
3x 2 2
53 3
• The indices are subtracted in division = − 3x 6xy yx y y = 2 2x y y 3 3 2 2 2

x a x m
m+
a a n
n
3
a =
a
a
x
3
m m− = = − 6x 5 5 = 5 = = y3x 2x 3 3 = y
y
a
a m
n n
m = a x a = a m+ n − 6x− 6x y y 2x 32
2x 32
5
a
a a a n m m = m n = − 6x 3x y y = 2xy
m−
n
a m− nm−
n = a=a
a n n a = a m− n − 6x 5 y 2x 3
a a aa 3x 3 y 2 2
n m
=
n
m−
2
3
m.
m
n a=
n
• In case of index of an index, both the indices are multiplied mutually = 3x 2 y
a
[
a ] =
3x 3
y 2

xy 23
n
m n a m. n = 3x y3x y = 3 3x 2 2 y
2
a ] =
3x
y y
[ m nm n a m. nm. n m. n = = xy 3x = 3x= y = 3x 2 y
[ a ][
xy xy =
a ] = = m
a a n
a ] =
a
[

xy 3
m
1/m
2
• A fractional index shows root of a number 45a = 3x 2 c y 2 = 3x 2 y
a
=
m.
b
n
a m
n
1/m m a ][ = a = 2 2 xy
b
a 1/m
1/m = m m a = 45 9a ba ba 2 2 2 c 2
45a 2 2
a a
45
= = 1/m
a a m
c c c 2
a
a
c
b
2 45a
=
= =
c
=
9a 2 2
• In case of an index having minus sign, the sign can be changed by taking the number from numerator to

9a
c c
9a

1 1/m
m
22
2
m
−
= a
a
=
45
a

denominator or vice versa = 9aa cb c
1
m
−
m
a − − m m = a1 1 2
m
a a = = a − a m m= 1 m 9a c
m
a a
a 1
1
m m
and = a a − =
1 m m m
−
a 1 1 m = a= 1 a
=
a m m
a
−
− −
a m m = a m
a a
−
m
a m / n = a 1 = a m
n m
a

m /
n
n m m
−
• If an index contains both the numerator and denominator then it means that the number has ‘index’ as well as
a
a
= n n
m / /
n n
m
a m m

a a
‘root’. 2 a = = m / 2 = n m
a a n
a

3x + 2y m / n m
2
2 n
2
2y
2 + a
2x + 3y 2 2 = a
3x 2 2
3x +
3x
2y 2y
2 +
2x +3x
_______ +
Basic problem22 2 3y 2 2 2 2y 2
3y
2x + +
2x
2 _______
2 3y 2

x + 5y 2x + 2 3y 2 2
_______
_______
Addition 2 2 3x + 2y
x +
2 2
_______ 22 2 5y _______ 2
3y
5y 5y2x +
x + +
x
2 _______ 2
2
1 5x y + 3xy + 8x y + 7xy 2
x +
2
5y
2
_______ _______
_______
_______
2 2
2
x +
= 5x y + 8x y + 3xy + 7xy 2
5y
2
2
12x 3 y _______
2
=

3
2 2
3xy
= 13x y + 10xy 2
12x
y

2 23 23
3xy
12x
=
4x
y y y
12x
3
2
3 2
3xy
12x
= 3xy= y
2 Add 5a , + 12b , - c , + a , - 4b , + 3
3
3
3
3
y
=
3xy
4x 2 2
4x y y 2 3 2
4x
5a + 12b + (- c ) + a + (- 4b ) + 3
3
15y 3 15 3 4x 12x y y 3 = 3xy 3
10 2
3 =
3 4x
15y 15 = y y 10 3 y
= 6a + 8b - c + 3
10
5 15
15
15y
15y
15y
15
10
5 = y=
15y
Subtract5 5 15y y 515 = y 10
15y
15y

15yy
1 3a 2 x 4a 15 5a 2 3 y= 2 10 2 2
Subtract 2x - 3y from 3x + 2y
x
2 x 4a 15y 5 3
x
3a 2 2 4 4 x 4a 2 10a 5a x 5a x 5a 3 3 3
3a
6a 4a x x
3a
x
3a
6a 4 4 x 10a 4a x 5a
6a
10a
6a
x 10a x 4 2
60a 3 6 6a x a x 4 10a5a x a 3
6
60a 6a
= = 60a 5 6 6 = = a 4 x 10a
a
60a
60a
a
= = 5 = a= 60a 6 30
60a 5 5 = = a
60a 60a 60a
60a
5 6
− 25a 15 = 5 = a CITS : WCS - Electrical - Exercise 4
= 1560a
−
8 15
= − 25a− 25a −15
−25a
5a

− −
= = − 5a 8− 8− 8 25a 15
=
815
−
4x 2 y − 5a− 5a −− 5a 25a
= 2 = 2x = 2
2
4x 2
= 4x y4x y = 2x 2 2 − 5a − 8
2y 2
y

2
= = 2y = 2x= y4x 2x 2
2y= 2y 2 = 2x
2y
= 4x y = 2x 2
2y