Page 16 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

Addition of fraction
1 1 5
Add + + 1
2 8 12 + 1 + 1
2
4
8
To add these fractions we have to find out L.C.M of denominators 2,8,12.
1 1 5 12 3 10 L.C.M = 2,4,8 = 8
+ Find L.C.M of 2,8,12 ++=+
2 8 12 24 24 24 1 1 1 4 + 2 + 1 7
Step 1 L.C.M + + = =
2 4 8 8 8
2 2,8,12
12 + 3 + 10 25 1
= 2 1,4,6 = = 1 1 3 1 3
24
1,2,3 24 24 5 4 − 3 4 = 5 − 3 + 4 − 4

5
1
1
Factors are 2,2,2,3
Add + 1 1 + 1 5 9 15 = 2 + 1 1 − 1 3 = 1 2 1 − 3

15
1
9 5
Hence L.C.M = 2 x 2 x 2 x 3 = 24 )
subtract 9 Ad d 2 Add + 8 + 12 + 12 − 9 1 4 + 1 1 4 + 1 1 4 1 4
from
or(17
17 +
2
8
4 +
32
+
Step 2 2 8 16 12 16 32 9 2 32 + 8 + 38
9 − 4
= 4
8
− 2
1 1 5 12 3 10 = L.C.M = 2,4,8 = 8

+ 1 + 1 1 =5 1 + 12 3 +3 10 4 4 L.C.M 4 2,4,8 == 8
5
5
10
3
8
12
1
1
Subtractin + Add g 12 + + 24 = + = 24 + 24 + 1 1 L.C.M = 1 1 2,4,8 = 2 + 1 7
fractions
2
8
4 +
1 1
+
+
=
+
8 2
2 Add 8 + 12 1 12 128 24 24 24 + 24 24 = 6 + + 3 + 11 + 1 1 4 + 8 4 + 2 1 = 1+ 8 = 7
32 24
2
1 = 1
5
1
= 1
= 1
7
2 +
8 +
4 +
=
+
2 2
=
2 2
4
12 + 511 2 8 3 12 25 3 1 10 1 4 1 + 4 4 + 1 + 8 2 8 8 8 8 = 8 8
8
2 +
3
10 12
2,4,8 =
L.C.M =
3 +
we get 8 + 3 + = 8 = 1 25 + 1 2 4 8
= 10+
= 12 + =++
25
32
1
1
3
3
24 1= 24
24 12
= 8
1
1
1
4 +
3
= 51
1 2 12 + 3 + 32 10 1 24 24 = 24 = 1 10 1 L.C.M − = 3 1 2,4,8 5 − 8= 3 + 2 + 1 − 1 7 3
12
= 3
5
1
= 5
24
+
3
3
1
+ + Add 24 + + + 24 24 24 24 1 + 4 3 = = 5 − 4 3 + = 4 −
=
+
4 5
−
5 − 8
924
24
8
2 Subtraction of fraction 1 5 2 1 1 − 4 1 4 3 8 1 41 = 4 2 ++ 3 + − 8 4
3 12
24
4 7
1
7 8
2
5 12
4
3
+
4 =
3
4 + =
−
solve 3 4 15 103 ++ + 6 8 − 4 16 9 32 1 9 15 2 = 2 4 + + 1 − 1 8 = 2 3 8 1 − 1 8 3
12
25
2 + 4 84
1
1
3
3
=
=
1
subtract 9 15 5 from = 17 9 3 or(17 9 − 9 9 15 ) 15 =1 2 + 3 − 2,4,8 4 2 − 1 4 − 3
9
15
4 2 +
=
4 −
=

=
24 10
12
1
32 9 ct
16 17
subtra24
from
16

subtract312 + 1 9 + 10 = 24 1 + or(17 − 9 32 9− ) ) 5 L.C.M = 4 4 5 − 4 2 8= 4 4 4 4
+
25
−
=
−
from
or(17
3 +
3
4
+
17 +
1
= 2 8 32 12 32 24 = 16 24 16 24 16 16 32 32 1 9 − 9 1 3 3 4 = 3 1 9 − 3 9 −2+1 3 1+ 3 4 7
=
4
4
= 1
4
5
7
9
3
24
24
24
9
3
Step 1: Subtract whole number first 17 - 9 = 8 5 4 = + 3 4 − + 5 −= 9 − 3 − =
4 = =3 +
+
−
−
−
3

Subtractin 16 g fractions = 3 9 3 15 4 = 2 2 + − 1 − = 3 4 8 = 2 1 4 8 4 − 3 4 8
4 4 4
4
32 9
8 15

=
4
fraction
3
g
32 s =
1

9
subtract Subtractin 17 or(17 9 ) = 6 4 = 6 4 = 3 4 1 3 1 4 4
Step 2: L.C.M of 16,32 = 32 −
from
4
g
Subtractin
fractions
=
1 3
32
16
3
1
12 + 32 103 + = 9 25 = 1 1 32 9 16 15 32 = 2 + 6 1 2 = = 2 1−
15
= 2
4 = −
=
=9
1 3
Since number 16 divides the number 32
from

subtrac 9 t 24 + 24 10 − 3 9 24 or(17 24 − 9 ) = 14 − =3 2 = =9 − 2 2 4 1 3
17
3
2 4
4 3 4
28 −
4
=3
5 −
=
2
we3
3
get
8 +

3

Subtracting fractions = 33 + 16 8 8 32 8= = 3 16 32 9 5 4 4 3 − 4 4 9 − 3 4 3 + 4 − 4
we
32 32 8 get
g
Subtractin
fractions
=
get
we

8 +
32
3
6
32 32 32 3 32 = 4 − 4 = 1 3 4 1 1 3
=
=
Subtractin 7 5 9 = 9 9 15 = = 2 + − 1 = 2 −
15 fractions g
3
or(17
subt 52 − 63 lve ract 9 3 + 19 − 73 from 17 5 16 − 5 32 9 16 − 9 ) 6 4 3 2 4 1 2 4 4
9
so
4
4

3
Adding with whole number from Step 1
3
7
1
= 4 3 olve 32
32 −
s
we
8
8 +
3
solve get 324 6 8 6+ − 8 = 4 16 4− 16 32 32 = 4 = 92 = 3 2 9 − 3
−
+
32
4 3 32 16 32 = − =
8
3
w get e 8 + = 8 3 4 4 4
9 32
7 32
3
Subtractin g 5 fractions = 9 6 3 1
5
1 7
33 3
6
4
solve 3 + 3 + − 7 − − 5 9 − 9 32 = = = 1
= 7
= 3
1 5
8 +
32 −
16 −
4
32 + 4
32 −168
−
Common fractions 32 32 4 2 2
5
9
3
4 7
8
16
solve 3 we 4+ 8 6 8 + − 16 3 4 16 = 32 3
−
Problems with plus and minus sign
get

8
8
32
4
32
24 +

Example73 328 − 5 1 3 90 − 9 32
10 −
1 24 +
6 28 −
= −
−
5 + + 28 − 10 − 9 9
24 +
32
32 5
3 4 32 8 5 16 32 32 9
3 7
7 9
solve 3 + + − 6 − 4 −
32 −
3 4 by 8 4 4 1 3 8 326 × 4 16 32
3
=
=
52 −
19
28 −
9
10 −
8 24 +
7 =
Rule to be followed 14
8 52
7 19−
19
52 −
=
32
32
=
32 9
24
7 10−
3 28+
5 9−
1 Add all whole numbers
3
5
2
5 32
−
+
−
=
×
×
8 32
32
4
16
2 add all + Numbers
3
16
4 33
8 1

= 52
= −
1 33 19
1
1
33
=
32 =
3 Add all - Numbers
32 1=
=
=
5
5 24 + 1952 − 28 − 1 10 − 9
32
5 32
32 32
×32
= 32
2
÷
=
4 Find L.C.M of all denominators
=
16 32 32 3 16 5 3
32

5 + 1 33 3 1= =3 6 1 3 3
=
5
= 32
5 + 32
33 1 32 1+ 1 32 6 32 6= 32
52
32
1
=
144
2 1 3 = = 32 19− 14 7 3 49 16
22 3
4
32
4 ÷ 3 =by 3 ÷= 4 32 3 = × 3 4 × = 4 3 = 3 = 1 3
32
3
4
3 7 ×
22
3 7 8 5 + 3 7 by 3 78 = 3 = 14 = 14 33 33

by
×
=
7 6
8 1
7
=
8
8
7
32
CITS : WCS - Electrical - Exercise 1 8 2 33 7 5 1 3 32 5 14 CITS : WCS - Electrical - Exercise 1
3
3
5 + = 1 × 2 = × 3 1= 6 = 5 5
2 4
5 4
5 3
3 3 32
3 32 4 × 8 × 32 16 =
3 32
by × = × × = = 16
4
8
3
3 8 3 7 4 8 8 7 1614
3
4
4
3
5by 5= 5 × = 32
3
=5
2
÷ 5
7
8
7
8 5 2 15 + 5 3 = 5 5 6 × 5 3 5 14 = 32
32
32 ÷
5 ×
16 ÷ × 32 = × 16 = × = 32 = 2 = 2
16
16 3 3 32 4 32 16 168 5 16 5 5
5
2
3 × 4 × 3 = 4 3
5
5 3 by 84 = 5 × 16 32 =
8
7
= 14
2 1÷ 14= 22× 78 14 2 7 49 16
4 ÷ 3 2 16 1 5 = 1 32 14 5 22 32 14 ×14 7 =7 49 = 1 49 16 16
÷ 14 16
= 22 5
2 5
3 =
3 =
33 =
4 3 4 ÷ 3 3 2 =÷ 7 3÷ = 3 ÷ 5 × 7 ÷ =5 2 × 22 × 22 33 1 33 1= 33
=
=
=
7
3
7
3
3 16 7 × 1632 3 × 7 = 5 3 22 33 33
3 4 8 16
2 1 14 22 14 7 49 16
4 ÷ 3 5 = 5 ÷ 5 =32 × = = 1
2 3 1 7 ÷ 14 3 = 7 × 14 3 = 7 2 22 49 33 16 33
22
4 ÷ 3 16 = 32 ÷ 16 = 5 × = = 1
3 7 3 7 3 22 33 33
2 1 14 22 14 7 49 16
4 ÷ 3 = ÷ = × = = 1
3 7 3 7 3 22 33 33