Page 39 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

28+ = + 7 28+
+ 4 + 4 = + 7
+ 56 = − 14 + 56
- 4 - 4 = − 14
- 72 = −8 28+ = + 7 - 72
4
+ 9 + + 56 + 9 = −8
− 96 = − 14 − 96
=
+16
+16
=
-
4
5 is transposed from left side to the right side by changing its sign from + to –.
− 6
− 6
5y 20 - 72 = −8 5y 20
=
=
+
9
= 20. Multiply both sides by 4. Then x 4 = 20 x 4.
5
5
5
5
− 96
x = +16 x
− 6

4 5y 20 x = 80,
4
5x = 25 = 5x 25
5 5 x 5 5 5x = 25. = 5
5
10a
Divide both sides by 5 then 10a
4
2a 5x 25 2a
− 8ac 5 = 5 x = 5. − 8ac
2bc
2bc
10a
7p
6n −
5m −×
− When transposing numbers or letter symbols from one side to the other side multiplication becomes
7p
5m −×
6n −
−
2a
28mn
−
−
28mn
division and the division becomes multiplication.
8ac
5a + 20 − 5a + 20
The equality of an equation remains unchanged when both sides of the equation are treated in the
7a + 28 − 2bc 6n − 7p 7a + 28
5m −×
m
m
a same way. When transposing from one side to the other side,
a
n
m−
m−
n
−
28mn
a
=
a
n
20
5a +
a a plus quantity becomes minus quantity. n =
a
3
3
7a +
28
2 a minus quantity becomes a plus quantity = 2 − 2 = 2 = 2
2
3
1
1
3
2 =
2
2 =
2 −
=
m
2 2 a = a m− n 2 2
a multiplication becomes a division
2× 2× 2 = 8 = 2 a n 2× 2× 2 8
3
2
4
2×
2
a division becomes a multiplication. 1 2× 2 = 4 = 2
3
n
a n  a  n 2 = 2 − 2 = 2 = 2  a  n
a
2
To solve simple equations isolate the unknown quantity which is to be found on the left side of the
=


=



n
b 
b equation. 2× 2× 2 = 8 = b 2 n  b 
2 3 =   2   2 = 2× 2 = 4 n 2× 2 n 4 2 3  2  2 2× 2 4
2
Example 3  3× 3 9 a n =   a   3 2 =   3   = 3× 3 = 9

3
b 
1
b
−
n
• Solve for x if 4x = 3(35 – x ) 3  2  2 2× − 2 n = 4 1
a
=
a
n
2

a

=
4x = 105 – 3x (brackets removed)  = = a 1 n
1
2
2
−
2 = 3  3  3 2 − × 2 3 = 9
2
2
1
4x + 3x = 105 (By transposing –3x on the right side to the left side)
2
n
−
2
a
=
2
2
3 
3 
7x = 105
  1  =   7   − 2 a 1 n   1  2 =   7   2
=

2
4 
4 

 7 x = 15 (dividing both sides by 7) 2  7 4  7 49 4 
7
49
2
4 × 4 = 16  3  2  7  2 4 × 4 = 16
 1  =  
 4   4 
7 × 7 = 49
4 4 16
26
CITS : WCS - Electrical - Exercise 4