Page 35 - WCS - Electrical
P. 35
28+
WORKSHOP CALCULATION & SCIENCE - CITS
=
7
+
28+ + 4 = + 7
+ + 56
4
+ - 56 = − 14
4
- - 72 = − 14
4
- + 72 = −8
9
=
−8
− 96 9
+
− 96 = +16
− 6
+16
=
5y − 6 20
5y = 20
5
5
=
x 5 5
x
When an expression contains addition, subtraction, multiplication and division, perform the
4
25
5x
multiplication and division operations first and then do the addition and subtraction.
4
5x = 25
5
5
=
5
Example 10a 5
10a
2a
12 x 8 – 6 + 4 x 12 = 96 – 6 + 48 = 138
8ac
2a
− 8ac
2bc
102 x 6 – 6 x 2 + 3 = 17 – 12 + 3 = 8
−
5m −×
− 2bc 6n − 7p
Parentheses and grouping symbols 6n5m −×− − 28mn − 7p
5a + − 20 28mn
( ) Brackets 5a + 20
28
7a +
m
{ } Braces a 7a + = 28 m− n
m
a
n
7 + (6–2) = 7 + 4 = 11 a a 3 n = a m− n
1
3
6 x (8–5) = 6 x 3 = 18 2 a 3 = 2 − 2 = 2 = 2
2
3
1
2
=
Parentheses 2 2 2× 2 − 2 = = 2 = 2
8
2
2×
2
2
=
2×
2×
8
2
2
4
2×
These are symbols that indicate that certain addition and subtraction operations should precede multiplication
2
=
=
4
2
n
n 2×
a
a
and division. They indicate that the operations within them should be carried out completely before the remaining
=
n
n
a
a
operations are performed. After completing the grouping, the symbols may be removed.
b
b =
n
2
b
n
3
b
In an expression where grouping symbols immediately preceded or followed by a number but with the signs of
4
2
2
2×
2
2
3
=
=
=
2
2
4
2×
2
operation omitted, it is understood, that multiplication should be performed.
9
2
3
3×
3 =
3 = =
2
9
3
3×
n
1 3
3
−
Grouping symbols are used when subtraction and multiplication of negative number is done.
a
=
1
n
−
n
a
=
a
To remove grouping symbols which are preceded by negative signs, the signs of all terms inside the grouping
n
1 a
−
2
2
=
symbols must be changed (from plus to minus and minus to plus).
1
−
2
2
2 = 2
2 2
2
Parentheses which are preceded by a plus sign may be removed without changing the signs of the terms within
2
3
7
1
the parentheses. 1 2 = 7 2
3
4 =
4
7 4
7
49 4
When one set of grouping symbols is included within another set, remove the innermost set first.
=
×
7 7 49
16
4
4
×
=
When several terms connected by + or – signs contain a common quantity, this common quantity may be placed
4
4
16
in front of a parentheses.
8 + 6(4–1) = 8 + 6 x 3 = 26
(6+2) (9–5) = 8 x 4 = 32
Plus 4 less negative 7 is written as 4 – (–7).
Plus 4 times negative 7 is written as 4(–7).
4 – (–7) = 4 + 7 = 11
8 – (7–4) = 8 – 3 = 5
3 + (–8) = 3 – 8 = –5
7 + (4 – 19) = 7 + (–15) = 7 – 15 = – 8
3 {40 + (7 + 5) (8–2)}
= 3 {40 + 12 x 6}
= 3 x 112 = 336.
8x + 12 - quantity 4 may be factored out giving the expression 8x + 12 as 4 (2x + 3).
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CITS : WCS - Electrical - Exercise 4