Supplementary Course Module A: Simplifying Numeric Expressions
Assignment 3 ° Order of Operations; Number Systems
Order of Operations:
°
When evaluating an expression involving more than one arithmetic operation, the evaluation must be carried out
following a particular sequence of steps.
°
The order of precedence when evaluating expressions is described by the acronym
BEDMAS:
B
rackets
E
xponents
D
ivision /
M
ultiplication
A
ddition /
S
ubtraction
°
Nested brackets are simpli°ed by working from inner to outer.
°
Division / multiplication and addition / subtraction are worked from left to right (recall that division is really just
a special form of multiplication, and subtraction is the addition of the negative value).
examples:
20
±
4
²
2

{z
}
+3
= 20
±
8 + 3
= 15
3
°
5 + 4
2
{z}
±
= 3
²
5 + 16

{z
}
³
= 3 (21)
= 63
4 + 2
s
(
±
3) (
±
2) + 8
±
²
2
±
3

{z
}
³
2
= 4 + 2
r
(
±
3) (
±
2) + 8
±
(
±
1)
2

{z
}
= 4 + 2
r
(
±
3) (
±
2)

{z
}
+8
±
1
= 4 + 2
q
6 + 8
±
1

{z
}
= 4 + 2
p
9
= 4 + 2 (3)
= 4 + 6 = 10
Set Notation:
°
A set is a collection of distinct objects along with a rule to determine if any arbitrary object belongs to the
collection or not.
°
Notation:
f³ ³ ³ g
, where
³ ³ ³
indicates the statement (rule) for membership.
°
statement may be a listing of speci°c objects, an English sentence or a mathematical equation.
examples:
{house, shoe, tree},
{all WLU students with last name Smith},
f
x
2
R
j
x
2
= 5
g
°
The objects of a set are called its elements.
°
if
x
is an element of set
A
then we write
x
2
A
(capital letters usually denote sets, small letters are used for
elements)
°
if a set is denoted by a list, repeated entries are counted only once; thus
f
1
;
2
;
2
;
4
;
4
;
7
g
=
f
1
;
2
;
4
;
7
g
°
A set with no elements is called the empty set, and is written as
?
or
f g
.
example:
f
x
2
R
j
x
2
=
±
1
g
=
?
°
Two sets are said to be equal if they have exactly the same members; i.e., sets
A
and
B
are equal if
x
2
A
iff
x
2
B
.
1
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°
if
A
and
B
are equal sets, we write
A
=
B
(or
A
´
B
for emphasis, where
´
means identically equal to,
or equivalent)
°
A °nite set has a °nite number of elements; an in°nite set has an in°nite number of elements.
Set Operations:
°
Set
C
is called the intersection of sets
A
and
B
if the elements of
C
are exactly those elements common to
A
and
B
.
°
C
=
A
\
B
=
f
x
j
x
2
A
and
x
2
B
g
example:
f
1
;
2
;
5
;
9
;
7
g \ f±
3
;
4
;
5
;
7
g
=
f
5
;
7
g
°
Set
D
is the union of sets
A
and
B
if
D
consists of those elements which are either in
A
or in
B
or in both.
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 Spring '10
 HU
 Real Numbers, Order Of Operations, Complex number

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