Download Important Pronunciation The Opposite or Negative of a Whole Number

FLC
Ch 2
Math 20 Arithmetic
Sec 2.1: An Introduction to the Integers
The Opposite or Negative of a Whole Number
For every whole number , there is a unique number – , called the opposite or negative of , such that
( )
.
Examples
Consider 4, -4, 7, -7, 8, -8, 1, -1, etc.
Important Pronunciation
The symbol
is pronounced (1) “negative three” or (2) “the opposite of three”
Defn The infinite collection of numbers {
} is called the set of integers, which
is denoted by .
0
Ex 1
Insert
or
in each box to make a true statement.
a)
b)
e)
c)
f)
d)
g)
( )
h)
( )
( )
Defn The absolute value of an integer is defined as its distance from the origin (zero).
Ex 2
| |
(
Simplify each expression.
| |
|
)
( (
))
|
|
|
( ( ( ( ))))
|
( |
|
|
|)
|
| |
Page 1 of 9
FLC
Ch 2
Ex 3
Provide a number line sketch with your answer for each problem.
a) Find two integers on the number line that are 4 units away from the integer 0.
b) Find two integers on the number line that are 4 units away from the integer 3.
c) Find two integers on the number line that are 2 units away from the integer -3.
Ex 4 (#68)
Profits and losses for the first six months of the fiscal year for a small business are shown in the
following bar chart. Create a table showing the profit and loss for each month. Use positive integers for the
profit and negative integers for the loss. Create line graph using the data from your table.
Sec 2.2: Adding Integers
Defn A vector is a mathematical object that possesses two important qualities:
(1) magnitude or length, and (2) direction.
Represent 4 and -7 on a number line using a vector.
Ex 5
String
What integer is represented by each vector?
Page 2 of 9
FLC
Ch 2
Adding Integers with Like Signs (Using Vectors)
Examples
Magnitude and Absolute Value
If
the vector that represents the integer .
is an integer, then | | gives the magnitude or length of
Adding Two Negative Numbers
(1) Add the magnitudes of the integers.
(2) Prefix the common negative sign.
More Examples…
Adding Integers with Unlike Signs (Using Vectors)
Examples
Adding Two Integers with Unlike Signs
(1) Subtract the smaller magnitude from the larger magnitude.
(2) Prefix the sign of the number with the larger magnitude.
Page 3 of 9
FLC
Ch 2
More Examples…
Ex 6
Simplify. (Find the sum.)
a)
b)
f)
k) PP
(
)
(
)
g)
(
c)
)
(
(
d)
)
h)
)
l) PP
i)
m) PP
(
(
(
e)
)
)
n) PP
)
(
)
j)
o) PP
(
)
Additive Identity Property The integer zero is called the additive identity. If is any integer, then
Additive Identity Property Let represent any integer. Then there is a unique integer – , called the
opposite or additive inverse of , such that
( )
Ex 7
( )
State the property of addition depicted by the given identity.
a)
b)
( (
(
))
(
)
(
)
c)
(
)
Page 4 of 9
FLC
Ch 2
Ex 8
a)
Simplify. (Group for efficiency.)
(
)
(
b)
)
c)
(
)
(
d)
)
(
)
Sec 2.2: Subtracting Integers
Subtraction is the opposite of addition. Thus, if we subtract, we are adding the opposite.
Defn Subtraction means “add the opposite”. That is, if and are any integers, then
(
Ex 9
Simplify.
a)
f)
)
(
)
k) PP
Ex 10
b)
c)
g)
h)
i)
j)
l) PP
m) PP
n) PP
o) PP
(
d)
)
(
e)
)
Simplify.
a)
b)
(
)
(
c)
)
(
d)
)
e)
(
(
))
(
(
(
))
f)
)
(
)
(
(
))
g)
(
(
))
(
Page 5 of 9
)
FLC
Ch 2
Ex 11 (#56)
Typical summertime temperatures in Fairbanks, Alaska in July are 79 degrees Fahrenheit in the
daytime and 53 degrees Fahrenheit at night. What is the change in temperature from day to night?
Ex 12 (#60)
Freida’s scores on her first seven mathematics exams are shown in the following bar chart.
Calculate the differences between consecutive exams, then create a line graph of the differences of each pair of
consecutive exams. Between which two pairs of consecutive exams did Freida show the most improvement?
Sec 2.4: Multiplication and Division of Integers
Integer Properties of Multiplication
Let
and be integers.
Commutative Property of Multiplication
Associative Property of Multiplication
Multiplicative Identity Property
and
The integer 1 is called the multiplicative identity.
Recall that ( ) really means
.
Page 6 of 9
FLC
Ch 2
So (
) really means
(
)
(
)
Product of Two (+) Integers
( )( )
Product of (+) and (-) Integer
( )
( )( )
Multiplicative Property of Zero
( )
( )( )
( )
Multiplying by -1/Multiplicative Property of -1
(
)
(
)
Derive the rule for multiplying two negative integers using the
Unlike Signs
Product of Two (-) Integers
( )( )
( )
Recall Division involving zero
Ex 13
a)
d)
(
(
)[(
Like Signs
( )( )
( )
( )( )
( )
( )( )
( )
( )( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
State the property of multiplication depicted by the given identity.
)
(
)(
b)
)
)]
[(
)(
)](
c)
)
e)
[(
(
)( )]( )
)
(
(
)
(
)
)[( )( )]
Page 7 of 9
FLC
Ch 2
Ex 14
Simplify.
a)
h)
(
m)
(
b)
)( )(
)
Ex 15
)(
(
(
)
(
)
(
n)
)
(
c)
i)
d)
)
)(
e)
( )
)(
o)
)
j)
)
(
( )
p)
)
(
)(
(
(
)(
f)
)(
)( )
q)
)
(
)
(
(
k)
g)
)
)
r)
)
(
(
l)
s)
)
Evaluate.
a)
b)
c)
(
h)
e)
f)
g)
)
i)
(
d)
(
j)
k)
l)
m)
)
Sec 2.5: Order of Operations
Recall
Order of Operations (O.O.O.)
Page 8 of 9
)
)
FLC
Ex 16
Ch 2
Evaluate.
a)
b)
c)
d)
e)
(
g)
h)
(
j)
f)
)
(
)
i)
)
|
√
k)
l)
( )
(
)
|
(
(
)
)
(
| (
(
)
)|
)
(
)
Page 9 of 9