Transcript Applications of Negative Numbers & Absolute Value

Applications of Negative Numbers
&
Absolute Value
In
Algebra County
Negative Numbers are found in
weather reports, but not in sunny
Florida!
Zero
Down here, temperatures
are negative.
Negative
Numbers
are found
in stock
market
quotes
There, the stock market
went down.
When losing
weight, the weight
loss is a negative
number.
The number of feet
below
sea level
is a
negative
number.
The number of feet
below
sea level
is a
negative
number.
The number of feet
below
sea level
is a
negative
number.
The number of feet
below
sea level
is a
negative
number.
Negative
Numbers
are found
in
banking.
Checks are “subtracted” from
the bank statement.
Negative
Numbers
are found
in
Jeopardy scores.
ADDING INTEGERS
IN
ALGEBRA COUNTY
If it’s 70 degrees outside, and the temperature
gets 10 degrees cooler, how can we write it?
70  10  60
If it’s 5 degrees outside, and the temperature gets
10 degrees colder, how can we write it?
5  10  5
A positive added to a negative takes the sign
of the largest “number.” We subtract.
If it’s -10 degrees outside, and the temperature
goes down 10 degrees, how can we write it?
10  10  20
A negative added to a negative is a “larger”
negative. We add the “numbers.”
Another way to think of adding positive and negative numbers is by
using red and yellow colored counters.
35
3 and -5
 2
zero pairs
3  5
-3 and -5
No zero pairs
 8
Write these in your notes pages
1.
2.
3.
4.
5.
6.
 18  20 2
 11  9  2
 6  5  11
 1  7  8
29  7
75  2
MULTIPLYING
INTEGERS
IN
ALGEBRA COUNTY
-5 TIMES 6
CAN BE WRITTEN:
-5(6)
(-5)(6)
2(3) MEANS:
•2 GROUPS OF 3
•A 2 BY 3 ARRAY
-5 ·6
WE CAN PICTURE 2(3):
THESE ARE
ALL ARRAYS
WE CAN PICTURE 2(3)
AS 2 GROUPS OF 3:
Which?
Group or array?
Two rows of three
kitchen tiles
When we multiply:
Positive X positive =
Positive X negative =
+
-
Negative X positive =
Negative X negative =
+
Don’t get confused:
Positive + positive =
Positive + negative =
+
??
Negative + positive =
Negative + negative =
??
-
Negative + positive =
Why the question marks?
-4+6 =2 (positive)
-6+4 = -2 (negative)
??
Back to multiplication:
-(-3) means:
- 1(-3)
Negative 1 times negative 3
=3
The number 1 is very
important in Algebra County.
Also:
-(5) means:
Negative 1 times 5
- 1(5)
which is:
-5
Let’s work some
multiplication problems:
-2(5)
=
-10
3(-5)
-4(-2)
=
=
-15
8
- (-6)
=
6
-9(-11)
=
99
- (-13)
=
13