Transcript Introduction to Integers

 1)
Evaluate 7 cubed
 2) Solve: 2 •12 ÷ 3 + 2
 3) Solve: (5 +3) + 8 ÷ 2
zero
5,600
+
Real Numbers
Negative
Positive
3
INTEGERS
21/3
-
0
-1
427
Zero
Rational
Integers
 What
model can be used to show
positive and negative rational
numbers?
 How can I use models to prove
that opposites combine to 0?
 What is absolute value? How can I
show it on a number line?
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

integers- the set of whole numbers and their
opposites (positive or negative)
additive inverse- the sum of a number and its
opposite
absolute value- the distance of a number
from zero on a number line; shown by l l

Integers are positive and negative numbers.
…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5,
+6, …

Each negative number is paired with a positive
number the same distance from 0 on a number
line. These numbers are called opposites.
-3 -2 -1
0
1 2
3
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3
are called negative
integers. The number
negative 3 is written –
3.
Numbers to the right
of zero are more than
zero.
Zero is neither
negative nor
positive.
The numbers 1, 2, 3 are
called positive integers.
The number positive 4
is written +4 or 4.
30
20
10
0
-10
-20
-30
-40
-50
Let’s say your parents bought a car but
had to get a loan from the bank for $5,000.
When counting all their money they add
in -$5.000 to show they still owe the bank.
 If
you don’t see a negative
or positive sign in front of
a number it is positive.
9 = +9
Opposites and
Additive Inverses
•The opposite of a number is the same distance
from 0 on a number line as the original number, but
on the other side of 0; zero is its own opposite.
•When you find the additive inverse, you take the
opposites and add them together; the sum will
ALWAYS be ZERO.
–4 and 4 are opposites; when you find the
additive inverse you add (-4)+4=0
–4
4
•
•
–5–4–3–2–1 0 1 2 3 4 5
The integer (-9) and 6 are graphed
on the number line along with its
opposites; What would be the
additive inverses? How?
-9–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8 9
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
Reading Math
The symbol is read as “the absolute value of.”
For example -3 is the absolute value of -3.
Absolute Value Example 1
Use a number line to find each absolute value.
|8|
8 units
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
8 is 8 units from 0, so |8| = 8.
Absolute Value Example 2
Use a number line to find each absolute value.
|–12|
12 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3
–2
–1 0 1
–12 is 12 units from 0, so |–12| = 12.
2
Absolute Value Examples 3 & 4
2
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
7
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
Being in class<<<<<<talking on the phone
Playing X-Box>>>>>>Doing chores
What does the symbol “>” and “<“ mean?
You can compare and order integers by
graphing them on a number line.
•Integers increase in value as you move
to the right along a number line.
•They decrease in value as you move to
the left.
Remember!
The symbol < means “is less than,” and the
symbol > means “is greater than.”
Comparing Example 1
Compare the integers. Use < or >.
-4 > -11
-15 -14 -13 -12 -11 -10 -9 -8 -7
-6
-5
-4 -3 -2 -1
-4 is farther to the right than -11, so -4 > -11.
Comparing Example 2
Use a number line to order the integers
from least to greatest.
–3, 6, –5, 2, 0, –8
–8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8
The numbers in order from least to greatest
are –8, –5, –3, 0, 2, and 6.
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
What are integers? When would you use
negative numbers in the real world?
Do the numbers increase or decrease as you
move to the left of zero? What happens when
you move to the right of zero?

< means:

> means:
Place
homework in a
safe place within your
binder; remember to
get your planner
signed!! 