Download 1-6 to 1-8 Integers

1-6 to 1-8 Integers
What You’ll Learn
To find opposite and absolute value
To order integers
To add integers
To subtract integers and find range
To multiply integers
To divide integers
Understanding Integers

Integers are the set of positive and negative
whole numbers, including zero. Numbers to the
right of 0 on a number line are positive and
numbers to the left of 0 are negative. The
number -3 is a negative integer and the number 3
is a positive integer. The number zero is neither
positive nor negative, it is neutral.
Finding the Opposite

Find the opposite of -4


The opposite of -4 is + 4 because the two
integers are each 4 units from zero on the
number line
Find the Opposite of:



-8
13
-22
Finding Absolute Value

The absolute value of a number is
its distance from 0 on a number line

•
You write “the absolute value of -3 as /3/
Therefore 3 and /-3/ are the same
because they are the same distance
from zero
Comparing Integers


You can compare and order integers by
graphing. Numbers increase in value
from left to right
Compare -7 and 1 using the symbols
below




-5 is 5 units to the left of 0
1 is 1 unit to the right of 0
Numbers increase from values from left to
right
Therefore -5 < 1
Practice

Compare using symbols




-8__ 2
2___-2
3___-3
Order the numbers from least to
greatest

3,-1,-4, and 2
Adding Integers

When adding two integers with the
same sign, add their absolute
values. Then give the sum
(answer) the sign of the integers.



-3 + -2 = ?
|-3| + |-2| = ?
3 +2 = 5, then make the result
negative.
Adding Integers

When adding integers with different signs, first
find their absolute values. Then subtract the
lesser absolute value from the greater absolute
value, and give the result the sign of the integer
with the greater absolute value.
-7 + 3 = ?
|-7| = 7 and |3| = 3 (find the absolute
values)
7 - 3 = ? (subtract the lesser from the
greater)
7-3=4
/-7/ > /3/ (keep the sign of the greater
absolute value) - 4
Now You Try!!!
1.
65 + -7 =
A.
-72
B.
72
C.
58
D.
-58
2.
-98 + -21 =
A.
77
B.
-119
C.
-77
D.
119
3.
-8 + 9 =
A.
B.
C.
D.
-17
-1
1
17
Subtracting Integers

Subtracting integers is the same as
adding the opposite.
3 - -7 = ?
3 + +7 = 10 (add the
opposite)
3 + 7 = 10
Example 1: 25 - -10 = ?

Solution: Subtracting a negative
number creates a positive, so the
problem can be rewritten as:


25 + 10 = ?
25 + 10 = 35
Example 2: -48 - -18 = ?




Step 1: Rewrite the problem as:
-48 + 18 =
Step 2: Remember the rules for adding integers: To
add two integers with different signs, first find their
absolute values. Then subtract the lesser absolute
value from the greater absolute value. Give the result
the sign of the integer with the greater absolute value.
So we first find the absolute values.
|-48| = 48
|18| = 18
Step 3: Subtract the lesser absolute value from the
greater value. 48 - 18 = 30
Step 4: Give the result the sign of the integer with the
greater absolute value. Since 48 is the greater
absolute value, we give the result a negative sign.
-48 + 18 = -30
Range

The range of a data set is the
difference between the greatest and
the least values
Where is this??
Know yet???
How about now??
Finding the Range

The range of a data set is the
difference between the greatest and
the least values

Temperatures a Verkhoyansk, Russia,
have ranged from a low of -90 F to a
high of 98 F. Find the temperature
range in Verkhoyansk

98 – (-90) = 98 + 90 << Add the
opposite of -90
= 188

Find each range


53 to -47
-42 to -8
Find the range…

Between 24 and – 2

Between 7 and -3

Between 6 and – 6

Between -16 and -6
Multiplying Integers

To multiply integers, follow these rules.
•The product of two positive integers is
positive (Example: 9 x 4 = 36).
•The product of a positive integer and a
negative integer is negative (Example: 9 x -4 =
-36).
•The product of two negative integers is
positive (Example: -9 x -4 = 36).
Notice from the above examples that when you
multiply integers with the same sign, the answer
is positive. When multiplying integers with
different signs, the answer is negative
Multiply these Integers

5 (3) =

5 (-3) =

- 5 (3) =

-5 ( - 3) =
Dividing Integers

To find the quotient (answer to a
division problem) of two integers,
the following rules apply:


The quotient of two integers with
different signs is negative. Example:
16 ÷ -4 = -4.
The quotient of two integers with the
same sign is positive. Examples: 16 ÷
4 = 4 and -16 ÷ -4 = 4
Divide these Integers

14 / - 2 =

- 32 / -8 =

-56 / - 7 =

-121 / 11 =