Download CHAPTER 2 INTEGER REVIEW Integers are numbers that are

CHAPTER 2 INTEGER REVIEW
Integers are numbers that are negative or positive.
The number 0 is an integer, but it is neither negative nor positive. For
any two different places on the number line, the integer on the right is
greater (>) than the integer on the left.
Adding and Subtracting Integers
When adding two integers with the same sign, just ignore the signs, then
attach them on the answer.
-3 + -5 = - (3 + 5) = -8
When adding two integers with different signs, take the absolute values
(make both numbers positive), and subtract the smaller one from the larger
one. The sign of the integer with the larger absolute value will be the sign of
your answer.
7 + (-8)
The absolute value of 7 is |7| = 7
The absolute value of -8 is |-8| = 8 larger
8–7=1
Remember in the original problem, the integer whose absolute value was 8
was -8, so our answer is negative.
7 + (-8) = -1
Subtracting a negative integer is the same as ________ a _______ integer.
3 – (-5) = 3 + 5 = 8
-2 – (-3) = -2 + 3 = 1
Subtracting a positive integer is the same as _____ a _____ integer.
5 – 3 = 5 + (-3) = 2
-2 – 3 = -2 + (-3) = 1
Multiplying and Dividing Integers
(positive integer) X (positive integer) = (_____ integer)
(positive integer) ÷ (positive integer) = (______ integer)
(negative integer) X (negative integer ) = (______ integer)
(negative integer) ÷ (negative integer ) = (_______ integer)
(positive integer) X (negative integer) = (______ integer)
(positive integer) ÷ (negative integer) = (_______ integer)
(negative integer) X (positive integer ) = (negative integer)
(negative integer) ÷ (positive integer ) = (negative integer)
When a negative integer is raised to an even power, the result is _____.
(-2)4= (-2)(-2)(-2)(-2) = 16
When a negative integer is raised to an even power, the result is ______.
(-2)5= (-2)(-2)(-2)(-2)(-2) = -32
Exponents are only applied to the number directly diagonally left of it. If a
negative integer is raised to a power, it must be in parentheses () in order for
the exponent to apply to the negative number.
(-2)2
≠ - 22
(-2)2 = (-2)(-2) = 4
- 22 = - (2)(2) = -4
ORDER OF OPERATIONS
PEMDAS is still the rule for integers!
-15 + 3(-4 + 7)
= -15 + 3(3)
Do what’s inside the parentheses first (-4 + 7) = (3)
Next, are there exponents? ___
= -15 + 9
Do multiplication or division (Left to Righ) next
(Remember 3(3) is multiplication 3*3 = 9)
(always before addition or subtraction)
= -15 + 9 = -6 Now do addition. Remember rules for adding integers.
p. 132 #71
-2 + |6 – 42|
The absolute value sign is treated like a grouping symbol.
It is the same precedence as ( ).
|6 - 42| What comes first inside the absolute value sign,
the subtraction or the exponent?_____
SOLVING EQUATIONS WITH INTEGERS
EXAMPLE:
X + (-8) = -10
Remember, we “solve” an equation by finding what x is. Get
x by itself on one side of the equation to find what it is.
How? Do the opposite operation to both sides to remove
the constant term (-8) from the left side.
What is the opposite of adding (-8)?
Well we could say that subtracting (-8) is the opposite
operation, but remember subtracting a negative number
is the same as adding a positive, so subtracting -8 is the
same as adding 8. Let’s add 8 to both sides.
x + (-8) + 8 = -10 + 8
x + 0 = -2
x = -2
CHECK!!!!!!
-2 + (-8) = -10 ? Yes!
EXAMPLE
Solve –x = 9
Hey, isn’t x already by itself? But it’s –x, not x.
What do I do to get rid of the negative sign?
Remember, -x is just a short way of saying -1x.
-x = 9
-1x = 9
− 1x 9
=
−1 −1
x = −9
CHECK: When, plugging in x=-9, put parentheses around -9 like this (-9)
-(-9) = 9? Yes! -(-9) means the opposite of negative nine. What’s the
opposite of -9? ____