2. Warm- Up Exercises
1. What is the simplified fraction of 35%?
3. Order the following from greatest to least:
3.45, 3⅗, 54.3%, 3⅓
3. Warm- Up Exercises
4. Mike painted 120 houses in 4 months. Jack took two
more months to paint the same number of houses. If
they worked together to paint an additional 120 houses,
how many would each paint?
5. Prom tickets cost $10 for singles and $15 for couples.
Fifty more couples tickets were sold than were singles
tickets. Total ticket sales were $4000.
How many of each ticket type were sold?
4. Review of Systems Test
4. Which system of inequality best represents the graph?
A. y > -2 and y > x + 1 B. y < -2 and y > x + 1
C. y > -2 and y < x + 1 D. y < -2 and y < x + 1 E. None
A. y > -2 and y < x + 1 B. y < -2 and y > x + 1
C. y > -2 and y > x + 1 D. y < -2 and y < x + 1 E. None
5. Review of Systems Test
7. What is the solution to the following
system of equations?
A. ( 2, -2 ) B. ( -2, 2 ) C. No Solution
D. Infinite Solutions E. None
A. ( 2, -2 ) B. ( -2, 2 ) C. Infinite Solutions
D. No Solution E. None
6. Review of Systems Test
Which of the following graphs represents the solution
to the following system of inequalities? 6x – 2y < 6 and x - y < -1
A B C
D E. None
32. Negative and Zero Exponents
Take a look at the following problems and see if you
can find the pattern.
The expression a-n is the reciprocal of an
33. Negative and Zero Exponents
*Any number (except 0) to the zero power is equal to 1.
Since 2/3 is in parenthesis, we must apply the power of a
quotient property and raise both the 2 and 3 to the negative
2 power. First take the reciprocal to get rid of the negative
exponent. Then raise (3/2) to the second power.
42. Warm- Up Exercises
1. A board 28 feet long is cut into two pieces. The ratio of
the lengths of the pieces is 5:2. What are the lengths of
the two pieces?
5:7 = X:28; x1 = 20 ft., x2 = 8 feet.
2. The ratio of the length to the width of a rectangle is 5:2.
The width is 24 inches long. Find the length.
5:2 = x: 24; Length = 60"
3. What is: 5 6 • 5 - 2
= 5 4 ; 625
43. Warm- Up Exercises
4. (12) -5 • (12) 3
Since the bases are the same (12): the exponents
are added. -5 + 3 = -2; (12)-2 = 1/12 2 = 1/144
5. 4 2 • 35 • 24
4 3 • 35 • 22
6. Simplify: 5b • 6a4
= 30ba4 c
Definition: Mono-- The prefix means one.
A monomial is an expression with one term.
In the equations unit, we said that terms were separated
by a plus sign or a minus sign!
A monomial CANNOT contain a plus sign (+) or a
minus (-) sign!
54. Multiplying Monomials
When you multiply monomials, you will
need to perform two steps:
•Multiply the coefficients (constants)
•Multiply the variables
A simple problem would be: (3x2)(4x4)
And the answer is:
12x6 Remember, the bases
are the same, so you add the exponents
63. Multiplying Monomials Answers
1. (3x5y 2 ) (-5x3y 6 )
Multiply the coefficients. Then multiply the variables (add
the exponents of like variables).
-15x 8 y 8
2.(-2r3s7t4 )2 (-6r2t 6)
Raise the 1st monomial to the 2nd power.
(4r6s14t8) (-6r2t 6): Multiply the coefficients and add the
variables with like bases
= -24r 8s14 t14
64. Multiplying Monomials Answers, con't.
3. (4a2b2c3)3 (2a3b4c2)2
Raise the 1st monomial to the
(64a6b6c9) (4a6b8c4) 3rd power and the 2nd
monomial to the 2nd power.
Multiply the coefficients and add the variables with like bases
65. Dividing Monomials
As you've seen in earlier examples, when we work
with monomials, we see a lot of exponents. Hopefully
you now know the laws of exponents and the
properties for multiplying exponents, but what
happens when we divide monomials? You probably
ask yourself that question everyday.
66. Dividing Monomials
Expanded Form Examples
When you divide powers that have the same base, you subtract the
exponents. That's a pretty easy rule to remember. It's the opposite of
the multiplication rule. When you multiply powers that have the
same base, you add the exponents and when you divide powers that
have the same base, you subtract the exponents!
67. Dividing Monomials
That's an easy rule to remember. Let's look at one more
property. The Power of a Quotient Property. A Quotient is an
answer to a division problem. What happens when you raise a
fraction (or a division problem) to a power? Remember: A
division bar and fraction bar are the same thing.
71. Simplifying Monomials
Properties of Exponents and Using the Order of Operations
• If you have a combination of monomial expressions
contained with in grouping symbols (parenthesis or
brackets), these should be evaluated first.
• Power of a Power Property - (This is similar to evaluating
Exponents in the Order of Operations). Always evaluate a
power of a power before moving on the problem.
Example of Power of a Power:
• When you multiply monomial expressions, add the
exponents of like bases.