Name: _______________
Lesson 9
NYS Integrated Algebra
Bell Ringer:
A. New York State provides data on test scores to schools. Would this data be
considered quantitative or qualitative?
____________________________
B. Write a survey question that would collect qualitative data.
______________________________________________________________________________
______________________________________________________________________________
Simplifying Expressions
Before we begin simplifying we need to be sure that we understand the relationships
implied by the mathematical notation.
Let’s start with a simple example:
What is x  x ?
Remember that when we write
Then
x there is an invisible 1 in front of x .
x  x  __________________
When there is a common factor we can divide it out using the distributive property:
Therefore,
x  x  ________
Hopefully it is clear now that the coefficient on
x tells us ______________________________
______________________________________________________________________________________
The coefficient is attached to the variable by _________________________________ .
Remember that multiplication’s opposite operation is ____________________________ and
can only be “undone” by this operation.
The other notation that it is important to understand is exponents. An exponent is
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
Recall that x  _________
2
and x  _____________ .
3
Integrated Algebra
Lesson 9
1
Simplify
x3
. Start by writing this out as multiplication problems on top and bottom.
x2
How about
y5
?
y3
To write in simplest form (or simplify) means to _______________________________________
______________________________________________________________________________________
______________________________________________________________________________________
The rule for simplifying fractions with terms that have the same base is
____________________________________________________________
What happens when the exponent in the denominator is larger than the exponent in the
numerator?
Try this one first changing it to multiplication then canceling, then using the rule:
m2
m5
Negative exponents take some getting used to but they are really just a way to move a
term from numerator to denominator or visa-versa.
Practice: Simplify each of the following.
A.
3x
6
A. ___________
B.
8 y3
4y
B. ___________
2 x8
C.
8 x5
C.____________
D.
8y
12 y 4
E.
15m 2 x 5
10m 4 x
D.____________
E.___________
Integrated Algebra
Lesson 9
2
F.
24 p 6 q 5
16 p 7 q
F. ___________
G. Simplify and write without using fraction notation:
x3 y 5
x8 y 4
G. ___________
H. Rewrite using only positive exponents:
x 2 y 7
H. ___________
I.
3 4
Rewrite using only positive exponents: m n
I. ___________
J.
Rewrite using only positive exponents:
2
p q
5
J. ___________
K. Rewrite using only positive exponents: 5x
6
K. ___________
L. Rewrite as an addition problem:
5x
L. _________________
M. Expand using addition and multiplication:
4g 2
M. _________________
N. Expand using addition and multiplication:
3x 2 y
N. _________________
Integrated Algebra
Lesson 9
3
Integrated Algebra
Lesson 9
4
Name: _______________________________
Lesson 9
NYS Integrated Algebra
On Your Own:
1. *Copy
a.
b.
c.
the following definitions in your glossary:
coefficient
exponent
simplest form
2. *Simplify
x4
.
x2
______________
3
3. *Simplify
y
.
y5
______________
4m
4. *Simplify
.
8m 3
______________
3
5. *Simplify
21xy
.
14 x 4 y
______________
2 8
6. *Simplify and write without using fraction notation:
mn
m5 n 2
______________
7. *Rewrite using only positive exponents:
4
3 5
x y z
______________
1 4
8. *Rewrite using only positive exponents: m n
______________
9. *Rewrite as an addition problem:
4m
____________________________________
10. *Expand using addition and multiplication: 3z
3
____________________________________
11. *Expand using addition and multiplication:
2x3 y 2
____________________________________
Integrated Algebra
Lesson 9
5
12. A study is done to determine the average number of hours a high school student
sleeps. Would this be an example of quantitative data or of qualitative data?
13. Is
2x  8  12 an equation or an expression?
_____________________
_____________________
14. Evaluate
5s  3 for s  1
______________
Math Musings:
15. Write a survey question you could use to collect quantitative data.
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
My Data:
In the last 24 hours:
1. I spent _______________ minutes watching TV.
2. I spent _______________ minutes on the Internet.
3. I spent _______________ minutes emailing friends.
4. I spent _______________ minutes talking to or text-messaging friends by
phone.
5. I spent _______________ minutes on all homework.
6. I spent _______________ minutes on this math assignment.
7. I ate _____________ “real” meals.
8. I had _____________ snacks.
9. I spent ________________ minutes doing something “active” (phys ed, physical
work, sports, exercise, etc.)
10. My favorite color is:
_____________________________________
Integrated Algebra
Lesson 9
6