LESSON 3.1 Notes Day 2- Algebraic Expressions
Goal: How do you add, subtract, factor and multiply algebraic expressions?
Example 1 – Combining Like Expressions
Steve and Terry work as consultants and get paid per project. Steve is paid a project fee of
$50 plus $10 per hour. Terry is paid a project fee of $40 plus $12 per hour. Write an expression
to represent how much the company will pay if they hire both of them for a project. Let h
represent the number of hours they work together.
A) Write an expression to represent the fee plus the rate per hour for each:
Steve:
Terry:
B) Add both expressions to represent how much the company will pay in total:
The company will pay ______________________________ for both Steve and Terry to work on
their project.
Now try these with your group:
1) How much will Steve and Terry each make (individually) if the work 10 hours?
2) Work with your group to combine like terms on the following:
(4x + ½ ) – (8x – 5 ½ )
3) What are two different ways to calculate how much a company would pay to hire both
Steve and Terry to work on a 20 hour project? SHOW BOTH WAYS!
4) Explain how the distributive property allows you to combine 5x and 8x. (Hint: You may be
using it in reverse ).
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Example 2 – The Distributive Property
Jacob works for a ticket company and is selling tickets for a popular concert. He is excited
because he gets to keep 10% of the money he collects from his sales. Tickets on the floor
cost $75 each and tickets in the stands cost $45 each.
Write an expression to represent how much Jacob gets to keep.
A) Define your variables:
B) Write an expression to represent the amount that Jacob would collect from the ticket
sales:
C) What is 10% as a decimal?
D) Write an expression to represent the money Jacob gets to keep:
E) Use the distributive property to simplify your expression:
Now try these with your group:
1) How much will Jacob earn if he sells 120 floor tickets and 150 stands tickets?
2) How do you change a percent to a decimal?
3) How do you change a fraction to a decimal?
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Example 3 – Introduction to Factoring
Factor 4x + 8
A) Model the expression with algebra tiles. Draw your picture here:
B) Arrange the tiles to form a rectangle. Draw your picture here:
C) Since the length multiplied by the width equals area, the length and the width of the
rectangle are the factors of 4x + 8.
List the factors here:
D) Write equivalent expressions:
E) Look at the two expressions in “D”. Is there a way that you could have gotten the factors
without modeling with algebra tiles?
Now try these with your group:
1) Some people say factoring is like “undistributing”. What do you think they mean?
2) See if you can factor each expression:
a) 2x + 2
b) 3x + 9
c) 10x + 15
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Practice:
Simplify (add or subtract) each expression.
1) (3.2x + 12.5) + (4.8x – 14)
2) (15x + 9) – (4x + 7)
1
3
1
1
3) ( x + ) + ( x - )
2
4
2
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4) James’ parents pay him an allowance. Each week he gets paid $5 plus $3 for each chore
he does. His older sister gets $10 plus $2 for each chore she does.
A) Define your variable:
B) Write an expression to represent:
How much James makes:
How much his sister makes:
C) Write an expression to show how much both of them make together if they do the same
number of chores.
D) If they each do 12 chores, how much do they get paid individually? How much do they
make together?
5) A company sets up a food booth and a game booth at the county fair. The fee for the
food booth is $50 plus $10 per day. The fee for the game booth is $100 plus $8 per day.
Write an expression to show how much the company pays for both booths?
If they rent both for 7 days, how much will they pay?
6) A group of six people go out to eat. They decide to split the bill so each person pays 1/6
of the bill. Appetizers are $8 each and main dishes are $15. Write an expression to show how
much each person pays:
7) Factor:
a) 5x – 25
b) 10x – 60
c) 36x + 24
d) 12x + 10
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