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Essential Question: How do you use
the distributive property to simplify
expressions?
Before we
start…
Match the following:
1. 20  3  14   ?
2. 15 14  3  ?
3. 12  23  6   ?
A. 15 14  15  3
B. 12  23  12  6
C. 20  3  20 14
Properties of Addition
• The identity property states that the sum of a
number a and 0 is a. The number 0 is the
additive identity.
• The inverse property states that the sum of a
number a and its opposite is 0. The opposite of
a is its additive inverse.
Identify the property
 x  9  2  x  9  2
8.3   8.3  0
 y  0.7  0.7    y 
Properties of Multiplication
The Multiplicative Identity
• The identity property states that the product of
a number a and 1 is a.
• The number 1 is called the multiplicative
identity.
Identify the property
 x  7   0.5  x   7  0.5 
80  8
6  y  y   6 
Identify the property
9   1  9
1 v  v
 y  4  9  y   4  9
What is the distributive property?
• The distributive property allows you to rewrite
an expression as an equivalent expression to
find the product of a number and a sum or
difference.
• This combines multiplication and addition.
The Distributive Property
a  b  c   ab  ac
a  b  c   ab  ac
Another Way to Look at Distributive
Property
 b  c  a  ba  ca
 b  c  a  ba  ca
What is an expression?
• Recall an expression contains variables,
numbers and operations.
• Two expressions that have the same values of
the variable are called equivalent expressions.
Write an equivalent expression.
4  y  3
 y  7 y
Write an equivalent expression.
n  n  9
 2  n8
Write an equivalent expression.
5  x  6 
 x  7  3
Write an equivalent expression.
x  x  4
 7  x  5
• Turn to page 99 and complete #5, 9, and 15
with your partner.
5. 4  x  3
9.
 p  3 8
15.  2 x  3  x 
Terms and Coefficients
• The parts of an expression that are added
together are called terms.
 x  2x  8
terms
Terms and Coefficients
• The number part of a term with a variable part
is called the coefficient of the term.
 x  2x  8
coefficient
Constant and Like Terms
• A constant term has a number part but no
variable.
• Like terms are terms that have the same
variable part.
• Constant terms are also like terms.
• Identify the terms, like terms, coefficients, and
constant terms of the expression:
3x  4  6x  2
• Identify the terms, like terms, coefficients, and
constant terms of the expression:
7 y  8  6 y  13
How do I combine like terms?
• To combine like terms, add the coefficients
and use the common variable part.
• An expression is simplified if it has no
grouping symbols and if all of the like terms
have been combined.
Simplify 4  n  9  3  2  n 
Simplify 5  6  n   2  n  2
Simplify 15t   t  4
Simplify 3  x  8  4  x  2
Simplify  7  x  4  3  x  3
Simplify 4  x  3  7  x  6
• Turn to page 99 and complete #31 and 33 with
your partner.
31.
 4a  1 2  a
33. 6r  2  r  4 
Simplifying Expressions
• You can simplify expressions that are being
divided by the same number.
• To simplify, divide each term by the number.
36 x  24
6
2x  8
4
6 y  18
3
10 z  20
5
8 x  80
8
15 x  30
5
2  x  6
1
4  x  10 
2
Exercise Your daily workout plan involves a total of 50 minutes
of running and swimming. You burn 15 calories per minute when
running and 9 calories per minute when swimming. Let r be the
number of minutes that you run. Find the number of calories you
burn in your 50 minute workout if you run for 20 minutes.
Hiking Socks A local sports store is selling hiking socks for $2
off the regular price of a pair of socks. You buy 3 pairs of hiking
socks. Write an equation that gives the total cost t as a function of
the regular cost r of a pair of socks. Then find the total costs if
the socks regularly cost $10 per pair.
Pizza Party You are buying 10 pizzas for a party.
Cheese pizzas cost $11 each, and single topping pizzas
cost $13 each. Write an equation that gives the total cost
C (in dollars) as a function of the number p of cheese
pizzas that you buy. Find the total cost if 4 of the pizzas
you buy are cheese.
Movies Once a week, you either rent a movie for $4 or
see a movie in a theater for $9. Let r represent the
number of movies you rent in a year. Write and simplify
an expression in terms of r for the total amount you
spend on movies during the year. How much do you
spend if you go to the theater 20 weeks of the year?
• How do you use the distributive property to
simplify expressions?
Ticket Out the Door
• Simplify. Place your name on the paper and
place it in the basket.
8x  3  2 x 1