Transcript terms
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
80 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 n8
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