Transcript Chapter 3 Lesson 1 pgs. 98-102

Chapter 3 Lesson 1
pgs. 98-102
What you will learn:
Use the Distributive Property to
write equivalent numerical and
equivalent algebraic expressions
Vocabulary and Key Concept:
Equivalent expression (98): expressions that have the same
value Ex.) 3(4+2) and 34 + 32 both have the same
value of 18
Distributive Property (98): To multiply a number by a sum,
multiply each number inside the parentheses by the
number outside the parentheses.
a(b+c) = ab + ac
3(4+2) = 34 + 32
(b+c)a = ba + ca
(5+3)2 = 52 + 32
What two operations are combined by the Distibutive
Property?
Multiplication and Addition
Use the Distributive Property
Use the Distributive Property to write each expression
As an equivalent expression. Then evaluate the expression.
2(6+4)
26 +24
12 + 8 Multiply
20 Add
On your own:
5(7+3)
57 + 53
35 +15
50
(8+3)5
85 + 35
40 + 15 Multiply
55 Add
(10-3)(-5)
10(-5) - 3(-5)
-50 - (-15)
-35
Use the Distributive Property to solve a problem:
A one-day pass to an amusement park costs $40. A round-trip
bus ticket to the park costs $5. Write two equivalent expressions
to find the total cost of a one-day pass and a bus ticket for 15
students.
Method 1: Find the cost for 1 person, then multiply by 15.
15($40 + $5)
cost for one person
Method 2: Find the cost of 15 passes and 15 tickets.
cost of 15 passes
15($40) + 15($5) ---> cost of 15 tickets

Find the total cost.
Evaluate either expression to find the total cost.
15($40 + $5)= 15($40) + 15($5) Distributive Property
$600 + $75
Multiply
$675
Add
The total cost is $675
You can check your results by evaluating 15($45)
Simplify Algebraic Expressions
Use the Distributive Property to write each expression as an
equivalent algebraic expression.
3(x+1)
(y+4)5
3x + 31
y5 + 45
3x + 3 Simplify
5y + 20 Simplify
On your own:
4(x+3)
4x +12
-6(x+5)
-6x + (-30)
Simplify Expressions with Subtraction
2(x-1)
=2[x+(-1)]
=2x + 2(-1)
=2x + (-2)
=2x-2
Rewrite x-1 as x+(-1)
Distributive Property
Simplify
Definition of Subtraction
Your turn:
-3(n-5)
= -3[n+(-5)]
= -3n + (-3)(-5)
= -3n + 15
Rewrite n-5 as n+(-5)
Distributive Property
Simplify
Take a practice sheet by the door!