Transcript Lesson 3-1 and Lesson 3-2

LESSON 3-1 AND
LESSON 3-2
Distributive Property and Simplifying
Algebraic Expressions
I Can…
Use the distributive property to write
equivalent numerical expressions.
Use the distributive property to write
equivalent algebraic expressions.
Use the distributive property to
simplify algebraic expressions.
MULTIPLICATION AS REPEATED ADDITION
3(4) = 4 + 4 + 4
7(5) = 5 + 5 + 5 + 5 + 5 + 5 + 5
2(x + 3) = (x + 3) + (x + 3)
SKITTLES PRACTICE
How many of each color?
Three groups of 2 red and 1 yellow
Skittles Model
Algebraic Expression
Repeated Multiplication
3(2R + 1Y)
(2R + 1Y)
(2R + 1Y)
(2R + 1Y)
6R + 3Y
DISTRIBUTIVE PROPERTY
Words
Symbols
To multiply a number by a sum,
multiply each number inside the
parentheses by the number outside
the parentheses.
a(b+c) = ab + ac (b+c)a= ba + ca
Examples 3(4+2) = 34 + 32 (5+3)2=52 + 32
We call these EQUIVALENT
EXPRESSIONS because they
have the same value.
DISTRIBUTIVE PROPERTY AND ALGEBRA
The model shows 2(x +3)
There are groups of (x +3)
x 111
x 111
Separate the tiles into 2 groups
of x and 2 groups of 3.
2
x
x
2(x + 3)
2 (x + 3) = 2x + 23
= 2x + 6
111
2
111
EXAMPLE 1: USE THE DISTRIBUTIVE
PROPERTY
 Use the distributive property to write the expression as an
equivalent expression.
2(6 + 4)
2 (6 + 4) = 26 + 24
= 12 + 8
= 20
EXAMPLE 1: USE THE DISTRIBUTIVE
PROPERTY
 Use the distributive property to write the expression as an
equivalent expression.
5(8 + 3)
5 (8 + 3) = 58 + 53
= 40 + 15
= 55
EXAMPLE 2: 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.
① Write two equivalent expressions to find the total cost of
a one-day pass and a bus ticket for 15 students.
Method 1
Method 2
Find the cost for 1 person,
then multiply by 15
Find the cost of 15 passes
and 15 tickets. Then add.
① Find the total cost
EXAMPLE 3: SIMPLIFY ALGEBRAIC
EXPRESSIONS
 Use the distributive property to write each expression as an equivalent
algebraic expression.
3(x+1)
(y+4)5
EXAMPLE 4: SIMPLIFY ALGEBRAIC
EXPRESSIONS WITH SUBTRACTION
 Use the distributive property to write each expression as an equivalent
algebraic expression.
2(x-1)
-3(n-5)
SIMPLIFY EXPRESSIONS
There are 4 terms
 When plus or minus signs separate
algebraic expressions into parts,
each part is a
.
 The numerical part of a term that
contains a variable is called the
of the
variable.
are terms that
contain the same variables, such as
2n and 5n or 6xy and 4xy.
 A term without a variable is called a
.
Constant
x+
2 is the
coefficient
of 2x
+x+3
1 is the
coefficient of x
because x = 1x
• 2x and x are like terms
• 8 and 3 are like terms
SIMPLIFYING EXPRESSIONS
An algebraic expression is in
it has no like terms and no parentheses.
Rewriting a subtraction expression using addition
will help you identify the terms of an expression.
if
EXAMPLE 5: IDENTIFY THE PARTS OF AN
EXPRESSION
 Identify the terms, like terms, coefficients, and constants in the
expression 3x - 4x + y – 2. Then, SIMPLIFY.
3x - 4x + y – 2 = 3x + (-4x) + y + (– 2)
Terms
3x, -4x, y,
and -2
Like terms
3x and -4x
Coefficients
3, -4, 1
Constants
-2
= 3x + (-4x) + 1y + (– 2)
= (3+(-4))x + 1y + (– 2)
= (-1)x + 1y + (– 2)
= -x + y – 2
Definition of
subtraction
Identity Property
Distributive Property
Simplify