Transcript Generating Equivalent Expressions

GENERATING
EQUIVALENT
EXPRESSIONS
ENGAGE NY- LESSONS 1 & 2
VOCABULARY
Read over the vocabulary for this unit.
5X + 4 – 40 – 2X
3X – 36
ANY ORDER, ANY GROUPING
PROPERTY WITH ADDITION
• Rewrite 5x + 3x in expanded form
• Factor 5x + 3x using the distributive property
• Solve
FIND A VALUE FOR X
5x + 3x ≠ 8x or
5x – 3x ≠ 2x
Use a variety of positive and
negative rational numbers
ASSOCIATIVE PROPERTY
COMMUTATIVE PROPERTY
FIND THE SUM OF 2X + 1 AND 5X
& JUSTIFY YOUR STEPS
• (2x + 1) + 5x:
Original Expression
• 2x + (1 + 5x):
Associative Property of addition
• 2x + (5x + 1):
Commutative Property of addition
• (2x + 5x) + 1:
Associative Property of addition
• (2 + 5)x + 1:
Combined like terms using Distributive
Property
• 7x + 1:
Equivalent expression
• The ORANGE steps can be combined!
2X + 1 + 5X = 7X + 1
• Why was the associative property AND the commutative
properties both used?
• Did the use of these properties change the value of the
expression?
• How can we confirm that the expressions (2x + 1) + 5x and
7x + 1 are equivalent expressions?
FIND THE SUM &
JUSTIFY YOUR STEPS
• (-3a + 2) + (5a – 3)
FIND THE SUM &
JUSTIFY YOUR STEPS
• (-3a + 2) + (5a – 3): Original Expression
• -3a + 2 _ 5a + (-3):
Additive Inverse (add the opposite)
• -3a + 5a + 2 + (-3):
Any order, any grouping
• 2a + (-1):
Combined like terms
• 2a – 1:
Adding the inverse & simplify expression
ANY ORDER, ANY GROUPING
WITH MULTIPLICATION
•
2x  3
•
2 If a product of factors is being multiplied, the any order, any
grouping property allows us to multiply those factors in any order
by grouping them together in any way.
•
(x  3)
Associative Property of Multiplication
(any grouping)
•
2  (3  x)
Commutative Property of Multiplication
(any order)
•
6x
Simplify using multiplication
Original Expression
If a product of factors is being multiplied, the any order, any grouping
property allows us to multiply those factors in any order by grouping
them together in any way.
ANY ORDER, ANY GROUPING IN
EXPRESSIONS WITH ADDITION &
MULTIPLICATION
3(2x)
• (3  2) x
• 6x
ADDITIVE & MULTIPLICATIVE
INVERSES
• Is a ZERO sum game!...
• Meaning, they have a sum of zero and a
product of 1.
• –3 + 3 = 0: Additive Inverse
• 3  ⅓ = 1: Multiplicative Inverse
COMBINING EXPRESSIONS:
HORIZONTALLY VS. VERTICALLY
IN SUBTRACTION
• When lining up vertically, make sure each term is lined up
above or below its mate with its sign.
(2x + 3y – 4)
-(5x
+2)
• Find the additive inverse- and change ALL signs.
( 2x + 3y – 4)
+(–5x
– 2)
–3x + 3y –6
COMPLETE HOMEWORK