relationships that are always true for real numbers are called _____________, which are rules used...
TRANSCRIPT
Relationships that are always true
for real numbers are called
_____________, which are rules
used to rewrite and compare
expressions.
properties
PROPERTY DEFINITION EXAMPLE
CommutativeProperty
Addition
Multiplication
AssociativeProperty
Addition
Multiplication
Distributive Property
Changing Orderdoes not change the outcome
1 + 2 = 2 + 1a + b = b + a1 ● 2 = 2 ● 1a b = b a
(8 + 6) + 7 = 8 + (6 + 7)(a + b) + c = a + (b + c)4● (5 ●9) = (4 ●5) ● 9(ab) ● c = a ● (bc )
10 (1 + 7) = 10 ● 1 + 10 ●715(x - 4) = 15 ● x – 15 ●4
RegroupingOrder stays the same only ( ) move(Change who you associate
[hang out] with)
a(b + c) = ab + aca(b - c) = ab - ac
Property Definition Example
Identity Properties
Addition Addition
Multiplication Multiplication
Inverse Properties
Addition Addition
Multiplication Multiplication
Adding “0” = no change
Multiply by 1= no change
a + (-a) = 0
-17 + 0 = -17
1● 99y = 99y
14 + (-14) = 0
Property Definition Example
Zero Property of Multiplication
Multiplication Property of –1
Multiply by 0, you get 0
Multiply by -1, you change the sign
(7003)(0) = 0
-1(a) = -a-1(2) = -2-1(-5) = 5
Zero Property of Multiplication
Associative Prop. of Addition
Identity of Addition (Additive Identity)
Identity of Multiplication (Multiplicative Identity)
Commutative Prop. (Addition)
The “z” and the √ y have been
switched.
F. A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math.
G. A can hold 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math.
$7.75 + $2.40 + $1.25 = (7.75 +1.25 + 2.40) = 9.00 + 2.40 = 11.40
3●4 ●6 ●10 = 720
Using Properties for Mental Calculations
Writing Equivalent Expressions
(5 ● 3)n 15n
(7b + 4) + 8 7b + ( 4 + 8) 7b + 12
1 6x
(2.1 ● 4.5)x 9.45x
6 + (3 + 4h)
(6 + 3) + 4h
9+ 4h