Lesson 1-4
Objective - To simplify expressions using
properties of numbers.
Commutative - Order doesn’t matter! You can
flip-flop numbers around an operation.
Commutative Property of Addition
a+b=b+a
5+7=7+5
10 + 3 = 3 + 10
Commutative Property of Multiplication
a •b = b•a
8• 4 = 4•8
3 • 12 = 12 • 3
Associative - Re-grouping is ok! You can
re-group numbers together.
Associative Property of Addition
(a + b) + c = a + (b + c)
((4 + 2)) + 9 = 4 + ((2 + 9))
Associative Property of Multiplication
(a • b) • c = a • (b • c)
(3 • 5) • 7 = 3 • (5 • 7)
Commutative vs. Associative
Identities
Identify each property shown below.
Identity Property of Addition
x+0=x
1) 7 + 4 = 4 + 7
Zero is sometimes called the Additive Identity.
Identity Property of Multiplication
x •1 = x
One is sometimes called the Multiplicative Identity.
Commutative vs. Associative
Commutative
Associative
(2 + 7) + 8 = (7 + 2) + 8
Flip-flop
Comm. Prop. Of Add.
2) 6 • (2 • 8) = (6 • 2) • 8 Assoc. Prop. Of Mult.
3) 5 • 9 = 9 • 5 Comm. Prop. Of Mult.
4) (4 + 2) + 3 = (2 + 4) + 3 Comm. Prop. Of Add.
Commutative vs. Associative
Identify each property shown below.
(2 + 7) + 8 = 2 + (7 + 8)
1) (6 + 3) + 1 = (3 + 6) + 1 Comm. Prop. Of Add.
Re-group
2) 10 • (8 • 3) = (10 • 8) • 3 Assoc. Prop. Of Mult.
(2 + 7) + 8 = 8 + (2 + 7)
Flip-flop
3) 5 + 1 = 1 + 5 Comm. Prop. Of Add.
4) (7 • 2) • 4 = 4 • (7 • 2) Comm. Prop. Of Mult.
( ) does not imply Associative
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011
Lesson 1-4 (cont.)
Give the property that justifies each step.
Identify the property shown below.
1) 6 + 8 = 8 + 6
Comm. Prop. of Add.
Statement
16 + (27 + 84)
Reasons
Given
2) (10 • 4) = (4 • 10) Comm. Prop. of Mult.
16 + (84 + 27)
Comm. Prop. of Add.
3) (2 + 10) + 3 = (10 + 2) + 3 Comm. Prop. of Add.
(16 + 84) + 27
Assoc. Prop. of Add.
Comm Prop
Prop. of Mult
Mult.
4) 5 • (7 • 4) = (7 • 4) • 5 Comm.
(100) + 27
Add 16 and 84
5) 7 • 0 = 0 Mult. Prop. of Zero
127
Add 100 and 27
6) 7 + 0 = 7 Identity Prop. of Add.
7) 7 • 1 = 7 Identity Prop. of Mult.
Use the commutative and associative properties
to simplify each expression.
1) 25 • (37 • 4)
2) 12 + (29 + 8)
25 • (4 • 37)
12 + (8 + 29)
(25 • 4) • 37
(12 + 8) + 29
(100) • 37
(20) + 29
3700
49
Distributive Property
a(b + c) = a • b + a • c
or
a(b − c) = a • b − a • c
Order of Operations
Distributive
Property
3(4 + 5) = 3(9) = 27
3(4) + 3(5)
It works!
12 + 15
27
Why use the distributive property?
3(x + 2) = 3(x) + 3(2) = 3x + 6
Use the distributive property to help simplify the
following without a calculator.
1) 5(9.96)
2) 7(8.2)
5(10 − 0.04)
7(8 + 0.2)
Use the distributive property to help simplify the
following without a calculator.
3) 8($11.30)
4) 7 × 5.95
7(6 − 0.05)
8($11 + $0.30)
5(10) − 5(0.04)
7(8) + 7(0.2)
8($11) + 8($0.30)
50 − 0.20
0 20
56 + 1.4
14
$88 + $2.40
$2 40
7(6) − 7(0.05)
42 − 0.35
0 35
49.80
57.4
$90.40
41.65
Math 6 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2011