Download Properties of Math

Properties of Math
SWBAT identify the properties of
operations.
Warm Up:
• Ms. Dalton has 120 students. On a recent
assignment, 75% of students got a passing grade.
How many students got a failing grade?
• In a recent study, 4 out of 5 people preferred Coke
to Pepsi. What percent of people preferred Coke?
Commutative Property of Addition
13 + 8 = 8 + 13
Changing the order of the numbers does
not change the sum.
Algebraically: a + b = b + a
Commutative Property of Multiplication
12 · 5 = 5 · 12
Changing the order of the numbers does
not change the product.
Algebraically: a · b = b · a
Identity Property of Multiplication
9·1=9
Multiplying a number by 1 leaves it
unchanged.
Algebraically: a · 1 = a
Identity Property of Addition
4+0=4
Adding a number by 0 leaves it
unchanged.
Algebraically: a + 0 = a
Associative Property of Multiplication
2(5 · 3) = (2 · 5)3
When multiplying more than 2 numbers, the
way we group them does not change the
product.
Algebraically: a(bc) = (ab)c
Associative Property of Addition
(4 + 2) + 8 = 4 + (2+8)
When adding more than 2 numbers, the way
we group them does not change the sum.
Algebraically: (a + b) + c = a + (b + c)
Zero Property of Multiplication
15 · 0 = 0
Multiplying a number by 0 is always 0.
Algebraically: a · 0 = 0
High School Vs College B-ball
A standard size high school basketball court is 84 ft long and 50 ft
wide in the shape of a rectangle.
To find the area of the court you can
84 ft
50 ft
use the formula of A = l · w
A= 84 ft · 50 ft
A= 4200 ft2
High School vs College B-ball
Did you know that a college basketball court is usually 10 ft
longer than a high school basketball court?
10 ft
84 ft
50 ft
Can you think of a
method to find the
area of the college
basketball court?
High School vs College B-ball
We could do 84 · 50 + 10 · 50
4200 + 500
4700 ft2
Why parenthesis?
Or we could do 50(84 + 10)
50(94)
4700 ft2
The Distributive Property
The Distributive Property is a property in mathematics which
helps to multiply a single term and two or more terms inside
parenthesis.
Ex: 2(3 + 5) = 2 · 3 + 2 · 5
8(3 + x) =
a(3 + 5) =
The Distributive Property
The distributive property states that the
product of a number and a sum is equal to
the sum of the individual products of addends
and the number.
Ex: 2(x + 5) = 2 · x + 2 · 5
Practice
Use the distributive property to re-write each expression.
a) 10( a + 7) =
b) x( 3 + 10) =
c) 2(x + 10) =
d) 7(x + 3) =
e) a(10 + 9) =
f) 3x(x + 10) =
Making it Stick
Associative property of Addition
Associate with a GROUP of friends
Making it Stick
Identity Property of Addition
Yourself!
Making it Stick
Commutative Property of
Multiplication
Swap or Exchange
Practice Makes Perfect
Complete the following worksheets
independently.
Exit Ticket
1. Evaluate the expression below and list the
properties that you used.
12 + (8 + 46) + 80
2. Which property of multiplication is shown?
3 ·1=3
a. Commutative
b. Associative
c. Identity