1-3 Properties of Numbers
CCSS: A.SSE.1b, A.SSE.2, N.Q.3
Vocabulary
Using your textbook, define the following:
• Equivalent Expressions
• Additive Identity
• Multiplicative Identity
• Multiplicative Property of Zero
• Multiplicative Inverse/Reciprocal
• Commutative Property
• Associative Property
• Equivalent Expressions- expressions that represent the
same number
• Additive Identity- The sum of any number and zero is
equal to the number
• Multiplicative Identity- The product of any number and 1
is equal to the number
• Multiplicative Property of Zero- The product of any
number and zero is equal to zero
• Multiplicative Inverse/Reciprocal- Two numbers whose
product is 1
• Commutative Property- The order in which you add or
multiply numbers does not change their sum or product
• Associative Property- The way you group three or more
numbers when adding or multiplying does not change
their sum or product
Properties of Equality
Property
Words
Symbols
Examples
Reflexive
Property
Any quantity is
equal to itself
a=a
Symmetric
Property
If one quantity
equals a second
quantity, then the
second quantity
equals the first
If a=b, then b=a
5=5
4+7=4+7
8=2+6 then
2+6=8
Transitive Property
If one quantity
equals a second
quantity and a
second quantity
equals a third
quantity, then the
first quantity equals
the third quantity
If a=b, b=c, then
a=c
If 6+9=3+12
and
3+12=15,
then 6+9=15
Substitution
Property
A quantity may be
substituted for its equal
in any expression
If a=b then a may
be replaced by b
If n=11, then
4n=4*11
Example 1: Evaluate Using
Properties
1
Evaluate 7(4  3)  1  5
5
Name the Property used in each step
2 3  (4 2  8)
 2 3  (8  8)
 2 3  (0)
 60
6
Example 2: Real World
Item
Eric makes a list of
items that he needs to
buy for a party and
Balloons
their costs. Find the
total cost of these
Decorations
items
Food
Beverages
Cost ($)
6.75
14.00
23.25
20.50
Example 3: Use Multiplication
Properties
Name the property used in each step
5 7 4 25 2 7 4
 (5 2) (7 4)
 10 28
 280
Example 4: Common Core
A traveler checks into a hotel on Friday and
checks out the following Tuesday morning.
Use the table to find the total cost of the
room including tax
Day
Mon.-Fri.
Room
Charge
$72
Sat.-Sun. $63
Sales
tax
$5.40
$5.10
Example 5: Common Core
The table shows prices on
children’s clothing.
a. Interpret the expression
5(8.99)+2(2.99)+7(5.99)
b. Write and evaluate three
different expressions that
represent 8 pairs of shorts
and 8 tops
c. If you buy 8 shorts and 8
tops you receive a
discount of 15%. Find the
greatest and least amount
of money you can spend
on the 16 items at the sale
Shorts Shirts
Tank
Tops
$7.99
$8.99
$6.99
$5.99
$4.99
$2.99
Example 6: Accuracy
a. Elan has $13 that he wants to divide
among his 6 nephews. When he types
13/6 into his calculator, the number that
appears is 2.166666667. Where should
Elan round?
Example 7: Accuracy
Dante’s mother brings him a dozen cookies,
but before she leaves she eats one and
tells Dante he has to share with his two
sisters. Dante types 11/3 into his calculator
and gets 3.66666667. Where should
Dante round?
Accuracy: Practice
1. Jessica wants to divided $23 six ways.
Her calculator shows 3.833333333.
Where should she round?
2. Ms. Harris wants to share 2 pizzas
among 6 people. Her calculator shows
0.33333333. Where should she round?
3. The measurements of an aquarium are
12.9, 7.67, and 4.11 inches. Where
should the number be rounded?