Bell Quiz
Objectives
• Simplify expressions using the properties
of real numbers.
• Discuss the numeric example for each
property and relate it to the general
statement.
Properties of Addition and
Multiplication
• The properties of real numbers are used to
simplify expressions and write equivalent
expressions.
Identity Property of Addition
For every real number a,
a+0=a
Example:
5+0=5
Identity Property Of
Multiplication
For every real number a,
a∙1=a
Example:
5∙1=5
Commutative Property of
Addition
For every real number a and b,
a+b=b+a
Example:
5+2=2+5
7 = 7
Commutative Property of
Multiplication
For every real number a and b,
a∙b=b∙a
ab = ba
Example:
5∙2=2∙5
10 = 10
Associative Property of
Addition
For every real number a, b and c,
(a + b) + c = a + (b + c)
Example:
(1 + 2) + 3 = 1 + (2 + 3)
3+3 = 1+5
6
=
6
Associative Property of
Multiplication
For every real number a, b and c,
(a ∙ b) ∙ c = a ∙ (b ∙ c)
Example:
(1 ∙ 2) ∙ 3 = 1 ∙ (2 ∙ 3)
2∙3 = 1∙6
6
=
6
Example 1
Identifying Properties
Identify the property illustrated in each equation.
a. 1 ∙ 8 = 8
b. 13 + 5 = 5 + 13
c. (3 ∙ 4) ∙ 7 = 3 ∙ (4 ∙ 7)
d. (12 + 9) + 5 = (9 + 12) + 5
Lesson Practice
Identify the property illustrated in each equation.
a. 5 + (9 + 8) = (5 + 9) + 8
b. 0 + 10 = 10
c. 15 ∙ 3 = 3 ∙ 15
d. 17 ∙ 1 = 17
Example 2
Using Properties to Justify Statements
Tell whether each statement is true or false.
a. gh = hg
b. b + 1 = b
c. d + (e + f) = (d + e) + f
Lesson Practice
Tell whether each statement is true or false.
a. (ab)c = a(bc)
b. m – z = z – m
c. w + 0 = w
Example 3
Justifying Steps to Simplify an Expression
Simplify each expression
a. 16 + 3x + 4
b. (25) ∙ y ∙ (1/25)
Lesson Practice
Simplify each expression
a. 18 + 7x + 4
b. (1/3)d ∙ 3
Example 4
Application: Consumer Math
Envelopes, pens, and correction tape can
be purchased at an office supply store
for the following prices respectively:
$2.85, $5.35, and $2.15. Find the total
cost of the supplies.
Lesson Practice
Erasers, markers, and paper can be
purchased at the school store for the
following prices, respectively: $1.45,
$3.35, and $2.65. Find the total cost of the
supplies.