Download U2L1 – Properties and Identities Examples File

U2L1 – Properties and Identities Examples
Example 1
Using Properties of Addition
Distance This week, you rode in a car for 42 miles, rode a bike for 5
miles, and rode in a bus for 23 miles. Find the total distance.
Solution
The total distance is the sum of the three distances.
Use properties of
addition to group
together distances
that are easy to
add mentally.
42 + 5 + 23 = (42 + 5) + 23
=
(
+
=
+
=
+
(
Use order of operations.
Commutative property
of addition
Associative property
of addition
) + 23
+ 23)
Add
=
Add
Answer: The total distance is
Example 2
and
and
.
.
miles.
Using Properties of Multiplication
Evaluate 4xy when x = -8 and y = 15.
( )( )
= [4(
)]( )
=[
( )]( )
=
[( )( )]
=
( )
Substitute for x and for y.
=
Multiply
4xy = 4
Use order of operations.
Commutative property of multiplication
Associative property of multiplication
Multiply
and
and
.
.
Using Properties to Simplify Variable Expressions
Example 3
Simplify the expression.
a. x + 5 + 2 = (x + 5) + 2 Use order of operations.
= x + (5 + 2)
=x+
property of addition
Add 5 and 2.
b. 3(9y) = (3 • 9)y
=
Example 4
Multiply 3 and 9.
Identifying Properties
Statement
a. (3 + 2) + 4 = 3 + (2 + 4)
b. 0 + b = b
c. 1(-7) = -7
d. cd = dc
property of multiplication
Property Illustrated
Checkpoint
Evaluate the expression when x = 7 and y = 25.
2. 4x 2y
Checkpoint
Simplify the expression.
(4
Checkpoint
3)
Identify the property that the statement illustrates.