1. EXAMPLE 1
Using the Commutative Property
Tour Biking You are going on a 400 mile bike trip. You plan to cycle at an average speed of 12 miles per hour for 7 hours a day. Can you complete the trip in 5 days?
SOLUTION
Write a verbal model to find the total distance you can cycle in 5 days.

2. Using the Commutative Property
EXAMPLE 1
Using the Commutative Property =
Substitute known values. =
Commutative property of multiplication =
Multiply.
420 =
Multiply.

3. EXAMPLE 1
Using the Commutative Property
The unit for the result is miles.
days = miles
miles
hour
hours
day
Because 400 miles is less than the 420 miles you can cycle in 5 days, you can complete the trip in 5 days.
Answer

4. Using the Commutative Property
EXAMPLE 2
Using the Commutative Property
– – 16
= – (–16 )
Change subtraction to addition.
= –54 + (–16) + 35
Commutative property
of addition
= –
Add –54 and –16.
= –35
Add –70 and 35.

5. GUIDED PRACTICE
for Examples 1 and 2
1. What If? Suppose in Example 1 you only want to bike for 6 hours a day at an average speed of 14 miles per hour. Can you complete the trip in 6 days?
SOLUTION
Write a verbal model to find the total distance you can cycle in 6 days.

6. GUIDED PRACTICE for Examples 1 and 2 14 6 6 = 14 6 6 = 84 6 = 504 = =
Substitute known values. =
Commutative property of multiplication =
Multiply.
504 =
Multiply.

7. GUIDED PRACTICE
for Examples 1 and 2
The unit for the result is miles.
days = miles
miles
hour
hours
day
Answer
Yes , Because 400 miles is less than the 504 miles you
can cycle in 6 days, you can complete the trip in 6 days.

8. Use the commutative property to evaluate the expression.
GUIDED PRACTICE
for Examples 1 and 2
Use the commutative property to evaluate the expression.
4 (–9) 25 2.
(–9) =
Commutative property of multiplication
100 (–9) =
Multiply 4 and 25.
–900 =
Multiply.

9. Use the commutative property to evaluate the expression.
GUIDED PRACTICE
for Examples 1 and 2
Use the commutative property to evaluate the expression.
3. – –7
= – (–7)
Change subtraction to addition.
= –13 + (–7) + 34
Commutative property of addition
= –
Add –13 and –7.
= 14
Add –20 and 34.

10. Use the commutative property to evaluate the expression.
GUIDED PRACTICE
for Examples 1 and 2
Use the commutative property to evaluate the expression. 4. 3 7
8 + 4 + 3 7 =
+ 8 + 4
Commutative property of addition 4 7 3 +
+ 8 =
Associative property of addition 7
+ 8 =
Add inside grouping symbols.
1 + 8 =
Add.
= 9

11. Using the Associative Property
EXAMPLE 3
Using the Associative Property 3 5 + 2 = 3 5 + 2
Associative property
of addition 5 + 3 =
Add fractions.
Write as one. 5
1 + 3 = 4 =
Add.

12. Using the Associative Property
EXAMPLE 4
Using the Associative Property
5 (11 2)
5 (2 11) =
Commutative property of multiplication
(5 2) 11 =
Associative property of multiplication
10 11 =
Multiply inside grouping symbols.
110 =
Multiply.

13. Use properties to evaluate the expression.
GUIDED PRACTICE
for Examples 3 and 4
Use properties to evaluate the expression.
(– )
= 18 + (12 + (–34))
Commutative property of addition
= ( ) + (–34)
Associative property of addition
= 30 + (–34)
Add inside grouping symbols.
= –4
Add.

14. Use properties to evaluate the expression.
GUIDED PRACTICE
for Examples 3 and 4
Use properties to evaluate the expression. 4 5
8 + 1 + 4 5 =
+ 8 + 1
Commutative property of addition 1 5 4 + =
+ 8
Associative property of addition 5
+ 8 =
Add inside grouping symbols.
1 + 8 =
Add. 9 =

15. Use properties to evaluate the expression.
GUIDED PRACTICE
for Examples 3 and 4
Use properties to evaluate the expression.
12 ( ) 1 12 = 12 6) ( 1
Commutative property of multiplication = 12 6 1 ( )
Associative property of multiplication = 1 6
Multiply inside grouping symbols. = 6
Multiply.

16. Use properties to evaluate the expression.
GUIDED PRACTICE
for Examples 3 and 4
Use properties to evaluate the expression. 6 5
( ) = 3) ( 5 6
Commutative property of multiplication = ( 5 6 ) 3
Associative property of multiplication = 1 3
Multiply inside grouping symbols. = 3
Multiply.

17. GUIDED PRACTICE
for Examples 3 and 4
Evaluate the expression using mental math.
4 ( ) 1 4 = 23
–4 ( ) 46 =
– 4600
–21 –
(–29) =
(–6 ) 10 1 ( ) = –6