Using a Commutative Property

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 per day. Can you complete the trip in 5 days?

TOUR BIKING

Example 1

SOLUTION

Write a verbal model to find the total distance you can cycle in 5 days.

Using a Commutative PropertyExample 1

5••12 7= Substitute known values.

7••12 5= Commutative property of multiplication

•60 7= Multiply 12 and 5.

420= Multiply 60 and 7.

ANSWER

Because 400 miles is less than the 420 miles you can cycle in 5 days, you can complete the trip in 5 days.

Using a Commutative PropertyExample 2

+ 45–54 16– Change subtraction to addition.

= ( )–54 –16+ 45 +

16 Commutative property of addition

= –54 + + 45( )–

Add 54 and 16.= –70 + 45 – –

Add 70 and 45.= –25 –

Guided Practice

1.

for Examples 1 and 2

ANSWER yes

Use a commutative property to evaluate the expression.

2. 25••4 ( )–9 ANSWER –900

WHAT IF?In Example 1, suppose 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?

Guided Practice for Examples 1 and 2

ANSWER 14

Use a commutative property to evaluate the expression.

3. + 34–13 7–

4. + 6427 37– ANSWER 54