1. 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.

2. Using a Commutative Property Example 1 5127 = Substitute known values. 7125 = Commutative property of multiplication 607 = 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.

3. Using a Commutative Property Example 2 +45 – 5416– 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 –

4. Guided Practice 1. for Examples 1 and 2 ANSWER yes Use a commutative property to evaluate the expression. 2. 254 () –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?

5. Guided Practice for Examples 1 and 2 ANSWER 14 Use a commutative property to evaluate the expression. 3. +34 – 137 – 4. +642737 – ANSWER 54