1. EXAMPLE 1 Using the Commutative Property SOLUTION Write a verbal model to find the total distance you can cycle in 5 days. 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?

2. EXAMPLE 1 Using the Commutative Property Substitute known values. Commutative property of multiplication Multiply. 60 7= 12 5 7 = 420= 12 7 5=

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

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

5. GUIDED PRACTICE Write a verbal model to find the total distance you can cycle in 6 days. SOLUTION 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?

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

7. GUIDED PRACTICE The unit for the result is miles. 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. for Examples 1 and 2 days = miles miles hour hours day

8. GUIDED PRACTICE Use the commutative property to evaluate the expression. Commutative property of multiplication Multiply 4 and 25. Multiply. for Examples 1 and 2 4 (–9) 252. 100 (–9)= 4 25 (–9) = –900=

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

10. GUIDED PRACTICE for Examples 1 and 2 4 7 3 7 + + 8= 7 7 = 1 + 8= 4.4. 3 7 8 +8 + 4 7 + 3 7 = + 8 + 4 7 Use the commutative property to evaluate the expression. Commutative property of addition Associative property of addition Add inside grouping symbols. Add. = 9