1. Divide. Evaluate power. 27 3 2 2 – 3 = 27 9 2 – 3 EXAMPLE 1 27 9 2 – 3 = 3 2 – 3 3 2 – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from left to right. STEP 3 Evaluate the expression 27 3 2 2 3. – There are no grouping symbols, so go to Step 2. STEP 1 Evaluate powers. STEP 2

2. STEP 4 Add and subtract from left to right. 6 – 3 = 3 EXAMPLE 1 Subtract. ANSWER The value of the expression 27 3 2 2 – 3 is 3. Evaluate expressions

3. GUIDED PRACTICE for Example 1 1. Evaluate the expression 20 – 4 2 ANSWER 1. 4 2. Evaluate the expression 2 3 2 + 4 ANSWER 2. 22 3. Evaluate the expression 32 2 3 + 6 ANSWER 3. 10

4. GUIDED PRACTICE for Example 1 4. Evaluate the expression 15 + 6 2 – 4 ANSWER 4. 47

5. 24 – (9 + 1) = 2[9] EXAMPLE 2 Evaluate expressions with grouping symbols Evaluate the expression. a. 7(13 – 8) = = 35 Subtract within parentheses. Multiply. b.b. 24 – (3 2 + 1) = Evaluate power. =24 – 10 Add within parentheses. = 14 Subtract. c. 2[30 – (8 + 13)] = Add within parentheses. Subtract within brackets. = 18 Multiply. 7(5) 2[30 – 21]

6. EXAMPLE 3 Evaluate an algebraic expression Evaluate the expression when x = 4. 9x 3(x + 2) Substitute 4 for x. Add within parentheses. 18 36 = Multiply. =2 Divide. = 3(4 + 2) 9 4 3 6 9 4 =

7. GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression. 5. 4(3 + 9) = 48 6.6. 3(8 – 2 2 ) = 12 7. 2[( 9 + 3) 4 ] = 6

8. GUIDED PRACTICE for Examples 2 and 3 Evaluate the expression when y = 8. = 61 y 2 – 38. = 3 12 – y – 19. = 9 10y + 1 y + 1 10.

9. Standardized Test Practice EXAMPLE 4

10. Standardized Test Practice EXAMPLE 4 SOLUTION Substitute 1.25 for j and 2 for s. = 12(3.75 + 4) + 30 Multiply within parentheses. = 93 + 30 Multiply. = 123 Add. The sponsor’s cost is $123.The correct answer is B.. AB C D ANSWER = 12(7.75) + 30 Add within parentheses. = 12(3 1.25 + 2 2) + 30 12(3j +2s) + 30

11. EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the quantity 6 times a number n b. 3 times the sum of 7 and a number y c. The difference of 22 and the square of a number m 6n – 4 3(7 + y) 22 – m 2

12. GUIDED PRACTICE for Example 1 1. Translate the phrase “the quotient when the quantity 10 plus a number x is divided by 2 ” into an expression. ANSWER 1. Expression 10 + x 2

13. SOLUTION Cutting A Ribbon EXAMPLE 2 Write an expression A piece of ribbon l feet long is cut from a ribbon 8 feet long. Write an expression for the length (in feet) of the remaining piece. Draw a diagram and use a specific case to help you write the expression. Suppose the piece cut is 2 feet long. Suppose the piece cut is L feet long. The remaining piece is ( 8 – 2 ) feet long. The remaining piece is ( 8 – l ) feet long.

14. EXAMPLE 2 Write an expression ANSWER The expression 8 – l represents the length (in feet) of the remaining piece.

15. Write a verbal model. SOLUTION You work with 5 other people at an ice cream stand. All the workers put their tips into a jar and share the amount in the jar equally at the end of the day. Write an expression for each person’s share (in dollars) of the tips. Tips EXAMPLE 3 Use a verbal model to write an expression Translate the verbal model into an algebraic expression. Let a represent the amount (in dollars) in the jar. STEP 1 STEP 2 Amount in jar Number of people  a  6

16. EXAMPLE 3 Use a verbal model to write an expression ANSWER An expression that represents each person’s share (in dollars) is. a 6

17. GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 2, suppose that you cut the original ribbon into p pieces of equal length. Write an expression that represents the length (in feet) of each piece. ANSWER l p

18. GUIDED PRACTICE for Examples 2 and 3 WHAT IF? In Example 3, suppose that each of the 6 workers contributes an equal amount for an after- work celebration. Write an expression that represents the total amount (in dollars) contributed. ANSWER 6d, where d represents the amount contributed by each worker.

19. EXAMPLE 4 Find a unit rate A car travels 120 miles in 2 hours. Find the unit rate in feet per second. The unit rate is 88 feet per second. ANSWER

20. SOLUTION EXAMPLE 5 Solve a multi-step problem Training For a training program, each day you run a given distance and then walk to cool down. One day you run 2 miles and then walk for 20 minutes at a rate of 0.1 mile per 100 seconds. What total distance do you cover? STEP 1 Convert your walking rate to miles per minute.

21. EXAMPLE 5 Solve a multi-step problem Use unit analysis to check that the expression 2 + 0.06m is reasonable. Because the units are miles, the expression is reasonable. STEP 2 Write a verbal model and then an expression. Let m be the number of minutes you walk.

22. EXAMPLE 5 Solve a multi-step problem Evaluate the expression when m = 20. 2 + 0.06(20) = 3.2 ANSWER You cover a total distance of 3.2 miles. STEP 3