Divide.

Evaluate power.27 32 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 32 2 3.–

There are no grouping symbols, so go to Step 2.STEP 1

Evaluate powers.STEP 2

STEP 4Add and subtract from left to right.

6 – 3 = 3

EXAMPLE 1

Subtract.

ANSWER

The value of the expression 27 32 2 – 3 is 3.

Evaluate expressions

GUIDED PRACTICE for Example 1

1. Evaluate the expression 20 – 42

ANSWER

1. 4

2. Evaluate the expression 2 32 + 4

ANSWER

2. 22

3. Evaluate the expression 32 23 + 6

ANSWER

3. 10

GUIDED PRACTICE for Example 1

4. Evaluate the expression 15 + 62 – 4

ANSWER

4. 47

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. 24 – (32 + 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]

EXAMPLE 3 Evaluate an algebraic expression

Evaluate the expression when x = 4.

9x3(x + 2)

Substitute 4 for x.

Add within parentheses.

1836= Multiply.

= 2 Divide.

= 3(4 + 2) 9 4

3 6 9 4

=

GUIDED PRACTICE for Examples 2 and 3

Evaluate the expression.

5. 4(3 + 9) = 48

6. 3(8 – 22) = 12

7. 2[( 9 + 3) 4 ] = 6

GUIDED PRACTICE for Examples 2 and 3

Evaluate the expression when y = 8.

= 61y2 – 38.

= 312 – y – 19.

= 910y + 1 y + 1

10.

Standardized Test Practice

EXAMPLE 4

Standardized Test Practice

EXAMPLE 4

SOLUTION

Substitute 1.25 for j and 2 for s.

= 12(3.75 + 4) + 30 Multiply withinparentheses.

= 93 + 30 Multiply.

= 123 Add.

The sponsor’s cost is $123.The correct answer is B. .A B C D

ANSWER

= 12(7.75) + 30 Add within parentheses.

= 12(3 1.25 + 2 2) + 3012(3j +2s) + 30

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 – m2

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 + x2

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.

EXAMPLE 2 Write an expression

ANSWER

The expression 8 – l represents the length (in feet) of the remaining piece.

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 2Amount

in jarNumber

of people

a 6

EXAMPLE 3 Use a verbal model to write an expression

ANSWER

An expression that represents each person’s share (in dollars) is .a

6

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

lp

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.

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

SOLUTION

EXAMPLE 5 Solve a multi-step problem

TrainingFor 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.

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 2Write a verbal model and then an expression.Let m be the number of minutes you walk.

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