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Order of Operations

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Chapter 1 15 Glencoe Algebra 1

1. SCHOOLS Jefferson High School has 100 less than 5 times as many students as Taft High School. Write and evaluate an expression to find the number of students at Jefferson High School if Taft High School has 300 students.

2. GEOGRAPHY Guadalupe Peak in Texas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an expression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet.

3. TRANSPORTATION The Plaid Taxi Cab Company charges $1.75 per passenger plus $3.45 per mile for trips less than 10 miles. Write and evaluate an expression to find the cost for Max to take a Plaid taxi 8 miles to the airport.

4. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number π gives the area. Write and evaluate an expression for the area of a circular pizza below. Approximate π as 3.14.

5. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her experiment is five times as large after any six-day period. She observes 20 fruit flies on October 1. Write and evaluate an expression to predict the population of fruit flies Lavania will observe on October 31.

6. CONSUMER SPENDING During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles driven.

a. Write an algebraic expression to represent the amount Devon paid for additional mileage only.

b. Write an algebraic expression to represent the number of miles over 200 miles that Devon drove the rented car.

c. How many miles did Devon drive overall if he paid a total of $174 for the car rental?

7 in.

1-2 Word Problem PracticeOrder of Operations

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Chapter 1 11 Glencoe Algebra 1

Evaluate Numerical Expressions Numerical expressions often contain more than one operation. To evaluate them, use the rules for order of operations shown below.

Order ofOperations

Step 1 Evaluate expressions inside grouping symbols.Step 2 Evaluate all powers.Step 3 Do all multiplication and/or division from left to right.Step 4 Do all addition and/or subtraction from left to right.

Evaluate each expression.

a. 34

34 = 3 ․ 3 ․ 3 ․ 3 Use 3 as a factor 4 times.

= 81 Multiply.

b. 63

63 = 6 ․ 6 ․ 6 Use 6 as a factor 3 times.

= 216 Multiply.

Evaluate each expression.

a. 3[2 + (12 ÷ 3)2]3[2 + (12 ÷ 3)2] = 3(2 + 42) Divide 12 by 3.

= 3(2 + 16) Find 4 squared.

= 3(18) Add 2 and 16.

= 54 Multiply 3 and 18.

b. 3 + 23 −

42 ! 3

= 3 + 8 − 42 ․ 3

Evaluate power in numerator.

= 11 − 42 ․ 3

Add 3 and 8 in the numerator.

= 11 − 16 ․ 3

Evaluate power in denominator.

= 11 − 48

Multiply.

3 + 23

− 42 ․ 3 3 + 23

− 42 ․ 3

ExercisesEvaluate each expression.

1. 52 2. 33 3. 104

4. 122 5. 83 6. 28

7. (8 - 4) ․ 2 8. (12 + 4) ․ 6 9. 10 + 8 ․ 1

10. 15 - 12 ÷ 4 11. 12(20 - 17) - 3 ․ 6 12. 24 ÷ 3 ․ 2 - 32

13. 32 ÷ 3 + 22 ․ 7 - 20 ÷ 5 14. 4 + 32 −

12 + 1 15. 250 ÷ [5(3 ․ 7 + 4)]

16. 2 ․ 42 - 8 ÷ 2 − (5 + 2) ․ 2

17. 4(52) - 4 ․ 3 − 4(4 ․ 5 + 2)

18. 52 - 3 − 20(3) + 2(3)

1-2 Study Guide and InterventionOrder of Operations

Example 1 Example 2

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Chapter 1 12 Glencoe Algebra 1

Evaluate Algebraic Expressions Algebraic expressions may contain more than one operation. Algebraic expressions can be evaluated if the values of the variables are known. First, replace the variables with their values. Then use the order of operations to calculate the value of the resulting numerical expression.

Evaluate x3 + 5(y - 3) if x = 2 and y = 12.x3 + 5(y - 3) = 23 + 5(12 - 3) Replace x with 2 and y with 12.

= 8 + 5(12 - 3) Evaluate 23.

= 8 + 5(9) Subtract 3 from 12.

= 8 + 45 Multiply 5 and 9.

= 53 Add 8 and 45.

The solution is 53.

ExercisesEvaluate each expression if x = 2, y = 3, z = 4, a = 4 −

5 , and b = 3 −

5 .

1. x + 7 2. 3x - 5 3. x + y2

4. x3 + y + z2 5. 6a + 8b 6. 23 - (a + b)

7. y2

− x2 8. 2xyz + 5 9. x(2y + 3z)

10. (10x)2 + 100a 11. 3xy - 4 −

7x 12. a2 + 2b

13. z2 - y2

− x2 14. 6xz + 5xy 15.

(z - y) 2 − x

16. 25ab + y − xz 17. 5 a 2 b − y 18. (z ÷ x)2 + ax

19. ( x − z ) 2 + (

y − z )

2 20. x + z

− y + 2z

21. ( z ÷ x − y ) + ( y ÷ x

− z )

1-2 Study Guide and Intervention (continued)

Order of Operations

Example

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