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? ESSENTIAL QUESTIONHow can you use the order of operations to evaluate algebraic expressions?

L E S S O N

10.2Evaluating Expressions

Evaluating ExpressionsRecall that an algebraic expression contains one or more variables. You can substitute a number for that variable and then find the value of the expression. This is called evaluating the expression.

Evaluate each expression for the given value of the variable.

x - 9; x = 15

15 - 9

6

When x = 15, x - 9 = 6.

16 __ n ; n = 8

16 __ 8

2

When n = 8, 16 __ n = 2.

0.5y; y = 1.4

0.5(1.4)

0.7

When y = 1.4, 0.5y = 0.7.

6k; k = 1 _ 3

6 ( 1 _ 3 )

2

When k = 1 _ 3 , 6k = 2.

EXAMPLEXAMPLE 1

A

B

C

D

6.EE.1.2c

Evaluate expressions at specific values of their variables.

6.EE.1.2c

Substitute 15 for x.

Subtract.

Substitute 8 for n.

Divide.

Substitute 1.4 for y.

Multiply.

Substitute 1 __ 3 for k.

Multiply.

HINT: Think of 6 as 6 __ 1 .

269Lesson 10.2

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Using the Order of OperationsExpressions may have more than one operation or more than one variable. To evaluate these expressions, substitute the given value for each variable and then use the order of operations.

Evaluate each expression for the given value of the variable.

4(x - 4); x = 7

4(7 - 4)

4(3)

12

When x = 7, 4(x - 4) = 12.

4x - 4; x = 7

4(7) - 4

28 - 4

24

When x = 7, 4x - 4 = 24.

w - x + y; w = 6, x = 5, y = 3

(6) - (5) + (3)

1 + 3

4

When w = 6, x = 5, y = 3, w - x + y = 4.

x 2 - x; x = 9

(9) 2 - (9)

81 - 9

72

When x = 9, x 2 - x = 72.

EXAMPLE 2

A

B

C

D

Evaluate each expression for the given value of the variable.

1. 4x; x = 8 2. 6.5 - n; n = 1.8 3. m __ 6 ; m = 18

YOUR TURN

Is w - x + y equivalent to w - y + x? Explain any

difference in the order the math operations

are performed.

Math TalkMathematical Practices

Is

Math Talk

6.EE.1.2c

Substitute 7 for x.

Substitute 7 for x.

Multiply.

Multiply.

Subtract.

Substitute 6 for w, 5 for x, and 3 for y.

Substitute 9 for each x.

Evaluate exponents.

Subtract.

Subtract.

Add.

Subtract inside the parentheses.

Unit 4270

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Evaluate each expression for n = 5.

4. 3(n + 1) 5. 4 (n - 4) + 14 6. 6n + n 2

Evaluate each expression for a = 3, b = 4, and c = 6.

7. ab - c 8. bc + 5a 9. a 3 - (b + c)

Evaluating Real-World ExpressionsYou can evaluate expressions to solve real-world problems.

The expression 1.8c + 32 gives the temperature in degrees Fahrenheit for a given temperature in degrees Celsius c. Find the temperature in degrees Fahrenheit that is equivalent to 30 °C.

Find the value of c.

c = 30 °C

Substitute the value into the expression.

1.8c + 32

1.8(30) + 32

54 + 32

86

86 °F is equivalent to 30 °C.

10. The expression 6 x 2 gives the surface area of a cube, and the expression x 3 gives the volume of a cube, where x is the length of one side of the cube. Find the surface area and the volume of a cube with a side length of 2 m.

S = m 2 ; V = m 3

11. The expression 60m gives the number of seconds in m minutes. How many seconds are there in 7 minutes?

seconds

YOUR TURN

EXAMPLEXAMPLE 3

STEP 1

STEP 2

YOUR TURN

6.EE.1.2c

Substitute 30 for c.

Multiply.

Add.

271Lesson 10.2

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Guided Practice

Evaluate each expression for the given value(s) of the variable(s). (Examples 1 and 2)

1. x - 7; x = 23 2. 3a - b; a = 4, b = 6

3. 8 _ t ; t = 4 4. 9 + m; m = 1.5

5. 1 _ 2 w + 2; w = 1 _ 9 6. 5(6.2 + z); z = 3.8

7. The table shows the prices for games in Bella’s soccer league. Her parents and grandmother attended a soccer game. How much did they spend if they all went together in one car? (Example 3)

a. Write an expression that represents the cost of one carful of nonstudent soccer fans. Use x as the number of people who rode in the car and attended the game.

is an expression that represents the cost of one carful of nonstudent soccer fans.

b. Since there are three attendees, evaluate the expression 12x + 5 for x = 3.

12( ) + 5 = + 5 =

The family spent to attend the game.

8. Stan wants to add trim all around the edge of a rectangular tablecloth that measures 5 feet long by 7 feet wide. The perimeter of the rectangular tablecloth is twice the length added to twice the width. How much trim does Stan need to buy? (Example 3)

a. Write an expression that represents the perimeter of the rectangular tablecloth. Let l represent the length of the tablecloth and w

represent its width. The expression would be .

b. Evaluate the expression P = 2w + 2l for l = 5 and w = 7.

2( ) + 2( ) = 14 + =

Stan bought of trim to sew onto the tablecloth.

Women’s Soccer Game Prices

Student tickets $6

Nonstudent tickets $12

Parking $5

9. How do you know the correct order in which to evaluate algebraic expressions?

ESSENTIAL QUESTION CHECK-IN???

Unit 4272

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Independent Practice10.2

Name Class Date

10. The table shows ticket prices at the Movie 16 theater. Let a represent the number of adult tickets, c the number of children’s tickets, and s the number of senior citizen tickets.

Movie 16 Ticket Prices

Adults $8.75

Children $6.50

Seniors $6.50

a. Write an expression for the total cost of the three types of tickets.

b. The Andrews family bought 2 adult tickets, 3 children’s tickets, and 1 senior ticket. Evaluate your expression in part a to find the total cost of the tickets.

c. The Spencer family bought 4 adult tickets and 2 children’s tickets. Did they spend the same as the Andrews family? Explain.

11. The area of a triangular sail is given by the expression 1 _ 2 bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?

A = in. 2

12. Ramon wants to balance his checking account. He has $2,340 in the account. He writes a check for $140. He deposits a check for $268. How much does Ramon have left

in his checking account?

13. Look for a Pattern Evaluate the expression 6x - x 2 for x = 0, 1, 2, 3, 4, 5, and 6. Use your results to fill in the table and describe any pattern that you see.

x 0 1 2 3 4 5 6

6x - x 2

14. The kinetic energy (in joules) of a moving object can be calculated from the expression 1 _ 2 m v 2 , where m is the mass of the object in kilograms and v is its speed in meters per second. Find the kinetic energy of a 0.145-kg baseball that is thrown at a speed of 40 meters per second.

E = joules

15. The area of a square is given by x2, where x is the length of one side. Mary’s original garden was in the shape of a square. She has decided to double the area of her garden. Write an expression that represents the area of Mary’s new garden. Evaluate the expression if the side length of Mary’s original garden was 8 feet.

6.EE.1.2c

273Lesson 10.2

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Work Area

16. The volume of a pyramid with a square base is given by the expression 1 _ 3 s 2 h, where s is the length of a side of the base and h is the height. Find the volume of a pyramid with a square base of side length 24 feet and a height of 30 feet.

17. Draw Conclusions Consider the expressions 3x(x - 2) + 2 and 2x 2 + 3x - 12.

a. Evaluate each expression for x = 2 and for x = 7. Based on your results, do you know whether the two expressions are equivalent? Explain.

b. Evaluate each expression for x = 5. Based on your results, do you know whether the two expressions are equivalent? Explain.

18. Critique Reasoning Marjorie evaluated the expression 3x + 2 for x = 5 as shown:

3x + 2 = 35 + 2 = 37

What was Marjorie’s mistake? What is the correct value of 3x + 2 for x = 5?

FOCUS ON HIGHER ORDER THINKING

Unit 4274

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