Chapter 3: Algebraic Expressions

Parts of an Expression

100

What is constant in the following expression:

2x + 4 

4

200

What is the coefficient in the following expression:

15 + 5m

5

300

Name all the coefficients in the following expression:

2y + 4 + x

2 and 1

400

List the terms in the following expression:

5y - 3x + 2

5y, -3x, 2

500

What are the coefficients in the following expression:

10x² - 7y + 8 + x²

10, -7, 1

Properties

100

What property is illustrated by the statement?

3 + 2 = 2 + 3

Commutative Property

200

Factor using the GCF:

16 + 12

4(4 + 3)

300

What property is illustrated by the statement?

2 + (3 + 4) = (2 + 3) + 4

Associative Property

400

Factor using the GCF:

15x + 5

5(3x+1)

500

What property is illustrated by the statement?

3(2x - 5) = 6x - 15

Distributive

Evaluating Expressions

100

Evaluate 3x for x = 2

3(2)

6

200

Evaluate 5y + 3x for y=2 and x=4

5(2) + 3(4)

10 + 12

22

300

Evaluate 3x - 4 for x=1.4

3(1.4) - 4

4.2 - 4 

0.2

400

Evaluate 15 - 6x + y for x= 1/2 and y=5

15 - 6(1/2) + 5

15 - 3 + 5

12 + 5

17

500

Evaluate x + 2y² - 3y where x=6 and y=4

6 + 2(4)² - 3(4)

6 + 2(16) - 3(4)

6 + 32 - 12

38 - 12

26

Simplifying Expressions

100

Simplify:

3x + 5x + 3

8x + 3

200

Simplify:

2(x + 3)

2x + 6

300

5(8m) + 3m

40m + 3m 

43m

400

2 + 4(2y + 3)

2 + 8y + 12

8y + 2 + 12

8y + 14

500

1 + 4(2x - 4) + 20

1 + 8x - 16 + 20

1 + 8x + 20 - 16

1 + 8x + 4

8x + 1 + 4

8x + 5

Mystery!

100

Write the following phrase as an algebraic expression:

The sum of 3 and a number w

3 + w

200

Write the following phrase as an expression:

The product of 3 and a number x plus 4

3x+4

300

You want to buy a pizza. The pizza costs $10, and each topping costs $0.75. Write an expression to represent the total cost of one pizza with t number of toppings. 

10 + 0.75t

400

The expression 15x + 10y represents the cost for x adults and y children to see a play. Use the expression to find the cost for 3 adults and 2 children to see the play. 

15(3) + 10(2)

45 + 20

$65

500

For the school play, Mr. Altmann spent $120 on set design, $8 on a T-Shirt for each cast member, and $40 on ticket printing.  If there are 'm' number of cast members, write a simplified expression showing how much Mr. Altmann spent in total.

120 + 8m + 40   (not final answer)

160 + 8m or 8m + 160 (simplified answer)