Chapter 5: Algebraic Expressions and Properties

Algebraic Expressions

100

Identify the terms, coefficients, and constants in the expression: 3+c+e

Terms: (There are 3) 3, c, e

Coefficients: 1, 1

Constants: 3

200

Write the expression using exponents: 

8(p)(p)(p)(p)(f)(f)

8p⁴f²

300

Evaluate the expression when c=4, d=6, and e=10. 

(60/d) - e

0

400

Evaluate the expression when m=5 and n=8.

6m/n-3

6

500

Twenty-five students go to lunch. Pizza costs $3 and sandwiches cost $2. Twelve students buy pizza. What is the total amount of money spent on sandwiches? 

The total cost of sandwiches is $26.00

Writing Expressions

100

Write the phrase as an expression:

3 times a number x 

3x

200

Write the phrase as an expression: 

eleven less than a number d

d-11

300

Write the phrase as an expression. Then, evaluate when x = 2 and y = 10.

12 more than the product of 5 and a number x

22

400

Write the phrase as an expression. Then, evaluate when x = 2 and y = 10. 

15 decreased by the product of a number x and 4

7

500

Write the phrase as an expression. Then, evaluate when x = 2 and y = 10. 

23 less than the quotient of 200 and a number x

77

Properties of Multiplication and Addition

100

Tell which property the statement illustrates:

3+5 = 5+3 

Commutative Property of Addition

200

Tell which property the statement illustrates:

12 + 0 = 12

 

Zero Property of Addition

300

Tell which property the statement illustrates: 

(6)(7) = (7)(6)

Commutative Property of Multiplication

400

(17)(1) = 17

Multiplication Property of One

500

Simplify the expression. Explain each step. 

2+(a+8)

Step One: 2+(8+a) Commutative Property of Addition

Step Two: (2+8)+a Associative Property of Addition

Step Three: 10+a

The Distributive Property

100

Use the distributive property to simplify the expression: 

7(2y+8)

14y+56

200

Use the distributive property to simplify the expression: 

7(3+x+4)

49+7x

or 

7x+49

300

Simplify the expression: 

5(3+m)-7

8+5m

or 

5m+8

400

Simplify the expression:

f+4(f-2) 

5f-8

500

Simplify the expression: 

3.1(p-2.7)

3.1p-8.37

Factoring Expressions

100

Factor the expression using the GCF:

49-14 

7(7-2)

200

Factor the expression using the GCF: 

2x-4

2(x-2)

300

Factor the expression using the GCF: 

8x-10y

2(4x-5y)

400

Factor the expression using the GCF: 

42x+28y

14(3x+2y)

500

Factor the expression using the GCF: 

18a-24b+9c

3(6a-8b+3c)