Over Lesson 1–2

A. A

B. B

C. C

D. D

A. 15B. 11C. 7D. 6

Evaluate the expression c + 8 – a if a = 4 and c = 3.

Evaluate the expression 7a – (2c + b) if a = 4, b = 2, and c = 3.A. 36B. 24C. 22D. 20

You have already evaluated numerical and algebraic expressions. (Lessons 1–1 and 1–2)

• Identify and use properties of addition and multiplication.

• Use properties of addition and multiplication to simplify algebraic expressions.

• properties

• counterexample

• simplify

• deductive reasoning

Find a Counterexample

State whether the following conjecture is true or false. If false, provide a counterexample.

Division of whole numbers is commutative.

Write two division expressions using the Commutative Property, and then check to see whether they are equal.

Answer: The conjecture is false.

12 ÷ 6 = 6 ÷ 12 State the conjecture.?

2 ≠ 0.5 Divide.

We found a counterexample. That is, 12 ÷ 6 ≠ 6 ÷ 12.So, division is not commutative.

A. A

B. B

C. C

D. D

A. true

B. false, 7 – 4 = 7 – 4

C. false, 7 – 4 ≠ 4 – 7

D. false, (7 – 4) – 2 ≠ 7 – (4 – 2)

State whether the following conjecture is true or false. If false, provide a counterexample.Subtraction of whole numbers is commutative.

Identify Properties

A. Name the property shown by the statement.

3 ● 10 ● 2 = 3 ● 2 ● 10

Answer: The order of the numbers changed. This is the Commutative Property of Multiplication.

Identify Properties

B. Name the property shown by the statement.

(2 + 5) + m = 2 + (5 + m)

Answer: The grouping of the numbers and variables changed. This is the Associative Property of Addition.

A. A

B. B

C. C

D. D

A. Commutative Property of Multiplication

B. Associative Property of Multiplication

C. Multiplicative Identity

D. Multiplicative Property of Zero

A. Name the property shown by the statement.

(4 ● 6) ● 2 = 4 ● (6 ● 2)

A. A

B. B

C. C

D. D

A. Commutative Property of Addition

B. Associative Property of Addition

C. Additive Identity

D. Distributive Property

B. Name the property shown by the statement.

12 + 9 = 9 + 12

Simplify Algebraic Expressions

A. Simplify 12 + (x + 18). Label the property for each step

Answer: 30 + x

Simplify.

Associative Property of Addition

Commutative Property of Addition

Simplify Algebraic Expressions

B. Simplify 5 ● (3 ● r). Label the property for each step

Answer: 15r

5 ● (3 ● r) = (5 ● 3)r Associative Property of Multiplication

= 15r Simplify.

A. A

B. B

C. C

D. D

A. 10a

B. 24 + a

C. 2a

D. 24a

A. Simplify (6 ● a) ● 4.

A. A

B. B

C. C

D. D

A. 19 + m

B. 19m

C. 5 + m

D. 12m + 7

B. Simplify 7 + (12 + m).