Upload
geoffrey-horn
View
215
Download
0
Tags:
Embed Size (px)
Citation preview
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).