Download Lesson 2-5

Name_____________________________________ Class____________________________ Date________________
Lesson 2-5
Properties of Numbers
1
Identify properties
NAEP 2005 Strand: Geometry
Topic: Mathematical Reasoning
2
Use deductive reasoning
Local Standards: ____________________________________
Lesson Objectives
Properties of Real Numbers
For every real number a, b, and c,
Commutative Property of Addition
Commutative Property of Multiplication
Example 3 7 Example 3 ? 7 +
Example (6 4) 5 (
Associative Property of Multiplication
)
Example (6 ? 4) ? 5 ?
(
?
Identity Property of Addition
Identity Property of Multiplication
Example 9 0 Example 6 ? 1 Inverse Property of Addition
For every a, there is an additive inverse
Example 5 (5) such that
.
Inverse Property of Multiplication
For every a (a 0), there is a multiplicative inverse 1a such that
Example 5 ?
)
.
1
Distributive Property
a(b c) Example 5(4 2) a(b c) Example 5(4 2) Multiplication Property of Zero
For every real number n,
Example 35 ? 0 Multiplication Property of –1
.
For every real number n,
.
Example 1 ? (5)
Deductive reasoning is
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Algebra 1 Lesson 2-5
Daily Notetaking Guide
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Associative Property of Addition
?
All rights reserved.
Vocabulary and Key Concepts.
Name_____________________________________ Class____________________________ Date ________________
Examples.
1 Identifying Properties Name the property each equation illustrates. Explain.
a. 3 ? a a ? 3
, because
b. p ? 0 0
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, because
c. 6 (6) 0
, because
()
d. z 1z 1 for z 0
, because
2 Shopping Suppose you buy a shirt for $14.85, a pair of pants for $21.95, and a
pair of shoes for $25.15. Find the total amount you spent.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
14.85 21.95 25.15 14.85 (
of Addition
)
Property
Property
of Addition
Add within parentheses first.
Simplify.
The total amount you spent was $
.
3 Justifying Steps Simplify 3x 4(x 8). Justify each step.
3x 4(x 8) 3x (
Property
)x 32
Property
x 32
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Daily Notetaking Guide
Subtract.
of Multiplication
Algebra 1 Lesson 2-5
31
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Quick Check.
1. Name the property that each equation illustrates. Explain.
a. 1m m
b. (3 4) 5 –3 (4 5)
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c. 3(8 ? 0) (3 ? 8)0
d. 2 02
e. np pn
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f. p q q p
2. At the supermarket, you buy a package of cheese for $2.50, a loaf of bread
for $2.15, a cucumber for $.65, and some tomatoes for $3.50. Find the total
cost of the groceries.
3. Simplify each expression. Justify each step.
a. 5a 6 a
b. 2(3t 1) 2
32
Algebra 1 Lesson 2-5
Daily Notetaking Guide