Algebra I. Lesson 1-4, last page

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Algebra I. Lesson 1
Definitions and Properties (Grades 9-12)

Pre-Test		Post-Test
Q&A	Basic Properties	Q&A

Instruction 1-4

Variables and Expressions | Open Sentences | Distributive and Additive Identity, Multiplicative Identity Property and Properties of Equality | Commutative and Associative Property | Summary

COMMUTATIVE AND ASSOCIATIVE PROPERTY

CA GR7 AF 1.3, CA HS Algebra 25.2

Commutative Properties

When we add or multiply two numbers, the order is not important. For example, 3 + 4 is the same as 4 + 3. Or, 4 × 9 is the same as 9 × 4. We describe these properties as below.

Associative Properties

Grouping of numbers is not important in addition or multiplication. For example in 4 + 7 + 9, adding the result of 4 + 7 to 9 is the same as adding 4 to the result of 7 + 9.

Similarly, in multiplication, when finding 5 × 12 × 7, the product of 5 and the result of 12 × 7 is the same as the product of (5 × 12) and 7.

Example.

a. 4 + (90 + 12) = (4 + 90) + 12

b. 23 × (31 × 7) = (23 × 31) × 7

Practice 5 (A Comprehensive Problem).In table below, determine the property used in each row.

EQUALITY	PROPERTY
a + 4 = 4 + a
m × 23 = 23 × m
34 + (x + n) = (34 + x ) + n
2 × (x + 19) = (2 × x ) × 19
7(m + n) = 7m + 7n

Video Instruction
*Availability of video links may vary. eTAP has no control of these materials.

Commutative & Associative Properties 9.2 [4:46]

Using Commutative & Associative Properties 9.2 [3:08]

Math Made Easy: Multiplication -- Commutative and Associative Properties [7:21]

for Students, Parents and Teachers

Now let's do Practice Exercise 1-4 (top).

Summary

Variable. A variable is used to denote an unknown quantity, either one whose measure is changing in different situations; or one whose value is a constant.

Expression. Any combination of variables and numbers using different operations is called an algebraic expression or simply an expression.

Open Sentence. An expression, which may be either true or false is called an open sentence.

Distributive Property of Multiplication over Addition. Let a, b, and c be real numbers. Then a(b + c) = ab + bc.

Additive Identity. Let a be any real number. Then a + 0 = 0 + a = a.

Multiplicative Identity. Let a be any real number. Then a × 1 = 1 × a = a.

Symmetric Property. Let a and b be two real numbers. If a = b then b = a.

Reflexive Property. Let a be a real number. Then a = a.

Transitive Property. Let a, b, and c be real numbers. If a = b and b = c, then a = c.

Commutative Property of Addition. Let a and b be real numbers. Then a + b = b + a.

Commutative Property of Multiplication. Let a and b be real numbers. Then a x b = b x a.

Associative Property of Addition. Let a, b, and c be real numbers. Then a + (b + c) = (a + b) + c.

Associative Property of Multiplication. Let a, b, and c be real numbers.
Then a × (b × c) = (a × b) × c

Next Page: Problems (top)