Ch 1.4 – Properties of Real Numbers

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Transcript Ch 1.4 – Properties of Real Numbers

Ch 1.4 – Properties of Real
Numbers
Vocabulary
1. Equivalent Expressions: two algebraic
expressions that have the same value for
all values of the variable(s)
2. Deductive Reasoning: the process of
reasoning logically from given facts to a
conclusion
3. Counterexample: an example showing a
statement is false
PROPERTY
COMMUTATIVE
ADDITION
a+b=b+a
MULTIPLICATION
ab = ba
ASSOCIATIVE
(a+b)+c = a+(b+c)
(ab)c = a(bc)
IDENTITY
a+0=a
a*1=a
INVERSE
a + (-a) = 0
a * (1/a) = 1;
a0
Multiplicative Properties
• Zero Property:
a*0=0
• Property of -1:
-1 * a = -a
The DISTRIBUTIVE PROPERTY
involves both, addition and
multiplication:
a(b + c) = ab + ac