# Study Guide for Algebra Test 2

Test 2 is on October 20 (Friday) in class. This test will cover section 3.3, chapter 5 and
chapter 6 of the book. The following are suggested problems. In addition, you should review
the homework as signments and your notes from class.

Material covered and problems suggested.

§3.3: Ordering and exponents . Know the properties of exponents .

Problems: Set A, page 141: 3, 7, 11.

§5.1: Divisors, factors, multiples. Tests for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11. Prime
and composite numbers, know how to find the prime factorization of a whole number. Fundamental
Theorem of Arithmetic . Prime factor test (how do you de termine whether a given
number is prime?).

Problems: Review the hw problems from this section.

§5.2: Know how to find GCF (a, b): Using the definition, using the prime factorization
method, using the Euclidean algorithm. Know how to find LCM (a, b): using the definition,
using the prime factorization method , using that LCM(a, b) · GCF(a, b) = a · b.
Problems: Review the hw problems from this section.

§6.1: Fractions, models for introducing fractions, equivalent fractions (when are two fractions
equal?), order of fractions ( if and only if a·d < c·b), density property of fractions
(know how to find a fraction between any two given fractions, how many fractions are there
between two given fractions?).

Problems: Review the hw problems from this section.

§6.2: Addition of fractions and its properties (closure property, commutative property,
associative property, additive identity property). Subtraction of fractions . Mental math and

Problems: Review the hw problems from this section.

§6.3: Multiplication of fractions and its properties (closure property, commutative property,
associative property, multiplicative identity property, distributive property over addition
and subtraction of fractions, multiplicative inverse ( or reciprocal ) of a fraction). Division of
fractions.

Problems: Set A, p. 269: 2, 4, 8g, 10, 15, 16, 20, 22.

Do the following computations, leaving your answer as a fraction in simplest form . Justify
each step by citing the property (or definition) used.

Simplify the following complex fractions :

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