Algebra Tutorials!  
Monday 24th of June
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Numbers, Factors, and Reducing Fractions to Lowest Terms

1. Prime Number: A prime number is any whole number greater than 1 that has exactly two divisors- itself and 1. (A number is a divisor of another number if it divides that number without a remainder.)

Ex: List the prime numbers that are smaller than 20.

1, 3, 5, 7, 11, 13, 17, 19

2. Writing the prime factorization of a number: To write the prime factorization of a number, write the number as a product of prime numbers.

Ex: Which of the following represents a prime factorization?

a. 12 = 6•2

b. 12 = 22 •3

b represents a prime factorization of 12.

You can use a factor tree to find a prime factorization. Express the given number as the product of two numbers. Then express each of those as the product of two numbers. Continue this process until the numbers no longer factor--you will then have the prime factors.

Note: The following divisibility tests will help you in deciding what numbers are factors of the given number.

Divisibility test for 2: A given number is divisible by 2 if it ends in an even digit.

Divisibility test for 3: A given number is divisible by 3 if the sum of the digits in the number is divisible by 3.

Divisibility test for 5: A given number is divisible by 5 if the last digit is 5 or 0.


3. Reducing a fraction to lowest terms: A fraction is said to be in lowest terms if the numerator and denominator have no common factors other than 1. To reduce a fraction to lowest terms, divide the numerator and the denominator by all of the factors that they have in common. If you do not know the common factors, write the prime factorization of the numerator and denominator, then divide out the common factors.

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