Algebra Tutorials!
   
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Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Inequalities
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Fractions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Powers
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Slope
Angles and Degree Measure
   
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Fractions

A. Parts of a fraction:

The numerator represents the number of parts of the unit being used.

The denominator represents the total number of parts within the one whole unit.

B. Types of fractions:

1. Proper fractions: fractions where the numerator is less than the denominator.

Examples include:

2. Improper fractions: fractions where the numerator is greater than the denominator.

Examples include:

3. Mixed number fractions: numbers that contain a whole number and a fraction.

Examples include:

4. Fractions in lowest terms: fractions where the numerator and denominator cannot be divided by a common number.

Examples include:

Examples of fractions that are not in lowest terms include:

a. because 5 and 10 are both divisible by 5 to become

b. because 5 and 10 are both divisible by 5 to become

Operations with fractions:

When ADDING or SUBTRACTING FRACTIONS, all denominators have to be the same number. If all denominators are not the same, you must find the lowest common denominator. The lowest common denominator is the smallest number that all the denominators will divide into evenly. After you find the common denominator, you must change each fraction into an equivalent fraction. An equivalent fraction has the same value as the original fraction but accommodates the new denominator. Once you find the common denominator and change the fractions into equivalent fractions, ADD or SUBTRACT the numerators, but do not add or subtract the denominators. Keep the common denominator as part of the answer. Reduce the answer to its lowest term if needed.

ADD:

Find the lowest common denominator, lcd.

15 is the lcd. Make the equivalent fractions. 3 will divide into 15

5 times. 5 times 2 = 10…. 5 will divide into 15

3 times. 3 times 4 = 12.

Add the numerators and keep the denominator. Reduce answer

to its lowest term.

When multiplying and dividing fractions, it is not necessary to find a common denominator. When multiplying fractions, multiply numerators together then multiply denominators together. Simplify the resulting fraction to its lowest term.

Ex:

Note: Cancellation may be used if any numerator will simplify with any denominator.

Ex: the numerator 2 will divide into itself 1 time and into the denominator 8 times.

Ex:

Divide: When dividing fractions, invert the second fraction and multiply.

Ex:

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