Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

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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.


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.


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.


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