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	Arithmetic Operations with Numerical Fractions
	Multiplying a Polynomial by a Monomial
	Solving Linear Equation
	Solving Linear Equations
	Solving Inequalities
	Solving Compound Inequalities
	Solving Systems of Equations Using Substitution
	Simplifying Fractions 3
	Factoring quadratics
	Special Products
	Writing Fractions as Percents
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Fractions
	Solving Linear Inequalities
	Adding Fractions
	Solving Systems of Equations -
	Exponential Functions
	Integer Exponents
	Example 6
	Dividing Monomials
	Multiplication can Increase or Decrease a Number
	Graphing Horizontal Lines
	Simplification of Expressions Containing only Monomials
	Decimal Numbers
	Negative Numbers
	Factoring
	Subtracting Polynomials
	Adding and Subtracting Fractions
	Powers of i
	Multiplying and Dividing Fractions
	Simplifying Complex Fractions
	Finding the Coordinates of a Point
	Fractions and Decimals
	Rational Expressions
	Solving Equations by Factoring
	Slope of a Line
	Percent Introduced
	Reducing Rational Expressions to Lowest Terms
	The Hyperbola
	Standard Form for the Equation of a Line
	Multiplication by 75
	Solving Quadratic Equations Using the Quadratic Formula
	Raising a Product to a Power
	Solving Equations with Log Terms on Each Side
	Monomial Factors
	Solving Inequalities with Fractions and Parentheses
	Division Property of Square and Cube Roots
	Multiplying Two Numbers Close to but less than 100
	Solving Absolute Value Inequalities
	Equations of Circles
	Percents and Decimals
	Integral Exponents
	Linear Equations - Positive and Negative Slopes
	Multiplying Radicals
	Factoring Special Quadratic Polynomials
	Simplifying Rational Expressions
	Adding and Subtracting Unlike Fractions
	Graphuing Linear Inequalities
	Linear Functions
	Solving Quadratic Equations by Using the Quadratic Formula
	Adding and Subtracting Polynomials
	Adding and Subtracting Functions
	Basic Algebraic Operations and Simplification
	Simplifying Complex Fractions
	Axis of Symmetry and Vertices
	Factoring Polynomials with Four Terms
	Evaluation of Simple Formulas
	Graphing Systems of Equations
	Scientific Notation
	Lines and Equations
	Horizontal and Vertical Lines
	Solving Equations by Factoring
	Solving Systems of Linear Inequalities
	Adding and Subtracting Rational Expressions with Different Denominators
	Adding and Subtracting Fractions
	Solving Linear Equations
	Simple Trinomials as Products of Binomials
	Solving Nonlinear Equations by Factoring
	Solving System of Equations
	Exponential Functions
	Computing the Area of Circles
	The Standard Form of a Quadratic Equation
	The Discriminant
	Dividing Monomials Using the Quotient Rule
	Squaring a Difference
	Changing the Sign of an Exponent
	Adding Fractions
	Powers of Radical Expressions
	Steps for Solving Linear Equations
	Quadratic Expressions Complete Squares
	Fractions 1
	Properties of Negative Exponents
	Factoring Perfect Square Trinomials
	Algebra
	Solving Quadratic Equations Using the Square Root Property
	Dividing Rational Expressions
	Quadratic Equations with Imaginary Solutions
	Factoring Trinomials Using Patterns

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Multiplying and Dividing Fractions

Multiplication

Multiply straight across: Multiply the numerators to get the new numerator. Multiply the denominators to get the new denominator.

Division

The first fraction is said to be “divided by” the second fraction. The fraction you are “dividing by” is called the “divisior.” To divide, “invert” the divisor (turn it upside down), then multiply.

(When a fraction is inverted we call the resulting fraction the “reciprocal” of the original number. Any whole number can be thought of as a fraction with 1 in the denominator. Since , the reciprocal of 2 is .)

Chain Multiplication and Division

There are times (especially in science classes in high school and beyond) when you need to multiply and divide a whole series of fractions and whole numbers. This is actually easy to do. Think of making a shish kabob: a skewer loaded up with chunks of meat, tomatoes, onions, bell pepper, mushrooms, etc. and cooked on a grill. Think of one long fraction bar as a skewer. To multiply a fraction in the list, simply skewer it on. To divide by a fraction, flip it over and skewer it on. Any whole number can be thought of as a fraction with 1 in the denominator, so can treat it like any other fraction. Multiplying by a whole number puts the whole number into the numerator. Dividing by a whole number puts the whole number into the denominator. (Once everything is in place we can ignore the 1’s.)