Product Rule for Exponents
Decimal Numbers and Fractions
The Slope of a Line
Adding and Subtracting Square Roots
Factoring the Difference of Two Squares
Linear Systems of Equations with Infinitely Many Solutions
Axis of Symmetry and Vertices
Types of Linear Equations
Sum of Squares
Subtract Fractions with Unlike Denominators
Solving equations
Solving Exponential Equations
Multiplying by 715
Adding and Subtracting Functions
Negative and Fractional Powers
Graphing Linear Equations in Two Variables
Solving Equations That Contain Rational Expressions
Dividing Polynomials
Polynomials in Several Variables
Multiplying Polynomials
Adding and Subtracting Fractions
Solving Absolute Value Inequalities
Simplifying Complex Fractions
Evaluating Rational Functions
Product Rule for Radicals
Domain and Range of a Function
Solving Linear Equations
Dividing Whole Numbers by Fractions
Reducing Rational Expressions to Lowest Terms
Dividing Polynomials
Factoring by Substitution
Dividing a Polynomial by a Monomial
Linear Inequalities
Adding and Subtracting Complex Numbers
What the Vertex Form of a Quadratic can tell you about the graph
Finding x
Adding and Subtracting Fractions with Like Denominators
Adding and Subtracting Fractions
Solving Equations
Graphing Linear Equations
Greatest Common Factors
Exponential Functions
Methods for Solving Quadratic Equations
Factoring Trinomials with Leading Coefficient Not 1
Properties of Natural Logs
Steps for Solving Linear Equations
Multiplying Binomials
Factoring Trinomials
Adding and Subtracting Mixed Numbers with Different Denominators
Simplifying Complex Fractions
Sum or Difference of two Cubes
Multiplying by 858
Graphing Quadratic Equations
Rational Expressions
Graphing Vertical Lines
Dividing Fractions
Multiplying Numers
Multiplying Two Numbers Close to but greater than 100
Factoring Trinomials
Equivalent Fractions
Finding the Least Common Multiple
Factoring Rules
Laws of Exponents
Multiplying Polynomials
Dividing Rational Expressions
Evaluating Polynomial Functions
Equations Involving Rational Exponents
Adding and Subtracting Fractions
Factoring Polynomials by Finding the Greatest Common Factor
Rules for Integral Exponents
Rationalizing the Denominator
Ratios and Rates
Factoring Trinomials
Multiplying Polynomials
Point-Slope Form of a Line
Multiplying Decimals
Solving Right Triangles
Solving Equations with One Radical Term
Adding and Subtracting Mixed Numbers
Adding and Subtracting Polynomials
Division Property of Square and Cube Roots
Inverse Functions
Factoring Trinomials
Writing Percents as Fractions
Solving Equations with One Radical Term
Graphing Systems of Inequalities
Multiplying and Dividing Monomials
Roots - Radicals 2
Solving Linear Systems of Equations
Multiplying and Factoring
Solving Equations with Rational Expressions


Equivalent fractions

If the top and bottom of any fraction are multiplied by the same number, the resulting fraction looks different, but it is equal to the original fraction. Finding equivalent fractions is used to reduce fractions, to find common denominators, and for many other things later on in math.

are all equivalent fractions.


Reducing Fractions

This process is used to express fractions in simpler form. Break down the numerator and denominator into their factors (e.g. 6 breaks down into 3 × 2 ). If any factors appear in both the numerator and denominator, cancel them out.

(a pair of 2’s and a pair of 3’s cancel out)



Consider the following multiplication problem.

The answer needs to be reduced. To reduce it we would spread out the numerator and denominator into their factors and cross out the ones that appear in both numerator and denominator.

Notice that factoring the result undoes the work we just did in multiplying the original numbers. We would have been better off to reduce first and multiply only the factors that survive . Let’s do the same problem again, reducing before multiplying:

A pair of 2’s and a pair of 3’s cancel out, leaving only a 2 in the denominator.

Notice that everything in the numerator cancels out. When this happens, what is left behind is not a 0, but rather a 1. That is because 1 is always a “hidden” factor in every number. It’s not written down unless it is needed. In this problem the numerator 2 × 3 could be thought of as 1 × 2 × 3, so when the 2 and 3 both cancel, what is left is the 1.


Set up the problem as before, cancel the factors that appear in both numerator and denominator (in this case only the 5’s), then multiply the surviving factors.

[Warning: Do not cancel in division problems until you have converted them to multiplication problems!!]