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Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
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Adding and Subtracting Fractions

Addition (when the denominators are the same)

Add the numerators. Keep the same denominator.


Subtraction (when the denominators are the same)

Subtract the numerators. Keep the same denominator.



Common Denominators

Since we can change the form of a fraction by multiplying the top and bottom by the same thing, we can force any two fractions to have the same denominator. The trick is to give both denominators all the same factors.

Note that if the denominators we want to match are 3 and 5, we can multiply 3 by 5 and 5 by 3 to convert both fractions to 15ths. (We actually didn’t change the fractions in the process, because we multiplied both top and bottom of each fraction by the same number in each case. That’s what keeps it all “legal.”)


Least Common Denominators

If two denominators have some factors in common, simply multiplying the denominators together will give you needlessly big numbers that have to be reduced later. Instead, spread out and compare the factors of both denominators and multiply each denominator by the factors it lacks.

Notice that both denominators contain 2 × 2 (marked in blue), but one has an extra 3 and the other has two more extra 2’s. If the first fraction is multiplied (top and bottom) by 4 ( = 2 × 2 ) and the second fraction is multiplied (top and bottom) by 3, all the factors in both denominators will match.

The little bit of extra work breaking the denominators into factors at this stage is easier than multiplying 12 by 16 and 16 by 12 (= 192), because you would then have to turn right around and reduce the resulting fractions which would by then involve much larger numbers.

Addition or Subtraction when the denominators are NOT the same

Convert the fractions to equivalent fractions having the same denominator, then add or subtract the numerators as before.

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