Free Algebra
Miscellaneous Equations
Operations with Fractions
Undefined Rational Expressions
Writing Equations for Lines Using Sequences
Intersections of Lines and Conics
Graphing Linear Equations
Solving Equations with Log Terms and Other Terms
Quadratic Expresions - Complete Squares
Adding and Subtracting Fractions with Like Denominators
Multiplying a Fraction by a Whole Number
Solving Equations with Log Terms and Other Terms
Solving Quadratic Equations by Factoring
Locating the Solutions of the Quadratic Equation
Properties of Exponents
Solving Equations with Log Terms on Each Side
Graphs of Trigonometric Functions
Estimating Products and Quotients of Mixed Numbers
The circle
Adding Polynomials
Adding Fractions with Unlike Denominators
Factoring Polynomials
Linear Equations
Powers of Ten
Straight Lines
Dividing With Fractions
Multiplication Property of Equality
Rationalizing Denominators
Multiplying And Dividing Fractions
Distance Between Points on a Number Line
Solving Proportions Using Cross Multiplication
Using the Quadratic Formula
Scientific Notation
Imaginary Numbers
Values of Symbols for Which Fractions are Undefined
Graphing Equations in Three Variables
Writing Fractions as Decimals
Solving an Equation with Two Radical Terms
Solving Linear Systems of Equations by Elimination
Factoring Trinomials
Positive Rational Exponents
Adding and Subtracting Fractions
Negative Integer Exponents
Rise and Run
Multiplying Square Roots
Multiplying Polynomials
Solving Systems of Linear Inequalities
Multiplication Property of Radicals
A Quadratic within a Quadratic
Graphing a Linear Equation
Calculations with Hundreds and Thousands
Multiplication Property of Square and Cube  Roots
Solving Equations with One Log Term
The Cartesian Coordinate Plane
Equivalent Fractions
Adding and Subtracting Square Roots
Solving Systems of Equations
Exponent Laws
Solving Quadratic Equations
Factoring Trinomials
Solving a System of Three Linear Equations by Elimination
Factoring Expressions
Adding and Subtracting Fractions
The parabola
Computations with Scientific Notation
Quadratic Equations
Finding the Greatest Common Factor
Introduction to Fractions
Simplifying Radical Expressions Containing One Term
Polynomial Equations
Graphing and Intercepts
The Number Line
Adding and Subtracting Rational Expressions with Different Denominators
Scientific Notation vs Standard Notation
Factoring by Grouping
Extraneous Roots
Variables and Expressions
Linera Equations
Integers and Substitutions
Squares and Square Roots
Adding and Subtracting Rational Expressions with Different Denominators
Solving Linear Inequalities
Expansion of a Product of Binomials
Powers and Exponents
Finding The Greatest Common Factor
Quadratic Functions
The Intercepts of a Parabola
Solving Equations Containing Rational Expressions
Subtracting Polynomials
Solving Equations
Adding Fractions with Unlike Denominators
Solving Systems of Equations by Substitution
Solving Equations
Product and Quotient of Functions
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Adding and Subtracting Fractions

FRACTION: If a and b are real numbers then the expression

is called a fraction. The top number a is called the numerator and the bottom number b is called the denominator. Division by zero is not allowed, so b ≠ 0 or the result is undefined.

Adding fractions

Remember that for addition all fractions must have common denominators. [The result must be checked to see if it will reduce to simpler form.]

I. Adding fractions with common denominators:

Keep the common denominator then add the numerators. Follow all of the properties for “signed numbers”.


II. Adding fractions that do not have common denominators:


Factor the denominators and find the least common denominator (LCD). Raise both (or all) fractions to have the LCD, then add the new numerators.



Equivalent Fractions: If the numerator and denominator are multiplied by a common factor the resulting expression is an equivalent fraction that has the same numerical value.

Multiply fractions: Multiply numerators times numerators and denominators times denominators.

Add Fractions with Different Denominators: If the fractions do not have common denominators [Factor the denominators and find the LCD. ] RAIISE all fractions to have common denominators,

then add the resulting numerators.

Another approach to this is to write the LCD in the denominator with a long “overbar” -- write the “first numerator” then compare its denominator with the LCD (the other factors will be the “missing factor”) which will be multiplied times the numerator.

Next, remember that the “sign goes with the number that follows it” and write the “next signed numerator” – compare its denominator with the LCD for the “missing factor” to multiply times that numerator. Repeat for all fractions in the sum.

Learn this well. These steps will also work with algebraic fractions that contain variables so you will probably want to “bookmark” these pages.



Adding mixed numbers – integers and fractions

One of the problems that students have difficulty with occurs when one of the “addends” is an integer. They forget that all integers have a denominator of 1.

Example 2:

III. In algebra some of the factors may be letters, or variables, which must be treated as “prime factors”. They will be left in the result as “literal sums”.

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