Algebra Tutorials!  
Wednesday 17th of April
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Adding Fractions

The objective of this lesson is very succinct:

  • That you learn how to add fractions correctly


Numerator and Denominator

The number or algebraic expression that appears on the top line of a fraction is called the numerator of the fraction.

The number of algebraic expression that appears on the bottom line of a fraction is called the denominator of the fraction.

Adding Fractions

Expressed in symbols, the rule for adding fraction is as follows:

Let’s break this down to see everything that is expressed in this rule.

The numerator of the sum is a·d + b·c.

You can remember the numerator without having to memorize this particular formula by remembering the pattern of cross-multiplying. To create the numerator, you multiply each numerator by the opposing denominator, forming a “cross” pattern.

To get the denominator of the sum, you just multiply the two denominators (b and d) together.


Work out each of the following sums of fractions.



Often it will be possible for you to simplify your fractional expressions by combining “like terms” just as you do when FOILing a polynomial. Although this kind of simplification is not always needed just to get the right answer, if can make your fractional expressions much easier to deal with. Remember to keep the numerator and denominator separate when combining like terms!


In Example (b), note how when the cross-multiplication is done, the “7” from the numerator of the first fraction multiplies the entire quantity (x + 1) that is in the denominator of the second fraction, not just the x. Also notice that when the two denominators are multiplied to create the denominator of the sum, the “10” from the denominator of the first fraction multiplies everything (i.e. the entire quantity (x + 1)) that appears in the denominator of the second fraction.


When simplifying fractions, simplify the numerator and denominator separately. You cannot combine like terms from the numerator with like terms from the denominator (or vice versa). Often you will need to FOIL when simplifying the numerator and denominator of fractions that involve algebraic expressions such as x.


This answer is not the simplest one that is possible. If you look closely at the middle fraction above, you can see that every single term in the numerator has at least one factor of (x + 1). The denominator also has a factor of (x + 1). These “common” factors can be factored out of the numerator and the denominator as shown below.

When you have a common factor that you have pulled out of every term in the numerator, and it matches a factor that shows up in the denominator, you can almost always cancel this factor from both the numerator and the denominator.

provided x ≠ -1.

The only situation when it is not okay to cancel the factor of (x + 1) from the top and bottom is when you have the x-value of x = -1 (i.e. the particular x-value that makes the factor of (x + 1) equal to zero).

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