Call Now: (800) 537-1660  
The Algebra Buster
The Algebra Buster

Adding Fractions

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.

Example

Work out each of the following sums of fractions.

Solution

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).

Start solving your Algebra Problems in 5 minutes!

 
Get Algebra Buster Today!
Stop spending your time and money on private Algebra tutors!  Download Algebra Buster now!  Algebra Buster installs on your computer and helps you learn to solve your algebra problems fast and easy in three simple steps...
  
Step 1: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor.
Step 2: Let Algebra Buster solve it.
Step 3: Ask for an explanation for the steps you don't understand.
  
That's really all there is to it! Order NOW and you will receive 30 Minutes of FREE Live Tutoring at Tutor.com!
  
  
What our customers say...
  
"I would like to thank the creator for preparing such a tremendous piece of software. It has made algebra simple by providing expert assistance with fractions and equations." 
                                               - Tabitha Wright, MN 
$58.99
Only: $39.99!
This limited time offer is only
good until September 9th
  
  

Algebra Buster can solve problems in these areas...

simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) 
factoring and expanding expressions 
finding LCM and GCF 
basic step-by-step arithmetics operations (adding, subtracting, multiplying and dividing) 
operations with complex numbers (simplifying, rationalizing complex denominators...) 
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) 
solving a system of two and three linear equations (including Cramer's rule) 
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) 
graphing general functions 
operations with functions (composition, inverse, range, domain...) 
simplifying logarithms 
sequences (classifying progressions, find the nth term of an arithmetic progression...) 
basic geometry and trigonometry (similarity, calculating trig functions, right triangle...) 
arithmetic and other pre-algebra topics (ratios, proportions, measurements...)
linear algebra (operations with matrices, inverse matrix, determinants...)
statistics (mean, median, mode, range...)

  

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Buster is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Buster solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Buster can solve problems in these areas...

simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) 
factoring and expanding expressions 
finding LCM and GCF 
basic step-by-step arithmetics operations (adding, subtracting, multiplying and dividing) 
operations with complex numbers (simplifying, rationalizing complex denominators...) 
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) 
solving a system of two and three linear equations (including Cramer's rule) 
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) 
graphing general functions 
operations with functions (composition, inverse, range, domain...) 
simplifying logarithms 
sequences (classifying progressions, find the nth term of an arithmetic progression...) 
basic geometry and trigonometry (similarity, calculating trig functions, right triangle...) 
arithmetic and other pre-algebra topics (ratios, proportions, measurements...)
linear algebra (operations with matrices, inverse matrix, determinants...)
statistics (mean, median, mode, range...)
Get Algebra Buster Today!
$58.99
Only: $39.99!
This limited time offer is only
good until September 9th
100% Money Back Guarantee!
 
 
Free Tutoring
  • Get 30 Minutes of FREE Live Tutoring from Tutor.com if you
    BUY NOW!



Testimonials
"I ordered the Algebra Buster late one night when my daughter was having problems in her honors algebra class. After we ordered your software she was able to see step by step how to solve the problems. Algebra Buster definitely saved the day."
Tami Garleff

 
Home    Why Algebra Buster?    Guarantee    Testimonials    Ordering    FAQ    About Us
What's new?    Resources    Animated demo    Algebra lessons    Bibliography of     textbooks
 

Copyright © 2009, algebra-online.com. All rights reserved.



Related pages: