These are links to pages.→   Arithmetic      Algebra      Fractions      Decimals      Ratio, Proportion, & Percent      Exponents      Factoring      Graphing 
 

      Fractions                                                               
                         Fractions- Introduction, 3 Types, Graph
                         Fractions- Simplify (Reduce to Simplest Form)
                         Fractions- Multiplication
                         Fractions with Variables & Exponents- Multiplication
                         Fractions- Division & Multiplication
                         Fractions with Variables & Exponents- Division (Some Negatives)
                         Fractions- Sum & Difference (Addition & Subtraction)
                         Fractions & Mixed Numbers- Sum & Difference (with Common Denominators)
                         Fractions, Whole, & Mixed Numbers- Sum & Difference
                         Complex Fractions 1- Simplify (Some with Variables)
                         Complex Fractions 2- Simplify (Negatives, Variables, & Exponents)

 Fractions- Introduction, 3 Types, Graph
I describe proper and improper fractions as well as mixed numbers.  I cover how to graph fractions using geometric shapes or number lines.  Lastly, I show how to convert between improper fractions and mixed numbers. The "Fractions - Introduction, 3 Types, Graph" link opens a sheet to help reinforce identifying the type of fraction, as well as how to graph each one.  It requires labeling by type and then matching each fraction with its graph.
Sheets Used in Video
Sheets Used in Video (Answer Key)


Fractions - Introduction, 3 Types, Graph
Fractions - Introduction, 3 Types, Graph (Answer Key)

 



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Fractions- Simplify (Reduce to Simplest Form)
My intention is for the concepts in the next two videos to be covered in succession; the Part 1 video covers the logic of, and procedure for, simplifying fractions.  The Part 2 video addresses negatives and zeros.
This "Part 1" video covers the logic of simplifying fractions.  Dividing by a "one" changes the look, but not the value of the fraction.  I cover fractions with numbers, variables, and both.  Many of the variables have exponents. The worksheet "Part 1 Video- Simplify (No Negatives or Zeros)" is intended for those who want to practice with simplifying fractions prior to doing the worksheet that includes negative fractions and zeros.
 
Sheets Used in Videos (Part 1 & Part 2)
Sheets Used in Videos (Part 1 & Part 2) (Answer Key)


Part 1 Video- Simplify (No Negatives or Zeros)

Part 1 Video- Simplify (No Negatives or Zeros) (Answer Key) 



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This "Part 2" video completes my presentation on simplifying fractions.  I address how to read and deal with negatives.  Lastly, I explain why fractions with zero in the numerator yield such a different answer than fractions with zero in the denominator. This worksheet covers material from both videos; it includes negatives and zeros.
 
Fractions- Simplify (For Both Videos) (Answer Key)




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 Fractions- Multiplication
I cover six examples of "multiplying fractions," but most of these problems also involve mixed numbers and whole numbers, to describe it more precisely.  I stress the importance of reducing prior to multiplying. The "Fractions- Multiplication" sheet has three columns of four problems each.  As usual, I suggest working the first column, checking and learning from any mistakes, then taking a short break prior to working the next column.  Taking breaks and avoiding the use of notes or examples helps to move the knowledge to your long-term memory.
 
Sheet Used in Video
Sheet Used in Video (Answer Key)


Fractions- Multiplication
Fractions- Multiplication (Answer Key)


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Fractions with Variables & Exponents- Multiplication
I cover eight examples of increasing complexity.  With the last four I also indicate how to subtract exponents when dividing variables. The "Fractions with Variables & Exponents- Multiplication" link has three columns of four problems each.  Learn from mistakes, take breaks, strive to work without notes or examples; develop your long-term memory.
Sheet Used in Video
Sheet Used in Video (Answer Key)


Fractions with Variables & Exponents- Multiplication
Fractions with Variables & Exponents- Multiplication (Answer Key)



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Fractions- Division & Multiplication
Assuming some familiarity with multiplication of fractions, I cover nine problems involving division with fractions, mixed numbers, and whole numbers. The last four problems start with division and multiplication, two of them involving parentheses. The "Fractions- Division & Multiplication" link has three columns of four problems each.  It is best to not do the entire sheet in one sitting; breaks of increasing duration help to develop your long-term memory.
 
Sheet Used in Video
Sheet Used in Video (Answer Key)



Fractions- Division & Multiplication
Fractions- Division & Multiplication (Answer Key)



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Fractions with Variables & Exponents- Division (Some Negatives)
I cover eight examples on division of fractions with variables and exponents.  A few problems involve negative terms.  I assume some familiarity with my previous fractions videos.   The "Fractions with Variables & Exponents- Division" link has three columns of four problems each.  Learn from mistakes, take breaks, strive to work without notes or examples; develop your long-term memory.
 
Sheet Used in Video
Sheet Used in Video (Answer Key)



Fractions with Variables & Exponents- Division
Fractions with Variables & Exponents- Division (Answer Key)


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  Fractions- Sum & Difference (Addition & Subtraction)
This video presents why common denominators are required for addition or subtraction of fractions.
This may help you to remember when common denominators are required!
Printing the sheet used in the video and working along with me may help you to understand and retain the information.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)






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I cover twelve examples, with a mix of common and unlike denominators, positives and negatives, as well as some with three fractions in a problem.   The "Fractions- Sum & Difference (Add & Subtract)" link has three columns of four problems each.  I suggest that you work a column, check and learn from mistakes, take a break.  Then try another column without notes or examples.  This will help to develop your long-term memory.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)


Fractions- Sum & Difference (Add & Subtract)
Fractions- Sum & Difference (Add & Subtract) (Answer Key)




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Fractions & Mixed Numbers- Sum & Difference (with Common Denominators)
I cover eight examples, four are straightforward, three involve simplifying the answer, and two require borrowing prior to subtracting. The "Fractions & Mixed Numbers- Sum & Difference (Com. Den.)" worksheet has three columns of four problems each.  As usual, I advise taking breaks between solving each colum of four problems.  
Sheets Used in Video
Sheets Used in Video (Answer Key)

 

Fractions & Mixed Numbers- Sum & Difference (Com. Den.)
Fractions & Mixed Numbers- Sum & Difference (Com. Den)  (Answer Key)



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Fractions, Whole, & Mixed Numbers- Sum & Difference
I cover nine problems, most of which require finding common denominators, (a few you can do in your head without finding common denominators) and many involve borrowing. With the last few, I show how to borrow and solve on paper as well as how to think about solving them in your mind instead, since writing these out can be a lot of work. None of the problems in the video or the worksheet start with common denominators.  The "Fractions, Whole, & Mixed Numbers- Sum & Difference" worksheet has three columns of four problems each.  As with the other worksheets, it is designed for you to get a good variety of problems by working one column.  Each column has a similar variety of problems.
Sheets Used in Video
Sheets Used in Video (Answer Key)



Fractions, Whole, & Mixed Numbers- Sum & Difference
Fractions, Whole, & Mixed Numbers- Sum & Difference (Answer Key)



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  Complex Fractions 1- Simplify  (Some with Variables)
I cover ten examples.  At a minimum--familiarity with simplifying fractions, multiplying fractions with variables, and combining like terms--is assumed.  On the first problem, I show that a complex fraction is a way of indicating division by a fraction.  With the remaining nine problems, I show how to find the least common denominator, and then how to use it to start simplifying the complex fraction.  Given the wide variety of possible configurations of complex fractions, I include two worksheets on this topic to provide some additional practice.  Each sheet has two columns of four problems each.  Any given column is intended to give a reasonable variety of configurations.  Thus, I suggest completing a column and learning from mistakes prior to attempting another column.  Perhaps a break of some minutes, hours, or days between Sheet A and Sheet B is well advised.
 
 
Sheets Used in Video
Sheets Used in Video (Answer Key)



Complex Fractions 1- Simplify (Sheet A)
Complex Fractions 1- Simplify (Sheet A) (Answer Key)

Complex Fractions 1- Simplify (Sheet B)
Complex Fractions 1- Simplify (Sheet B) (Answer Key)


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 Complex Fractions 2- Simplify (Negatives, Variables, & Exponents)
I build on concepts introduced in Complex Fractions 1- Simplify, covering ten more problems that are a bit more complicated.  This video has considerably more variables and exponents.  The last two problems have denominators with two terms (binomial denominators) so they may look unusual, after seeing so many problems with one term denominators (monomial denominators). Again, because of the wide variety of possible configurations, I have included two worksheets.  Each column provides you with a good variety of problems. 

 
 
Sheets Used in Video
Sheets Used in Video (Answer Key)



Complex Fractions 2- Simplify (Sheet A)
Complex Fractions 2- Simplify (Sheet A) (Answer Key)

Complex Fractions 2- Simplify (Sheet B)
Complex Fractions 2- Simplify (Sheet B) (Answer Key)



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