An Explanation: Common Denominators

The denominator of a fraction is the bottom number.  It tells us how many equal parts there are.  When we add or subtract fractions, it is important that the denominators are the same for all of the fractions added or subtracted.  This is called the common denominator.  Common means the same.  To do this we must find a common multiple (least common multiple) among the denominators.  That means find a number that both denominators will "go into."  For example:  1/5 and 1/3 has a LCM of 15 because 1/5 would have to be divided into thirds (because of the 1/3) which would leave you with 15 bars/pieces/slices etc.  1/3 would have to be divided into fifths. This would leave you with 15 pieces.  Try using the 1/5 and 1/3 fraction bar.  After you find the common denominator, you can proceed with adding or subtracting the fractions together.

  1/3=   _/15...3 goes into  15, ___ times        5/15    
+1/5=  _/15....5 goes into  15, ___ times    + 3/15
                                                                     8/15

1/3 and 1/5 canNOT be added unless there is a common denominator! 

I didn't know that!!

When Mrs. Truelove introduced the class to the fraction bars, I rolled my eyes and thought of it as silly.  I've never been a good mathematician and when we're talking about fractions, I pretty much tune everything out.  Who knew that "fraction bars" were the key to unlocking my understanding of fractions.  I have always understood how to use them in different operations but I never understood the concept.  For example, 4/5x1/2 is 4/5 of 1/2.  You would have to divide the half fraction bar into tenths and shade in 4 of the 10 bars which would equal four tenths (4/10) or two fifths (2/5).  Until I used the fraction bars I did not understand why it would equal two fifths besides 4 x 1 =4 and 5 x 2 = 10, reduced to 2/5.  Instead of hating fractions, I actually don't mind using them now.  I have had success with them every since.  I will definately use fraction bars to teach my class about fractions and I will encourage my students to use them in solving operations that involve fractions.