## Tuesday, October 18, 2011

### Using Love to Add Fractions

For the visual learner, I realized that terms such as lowest common denominator,  highest common denominator, and addition of two fractions was difficult.  So, I invented the Silly Story of Fraction Love.  In this story fraction people  may not socialize, fall in love, or even marry other fraction people with different "bottoms."  The students find this hilarious.

A big bottomed person (giggle) may not mix with a small bottomed person.  This is an easy concept to remember.   I chose this clip art because it was free and because their clothes will allow you to write fractions on them.  An example would be if the fraction 2/3 was on the boy's shirt and 3/6 was on the girl's shirt.  Notice that the "bottoms" or denominators are different sizes.  Unfortunately, these two kids can not be mixed or added together.  Unless...there was some MAGIC way for this to happen.

I now introduce my version of Cupid.  I call it the "Magic Mirror Multiplier."  I tell the students that it is magic because any number in a fraction placed over itself (like in a mirror) equals ONE.  I go over this concept over and over with as many different numbers until the class is laughing. " Is 24/24 equal to 1?"  "Is 5,000/5,000 equal to 1?"  Is 33.21/33.21 equal to 1?"  Is 2,000,000/2,000,000 equal to 1?"  After many, many examples, they get it.

Now, I show them how to make the "love connection" using the multiplier. I  put this symbol between the couple ( ---).   The students have to figure out what number to put on the bottom of the fraction to make the smaller bottom number the same as the bigger bottom number.  In the above example, it would be a 2 because 2 x 3 = 6.  We are only looking at the couple's bottoms at this point.  Then I ask them to mirror the 2 to make the magic happen.  The result is 2/2.
Result: 2/3 (2/2) + 3/6 = 4/6 + 3/6 = 7/6
Alas, true love has solved a fractions equation.  The 2/2 is the Magic Mirror Multiplier.

I have had graduating students who have come up to me years later and tell me how much the "Magic Mirror Multiplier" helped them through even higher math.  Enjoy!!1