Finding Half of an Odd Number Fraction

How to tackle the odd number fraction

Jeffrey Boerner,

When I was in college, I did woodworking on the side to help supplement my income.  In fact, at times, all the money I had to my name was from the woodworking I did.  I would take just about any cabinet of woodcraft job I could get my hands on.

As it turned out, I was pretty good at woodworking.  On one particular occasion, I needed some help to hang (on a wall) four or five rather large acoustic panels.  I asked a friend of mine, who was three times my age, and a fantastic woodworker, to help me.

We had to find the exact center of the panel, to mount the wall fastener, so it would hook into the exact right position.  Sounds easy, right?

I set the panel against the wall and measured it across the width.  The width of the panel was 43 and 7/8 inches.  As I always have done, I began to measure from both sides of the panel to find an equal distance to find the center.  There are other ways, like angling your tape measure to line it up with an even number on the tape and then marking the middle, but that is hard to do on a big panel, especially if you are alone on the job. Nevertheless, by trial and error I found the center alright, but it took me a while to do that and it wasn't quite as exact as I would have liked -- but "close enough" I thought. Hummmm.

My friend was watching me and laughing and shaking his head. Then he showed me his way of finding center of an odd fraction number.

I have used his method all my life and shown many people this easy tip. In fact, I won a couple of bucks betting that I could figure out half of an odd number fraction faster than anyone willing to put a dollar on the table!

Now I will show you:

Let's start with an easy one: Find the half of 7 and 5/8 --go ahead. 

How long did it take you? How about 23 and 7/8...harder?

Here is how you do it.  And this only works on odd number fractions.

Let's go back to 7 and 5/8

Step 1:  Reduce the whole number by 1 to get the next even number.  6

Step 2: Divide that number by 2.  3

Step 3: Add the numerator and denominator of the fraction together (5+8) 13
Step 4: Now double the denominator to get the new denominator (8x2) 16
Step four: Put it all together...the answer is 3 and 13/16   

Here it is in short form: Let use 23 and 7/8 as our next example.   23 - 1 = 22 divided by 2 = 11, 7+8 = 15 , 8 x 2 = 16, the answer is 11 and 15/16.

Shorter form: 67 and 13/16

66                                                                                                                                                                     
33
29
32                                                                                                                                                                                      
 answer is: 33 and 29/32

With a bit of practice, you can do it in your head and win the bet every time!  Unless, of course, someone else reads this blog and is on to your trick!  Then it is a match of wits.