Knitting Math 5 - increases and decreases

Ok.  We've covered gauge, long and short horizontal repeats, and vertical repeats.  Yes, there is still more, and we'll take the next step in little bites.  How do you place increases and decreases in an even way?
There's one equation in this math that is absolutely critical:  Stitches you have - stitches you want for decreases, and stitches you want - stitches you have for increases.  The answer will be stitches difference, or the number to decrease or increase respectively.  Grab your calculator and a pencil, and let's do it.

You know I love mittens, so I'm going to use them as the example here for increases.  In my cuff I have 40 stitches.  I need 48 for the body of the mitten, and the instructions say "distribute increases evenly" for the increase row - no specifics.  Yikes!

48-40=8, so I need 8 more stitches.  How to do it evenly?  Divide.  Divide stitches you have BY stitch difference= number of stitches between increases/decreases.  In this case, there are going to be 5 stitches between increases.

The way to implement is to knit a couple of stitches in the beginning of your row or round.  Increase one.  Then knit 5, increase one across or around.  The increases will be even, and they will be a couple of stitches in from your edges, making any seaming necessary easier.

The example here for decreases is a skirt on a child's garment.  The original skirt has 56 stitches.  The decreased row has 40. 

56 (stitches I have) - 40 (stitches I want)=16, so I need to decrease 16 stitches.  56/16=3.5.  Three and a half stitches between decreases - - ?  I have no idea how to make a half a stitch, but I can trade off between 3 stitches + one increase, and then 4 stitches + one increase.  That would work.  OR I can take that .5 (a remainder) and realize that it represents 8 stitches (3 x 16 = 48 48 +8 = 56).  I can put half of them at the beginning of my row or round, and half at the end.  I'll knit 4, then K3, M1 until I get to the last 4 stitches. 

Unless it's stated otherwise, do not increase or decrease on the first two stitches of a row or round.  It makes seaming much easier.  If your pattern tells you to, then do as it says.