   SEARCH HOME Math Central Quandaries & Queries  Question from Maci, a parent: We recently hosted a funraiser. Not everyone will receive a whole share of the profits because they did not participate the entire time. Several will receive only 1/2 or 1/3 share. How do I divide the profits? Hi Maci.

First, allocate the shares in a way that seems appropriate. Here's my example:

Total profits: $400 Andrew: 1 share Bev: 1/2 share Cosmo: 2 shares Dharma: 1/3 share Eli: 2/3 share Then add all the allocations together as fractions (find a common denominator): 1 + 1/2 + 2 + 1/3 + 1/3 = 6/6 + 3/6 + 12/6 + 2/6 + 4/6 = 27/6. Now divide the total profits by this value (to divide by a fraction, we can multiply by the reciprocal) to find the value of each full share: 400 x ( 6/27 ) =$88.89 per share.

Now give people their own allocations (I'm doing a bit of rounding on the cents):

Andrew: 1 share = 1 x $88.89 =$88.89
Bev: 1/2 share = 1/2 x $88.89 =$44.44
Cosmo: 2 shares = 2 x $88.89 =$177.78
Dharma: 1/3 share = 1/3 x $88.89 =$29.63
Eli: 2/3 share = 2/3 x $88.89 =$59.26.

To check this, you add up those allocations. The total (within the rounding) should match the total profit from before:

$88.89 +$44.44 + $177.78 +$29.63 + $59.26 =$400.

Hope this helps,
Stephen La Rocque     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.