   SEARCH HOME Math Central Quandaries & Queries  Question from Dee: If I had a certain % increase in profits for the entire year, why can't I add the profits I made for the first 1/2 of the year to the profit I made in the second 1/2 of the year to get the total year end profit percentage? Or how can I compare the increase/decrease for each 1/2 of the year to the total % increase/decrease? Hi Dee,

Your percentage increase in the first half of the year and in the second half of the year are percentages of different things and it makes no sense to add them.

Percentage increase is the increase as a percentage of the starting value.

Lets say your profit was $200 last year and in the first half of this year your profit was$225. Your increase was $25 and the starting value was$200 so your percentage increase in the first half of the year was

25/200 × 100 = 12.5%.

In the second half of the year your profit was $250 so the increase is again$25 but the starting value is $225 so the percentage increase in the second half of the year was 25/225 × 100 = 11.11%. Your profit over the entire year was$50 and the starting value was \$200 so the annual percentage increase was

50/200 × 100 = 25%.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.