Math CentralQuandaries & Queries


Question from Kenneth:


If someone is paid every two weeks, he receives 26 paychecks per year, (52 weeks/year)divided by (2 weeks/1 check) equals 26 paychecks per year.

However, if the calculation uses days instead of weeks, the answer is not exactly 26 paychecks. For example, 365 days divided by 14 days per paycheck
equals 26 1/14 paychecks. Fourteen days is equivalent to two weeks, isn't it?

Why is there this fractional amount of 1/14 of a paycheck?

I thank you for your reply and answer.


The number of days in a year is not a multiple of 7 (and so not of 14 either). That means that the number of weeks in a year isn't exactly 26. There are actually 52 1/7 weeks in a year (52 x 7 = 364). That means that there are 26 1/14 paychecks if you count this way too. The thing is, you only receive 26 of them during the year.



(52 weeks/year)divided by (2 weeks/1 check) equals 26 paychecks per year.

But there aren't exactly 52 weeks per year (52 x 7 = 364); there are 52 1/7 weeks (ignoring leap years.) Therefore, one year in fourteen (still ignoring leap years) , payday falls on Jan 1st and Dec 31st of the same year and we get 27 paycheques (loud cheers!)

Half of 52 1/7 is 26 1/14, so that is where that number comes from.

In fact, almost one year in four is a leap year, and in a leap year, if payday falls on Jan 1st or Jan 2nd you will get a 27th paycheque that year.


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