A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public tran

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public transportation, 1/9 cycle, and the remainder use other methods of transportation. How many employees use each method of transportation?

Find the remainder fraction:
Remainder = 1 - (1/4 + 1/6 + 1/8 + 1/9)

The least common multiple of 4, 6, 8, 9 is 72. So we divide 72 by each fraction denominator to get our multiplier:
1/4 = 18/72
1/6 = 12/72
1/8 = 9/72
1/9 = 8/72

Add those all up:
(18 + 12 + 9 + 8)/72
47/72

Now subtract the other methods out from 1 to get the remainder of who use other methods:
Remainder = 1 - 47/72

Since 1 = 72/72, we have:
(72 - 47)/72
25/72