Somewhere, you've likely been forced to learn how fractions work, and how to calculate 2/7 + 2/5. To some extent, fractions have been falling out of favor in the world, losing out to decimals. The New York Stock Exchange gave up fractions on April 9, 2001.
Much of the time, a decimal is okay. Sometimes, though, especially in mathematics, exact values are desired. Instead of a value being 3.00000000...00727..., it is exactly 3. Or exactly 10/35 + 14/35 = 24/35. For fractions themselves, the
Farey sequence is quite interesting—the
reduced fractions between 0 and 1 where the denominator is less than or equal to a particular value, like 7. For example, the
F7 Farey sequence is the the first row in the following block. The next row has the denominator. The third row is twice the reciprocal of the denominator squared. The fourth row is the denominator from the third row.