Why is the quarter a quarter?

Answer 1

The coin called a quarter is called a quarter because its value is a quarter of a dollar (25 cents times 4 equals 100 cents)

The quarter denomination is the only one that doesn't fit into a decimal (10-based) coinage system. Most other countries have 20-cent pieces instead of 25, because 1/5 of a dollar follows the pattern of the factors of ten: 1, 2, and 5.

But when the US first started minting coins the former colonies were also using a Spanish coin called a "milled dollar". It was large and had no smaller denominations, so to make change it was actually cut into pieces (!). Cutting it into 1/5 would be difficult, so people cut it into halves, quarters, and eighths. To simplify change-making using the new US Coins, the Mint decided to make coins worth a quarter of a dollar so they'd match the cut-up pieces of a Spanish milled dollar.

By the time the milled dollar was removed from circulation, people had become used to using 25 cent coins instead of 20 cent coins, and the denomination has stayed with us ever since.