What is a unit fraction?

A unit fraction is a rational number written as a fraction where the numerator is 1 and the denominator is a positive integer. In other words, it's a fraction of the form 1/n, where n is a positive integer (n > 0).

Here's some key information about unit fractions:

• Examples: 1/2, 1/3, 1/4, 1/100, 1/1000 are all unit fractions.

• Reciprocal: A unit fraction is the reciprocal of a positive integer. For example, 1/5 is the reciprocal of 5.

• Egyptian Fractions: Ancient Egyptians expressed all fractions as sums of distinct unit fractions. For instance, they wouldn't write 2/3, but rather 1/2 + 1/6. This system, while cumbersome for modern mathematics, provides fascinating insights into their number system.

• Representation on the Number Line: Unit fractions are easily visualized on the number line. Each unit fraction represents a division of the unit interval into equal parts. 1/n represents one of 'n' equal parts of the interval from 0 to 1.

• Addition and Subtraction: Adding and subtracting unit fractions can be challenging, especially without a common denominator. Finding a common denominator can be computationally intensive depending on the denominators involved.

In summary, while seemingly simple, unit fractions have a rich history and interesting properties that continue to be studied in number theory and the history of mathematics.