Why are fractions called rational numbers?
Why are fractions called rational numbers?
It is a common misconception that 'rational' numbers get their name because they make logical sense. In everyday English, 'rational' means reasonable, sensible, or logical. However, in mathematics, the term comes entirely from a different linguistic root.
The Root: Ratio
The word rational comes from the mathematical root ratio.
A rational number is any number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where the denominator $q$ is not equal to zero. Because a fraction fundamentally expresses a ratio between two whole numbers (for example, $\frac{3}{4}$ is a ratio of 3 to 4), numbers that can be written this way were named 'rational' numbers.
Historical Context
The terminology dates back to translations of ancient Greek mathematical texts. The Greeks used the word logos (meaning reason, proportion, or relation), which was translated into the Latin rationalis, meaning 'having to do with a ratio.'
So, the next time you work with fractions, remember that you are dealing with ratios, making them 'rational' in the mathematical sense of the word!