Proper and improper fractions
A fraction can be identified as proper or improper by comparing the numerator and the denominator. If a fraction is less than one then it is a proper fraction. If it is greater than or equal to one then it is an improper fraction. A fraction is less than one when the denominator is bigger than the numerator.
Our old friend Robert Recorde first wrote about improper fractions in 1542. Again, his spelling doesn’t look very good to us today but he wrote: “An improper fraction…that is to saye, a fraction in forme, which indede is greater than a unit.”
Robert is just saying that an improper fraction is greater than one. Today we say that an improper fraction is one or more. This is the same as saying if the denominator is equal to or smaller than the numerator then it is not a proper fraction.
A real, proper fraction is less than one.
