Definition
Improper fraction
An improper fraction is a positive fraction whose numerator is greater than or equal to its denominator.
Continue from this idea into connected AXIO math.
Boundary check: 13/5 covers two whole bars and 3/5 of another, so it is at least one whole.
What it means
Look at the top and bottom numbers. When the top number has counted at least one full set of the bottom-sized parts, the fraction reaches one whole or goes beyond it. “Improper” is only the name of this fraction type; it does not mean the mathematics is wrong.
Remember it
Top number at least as big as bottom means one whole or more.
Example
In 13/5, every group of five fifths makes one whole. Two groups use 10 fifths, with 3 fifths left, so 13/5 = 2 3/5.
Watch for
4/5 is not improper because 4 is less than 5, so the value is below one whole.
Common mix-up
5/5 is improper even though it equals exactly 1; the numerator is equal to the denominator.
Exact meaning
For a positive fraction, the fraction is improper when its numerator is at least as large as its denominator. Its value is therefore one whole or more, and it can be rewritten as a whole number or mixed number.