Less Than One

A proper fraction has a numerator smaller than its denominator: 3/7, 2/5, 11/12. It always represents less than one whole. This is the most intuitive type of fraction — you took some slices, but not the entire pizza.

On a number line, proper fractions live between 0 and 1. The closer the numerator is to the denominator, the closer the fraction is to 1. So 11/12 is almost a full pizza, while 1/12 is barely a nibble. Seeing a fraction as a point on the line turns an abstract ratio into a concrete distance you can picture and measure.