What are Percents?
It is important that students learn that percents are a certain type of fraction, expressed in parts out of one hundred (per cent). As explained in the Introductory page to these notes, students often seem to develop fractured, isolated ideas about rational numbers. They seem to believe that percents are different to fractions, and that concepts needed for common fractions, decimals, and percents are all separate and have to be learned one at a time. The graphic below shows two pictorial models, labeled as “0.75”, “75 hundredths”, and “75%”. The models show that these labels are equivalent, and refer to the same numerical amount. On the contrary, students should learn to perceive all rational numbers as being very similar, and as expressing the same ideas in somewhat different forms. Students will need a great deal of practice in naming fractions in different ways, converting one to another, and showing them using pictorial or concrete models.
