Operations on Fractions . In measurements, fractions appear whenever units are not small enough to express quantities in integers. For example, five quarter-dollars will buy you exactly as mush as a dollar and a quarter . This approach is doomed to failure. Indeed, this is impractical to keep adjusting units of measurements to measurements all the time.
Units of measurement are only valuable if employed universally.
For this they must be agreed upon and fixed. Fractions are unavoidable and sooner or later we all have to learn to work with fractions. The mathematical usage of the word fraction has a very clear everyday connotation as a part of a bigger object. It would be unthinkable nowadays to just introduce fractions as a pair of numbers and postulate their basic properties as did the famous German mathematician Edmund Landau some 70 years ago. Still, to express fractions one needs a pair of numbers with a meaning and intuition attached to them.