What are simple interpretations of a rational fraction?
The square in Fig. 1 is divided into four equally sized parts, consequently each of these parts is 1/4 of the square. If we treat the square as a unit or a whole, then any of its parts is just 1/4. Then the fraction 3/4 tells that we are considering three of these parts taken together, for example the three parts colored in blue. Exactly the same scheme applies to the rectangle and circle in Fig. 1. The rectangles in Fig. 2 illustrate the same kind of interpretation. Considering the parts that are not yellow, we deal with 1/3 and 2/6 whereas for the yellow parts with 2/3 and 4/6 respectively. Both pairs represent equivalent fractions describing or symbolizing the same rational number. Again, as for whole numbers, we can make any number of fractional representations of a given rational fraction. For example 1/3 can be also represented as 3/9 or 4/12. These examples show that simultaneous multiplication of the numerator and denominator of the fraction by the same non-zero number changes
