The proper fractions are those that result from the division between two numbers, where the numerator or dividend (the one that is located in the upper part of the fraction) is lower than the denominator or divisor (the one that is located in the lower part of the lower fraction) . For examples: 3/4, 20/73, 6/21, 64/133.
How are proper fractions expressed?
In this way, the proper fractions can be expressed by a number less than 1, that is, an effectively fractional number.
The concept of proper fraction is simple: you simply need to graph any geometric figure easily divisible into equal parts (for example, a circle, in which parts can be marked as bicycle spokes) and divide it into as many equal parts as the number that figure in the denominator.
Then you can scratch or color as many parts as indicated by the numerator, the proper fraction will be represented in this way.
People usually associate the idea of fraction with their own fractions, because in everyday life it is very common for the sale of different food products to be expressed in this way, offering ‘one quarter’, ‘half’ or ‘three quarters’ kilogram of something, all these fractions being their own, being inferior to unity.
Characteristics of proper fractions
A characteristic of proper fractions is that for many purposes they are usually represented by percentages, since it is a kind of “convention” to express the proportions with respect to the number one hundred.
The method to carry out the translation of a proper fraction (also an improper one, by the way) to the percentage form is looking for the numerator that transforms the fraction into an equivalent of denominator 100, by means of a ‘rule of three’ of type A (numerator) is to B (denominator) as X is to 100, representing in X the desired percentage.
Unlike the improper fractions (fractions greater than unity), proper fractions are not capable of being re-expressed as the combination between a whole number and another fraction, since this would require that the whole number be 0.
Proper fractions in mathematics
In the realm of mathematics, operations between proper fractions follow the general rules of operations between fractions: for addition and subtraction It is necessary to find the common denominator using equivalent fractions. Whereas for products and quotients it is not necessary to repeat this procedure.
It can also be ensured that the product between two proper fractions will always be a fraction of the same type, while the quotient between two proper fractions will require the larger to act as the denominator to also be a proper fraction.
Examples of proper fractions
Here are some proper fractions as an example: