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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 less than the denominator or divisor (the one that is located at the bottom of the low fraction).
See also: Examples of Fractions
How are they 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 just need 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 appears in the denominator.
Then, as many parts as indicated by the numerator can be scratched or colored, the proper fraction will be represented in this way.
People usually associate the idea of a fraction with their own fractions, because in everyday life it is very common for selling to be expressed weight of different food products in this way, offering ‘one quarter’, ‘half’ or ‘three quarters’ kilogram of something, all of these fractions being their own, being less than one.
characteristics
A characteristic of proper fractions is that for many purposes are usually represented by percentagesIt 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, using 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 susceptible to 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 mathematics, operations between proper fractions follow the general rules for operations between fractions: for addition and subtraction it is necessary to find the common denominator by means of equivalent fractions.Whereas for products and quotients it is not necessary to repeat this procedure.
It can also be assured that the product between two proper fractions will always be a fraction of the same type, while the quotient between two proper fractions will need the larger to act as the denominator to also be a proper fraction.
See also: Examples of Improper Fractions
Here are some proper fractions as an example:
- 3/4
- 100/187
- 6/21
- 1/2
- 20/7
- 10/11
- 50/61
- 9/201
- 12/83
- 38/91
- 64/133
- 1/100
- 1/8
- 8/201
- 9/11
- 33/41
- 40/51
- 23/63
- 9/21
- 1/8000
