Proper and improper fractions

The proper and improper fractions are those categories of fractions that result from classifying based on which of the components is greater, if the numerator or the denominator.

Proper and improper fractions

A fraction is one where the numerator is greater than the denominator, while in an improper fraction the opposite occurs, the numerator being less than the denominator.

Remember that a fraction is a division between two numbers. These are divided by a horizontal or oblique line, the top figure being the numerator, while the bottom one is called the denominator.

Own Fractions
Proper fractions
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Improper fractions

Differences between proper and improper fractions

The main differences between proper and improper fractions are as follows:

  • In absolute terms, a proper fraction is equivalent to a number between zero and unity. In contrast, an improper fraction is equal to a number greater than one.
Generating Fraction
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  • Unlike a proper fraction, an improper one can be expressed as a mixed fraction, that is, as one that has a mixed and a fractional component.
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  • Proper fractions are used to represent the portion of a whole that has been divided into smaller parts. For example 1/3 of a 30 kilometer road is equal to 10 kilometers of road. Instead, an improper fraction is used when we have more than one unit of a good or product (divisible). For example, suppose we have three sports courts that are divided into four sectors (of equal size) and we want to indicate that one and a half tracks will be used for a given event. This would be equivalent to saying that there will be six of the twelve sectors that were obtained by dividing the tracks into four. This is equivalent to saying that 6/4 (equivalent to 1.5) of the track will be occupied for the event.

Given these differences, it is also worth saying that both proper and improper fractions are divisible. That is, they are simplifiable until they become an irreducible fraction where the numerator and the denominator do not have divisors in common.

Another point to take into account is that the inverse fraction of an improper fraction is a proper fraction, and the same is true in the opposite sense.