Perhaps best, before moving forward with an explanation of the correct way to perform the Mixed FractionS Division, is to briefly review some definitions, which will allow us to understand this operation within its indicated context.
In this sense, it may also be relevant to focus this theoretical review on five specific notions: Fractions, Improper Fractions, Own Fractions, Whole Numbers, and Mixed Fractions, as these will be indispensable to have awareness of the nature of the elements involved in the Mixed Fractions Division. Here’s each one:
In this way, it can be said that Mathematics has defined fractions as those mathematical expressions, by means of which fractional numbers, i.e. non-whole or non-exact amounts, can be represented. Likewise, this discipline states that fractions are composed of two elements, each of which is in turn divided into the following:
- Numerator: First, there will be the Numerator, which will always occupy the top of the expression, while indicating how many parts of the whole have been taken or represents the fraction.
- Denominator: As for the Denominator, this element will occupy without exception the bottom of the expression. Its main task is to indicate in how many parts the whole was divided, from which some parts were taken, pointed out by the Numerator.
Likewise, it will be prudent to cast lights on the definition of Improper Fractions, which will be understood as those mathematical expressions, which composed of Numerator and Denominator, are characterized by having this first element of greater value than the Second. Like all fractions, so-called impropers also represent fractional numbers.
On the other hand, mathematics has also promulgated its definition of own fractions, which will also be assumed as mathematical expressions, used to represent non-exact or non-whole amounts, and which are distinguished by having a Numerator which, in terms of its quantity, is of less value than the Dedenominator that accompanies it.
Regarding Whole Numbers, Mathematics has indicated that these are numerical elements, through which whole or exact quantities are represented. These numbers consist of positive Whole Numbers, their negative inverses and zero, so they are used respectively to indicate exact amounts, absence or debt of specific whole amounts and even the total absence of Amount. These numbers make up the z-numeric group.
Finally, it will also be important to review the concept of Mixed Fractions, which is understood as a fraction type, which in addition to representing a fractional or not exact amount, has the characteristic of having an integer and a fraction of its own.
The use of this type of fractions usually corresponds more to the colloquial scope than the mathematician, and it is used whenever it is to express that of several units of the same entity or object, which have been divided equally, one has been taken completely or goes entities and parts of another. For example: last night we ate 1 1/2 pizzas.”
Mixed fraction division
Taking into account each of these definitions, it may be much easier to approach the notion of Mixed Fraction Division, an operation that will be understood as the mathematical procedure by which the existing quotient between two is calculated mixed fractions, that is, an expression composed of an integer and a fraction. To resolve these types of fractions, Mathematics indicates that the following steps must be followed:
- First, this being the simplest method, each of the mixed fractions must be converted into improper fractions, which will be done by multiplying the whole number by the denominator, and then adding it with the numerator, in order to obtain the numerator of the inappropriate fraction. The denominator will be the one that originally had the fraction. This operation can be expressed as follows:
- Once this is done, the fractions obtained must be divided, which will be achieved following the correct procedure expressed by the Mathematics, which consists of cross multiplication:
- Finally, the result, that is, the inappropriate fraction obtained is converted back to a mixed fraction, for which the following operation is performed:
Example of Splitting Mixed Fractions
However, the most efficient way to conclude an explanation of the Fractions Division will be through the presentation of a concrete example, which allows us to see in practice how each of the steps to be taken in resolving this ti is operations, as seen below:
Split the following mixed fractions:
It then begins by converting the following mixed fractions into improper fractions:
The fractions obtained are then divided:
It will then be sought to simplify the fraction, before converting it:
The process begins to convert it into a mixed fraction:
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September 26, 2019