Multiplying mixed fractions

Perhaps best, before addressing an explanation of the correct way to multiply mixed fractions, is to briefly review some definitions, which will allow us to understand this operation in its specific mathematical context.

Fundamental definitions

In this sense, it will then be relevant to focus this review on four precise notions: Fractions, Unsuitable Fractions, Integers, and Mixed Fractions, as these are the expressions inherent in the multiplication operation. Here’s each one:


Consequently, you can start by saying that mathematics has defined fractions as those expressions, used to represent fractional numbers or non-exact quantities. Also, such expressions will be composed of two elements, each of which are defined as follows:

  • Numerator: first, you will find the Numerator, which will be located, without exception, at the top of the fraction, having the responsibility to indicate how many parts of the whole have been taken, or are represented by the fraction.
  • Denominator: The Denominator will be the element at the bottom of the expression. Its main function is to indicate in which parts the unit or the whole is divided, from which the parts have been taken, indicated by the numerator of the fraction they constitute.

Improper fractions

In another order of ideas, it will also be necessary to revise the concept of Improper Fractions, which will be explained by the different authors as a type of fraction, that is, a mathematical expression, used to represent inaccurate or fractional amounts, while it is characterized by having a Numerator of higher value than the Denominator.


Thirdly, it will be prudent to throw lights on the definition of Whole Numbers, which are considered as elements through which you can account for exact or whole amounts. This type of numeric element consists of positive integers, their negative inverses and zero, so they will be used respectively to express exact quantities, absence or lack of specific whole amounts, or even the total absence of Amount. These numbers are the constituents of the Z numeric set.

Mixed fractions

Finally, it will be of great importance to review the definition of Mixed Fractions, mathematical expressions that are generally described by the different authors as a type of fraction, used to point out certain fractional amounts, and whose main feature is to be composed of an integer and a fractional number or fraction. This type of expression corresponds more to the colloquial scope than the mathematician, and are used when you want to account for a situation where the whole is made up of several units, divided into equal parts, and from which a total unity and some parts of another.

Multiplication of mixed fractions

With these definitions in mind, it is perhaps certainly much easier to address the correct way in which a multiplication operation should be solved, which has as multiplying and multiplier mixed fractions. In this case, the Mathematics states that each of the following steps should be followed:

  • First, this being the fastest and simplest method, it will try to convert each of the mixed fractions to improper fractions, which will be done by multiplying in each case the whole number with the denominator of the fraction, to add the product with the numerator, and obtain the numerator of the improper fraction, leaving as denominator the fraction that constituted the mixed expression originally had, an operation that can be expressed as follows:

  • Next, we will then proceed to multiply each of the improper fractions involved in the operation, using the method given below:

  • Having the result or product of this operation, if possible, will seek to simplify the improper fraction, dividing it among its common divider.
  • Finally, the simplified fraction will again become a mixed fraction, interpreting it as the final product of the operation.

Example of how to multiply mixed fractions

However, the best way to close an explanation of the appropriate way of multiplying mixed fractions may be through the presentation of a concrete example that would allow us to see in practice how each procedure related to the resolution of such operations, as seen below:

Multiply the following mixed fractions:

The first time each of the mixed fractions will be converted into improper fractions:

Having done this, the own fractions obtained will be multiplied:

Unable to simplify the fraction, it will be a choice to convert it into a mixed fraction. This will be taken as the final product of the operation:


Multiplying mixed fractions
Source: Education  
September 26, 2019

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