Multiplication of fractions

Perhaps it is best, prior to addressing the definition and other aspects of Fraction Multiplication, to briefly review some definitions, necessary to understand this mathematical operation within its precise context.

Fundamental definitions

In this sense, it may then also be necessary to focus this theoretical review on two specific notions: the first, the definition of Fractional Number itself, which will be useful when taking into account the nature of the elements numerical numbers based on which this operation occurs.

Likewise, it will be prudent to review the definition of fraction, as this is the mathematical expression involved in this operation. Here are each of these definitions:

Fractional numbers

Therefore, it will begin to say that fractional numbers have been explained by Mathematics as the numerical elements through which you realize non-integer amounts, which is why some authors point out that these numbers are called this way, as they point to the portion or fraction of a number, and not their entire amount.

Similarly, fractional numbers are identified by this discipline as one of the two elements that make up the set of Rational Numbers, also called a numerical set Q. Thus, Mathematics notes that fractional numbers can be expressed both in fractional form and in the form of a decimal expression.


With regard to fractions, most mathematical sources agree to identify it as a form of expression of fractional numbers, consisting of a division raised between two integers, each of which occupies its place and meets a function, as shown below:

  • Numerator: This will be the number at the top of the expression. Your mission will be to point out what part of the whole the fraction refers to.
  • Denominator: The denominator will constitute the lower number of the fraction. It is tasked with pointing out the whole of which a part expresses a part.

Multiplication of fractions

With these definitions in mind, it is likely to be much easier to approach a definition of Fraction Multiplication, which is understood as a mathematical operation, by which the product of two or more fractions is intended to be calculated. In this operation, it will not be distinguished whether or not fractions have the same denominator, since regardless of this fact, the multiplication will always be solved in the same way: multiplying the numerator of the first fraction by the numerator of the second, and the denominator of this by the denominator of the first fraction. This resolution can be expressed mathematically as follows:

In the event that the result can be simplified, it will then be searched then it will also determine the irreducible fraction of the product found.

Example of fraction multiplication

However, the most efficient way to complete an explanation of Fraction Multiplication may be through the exposure of a particular example, as can be seen below:

Find the product of this operation:

To solve this multiplication of fractions, the numerator of the first fraction will be multiplied by the numerator of the second, and the denominator of this fraction will be multiplied by the denominator of the first of them:

When obtaining this result, it can be noted that simplification should be made, which will also be achieved through the common divider method:

If this is the case that some of the factors that function as a numerator in the fractions involved match some of the denominator factors, both could be deleted, which is allowed and is known as cancellation.


Multiplication of fractions
Source: Education  
September 21, 2019

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