Multiplying fractions by an integer

Probably the best way to address an explanation of the correct way to resolve fractional and integer multiplication is to start by doing a theoretical review, in which some crucial definitions for understand this operation within its precise mathematical context.

Fundamental definitions

In this regard, it may also be prudent to delimit this revision to two specific notions: the very definitions of fractions and whole numbers, in order to be aware of the nature of the expressions or numerical elements involved in the Multiplication operation.  Here’s each one:


In this sense, it will begin to say that the different sources have been given the task of pointing out fractions as a type of mathematical expression, which is used to express fractional numbers, that is, that fractions will be representations of numbers or amounts that are not accurate or not whole.

Likewise, fractions are generally understood as an expression composed of two elements, each of which can be defined in turn as follows:

  • Numerator: First, you will find the Numerator, who will fulfill the task of indicating what part of the whole has been taken or that represents the fraction. This element will be located at the top of the expression.
  • Denominator: The Denominator will occupy the bottom of the expression. Its mission is to indicate in how many parts the whole is divided, of which the numerator represents a part.


In contrast, Whole Numbers will be elements that will serve to account for exact quantities. These numbers are made up of natural numbers, their negative inverses and zero, elements these which in turn constitute the Z Numeric Set. Unlike fractions, they will not have a numerator or denominator, and they are then made up of a single element.

Multiplying fractions with integers

Once these definitions have been revised, it will be much easier to understand the operation known as Fraction and Integer Multiplication, and that as the name that calls it indicates, it is an operation by which a product is sought to obtain between a fractional number, expressed as a fraction, and an integer.

However, because this is an operation that combines mixed elements, or of different mathematical nature, it will be necessary to specify the correct way to solve such operations, and that will be based on these simple steps:

  • The first thing to remember is that every whole number, mathematically speaking, has a denominator equivalent to one.
  • Assuming this, that is, the denominator of the whole number corresponds to the unit, the multiplication between two fractions can be expressed.
  • Conselus with what the Mathematics dictates, it is necessary to proceed to multiply the numbers that serve as a numerator, thus obtaining the numerator of the product.
  • Likewise, the names will be carried out in order to determine what is the product of the final fraction.
  • If there is any chance of simplifying the fraction, it must be done.

The way to solve this type of operation can be expressed mathematically as follows:

Example of Multiplication of Fractions and Integers

However, the best way to complete an explanation of the correct way to multiply fractions and integers may be to use some examples, which allow us to see in a practical way how every whole number can be expressed as a fraction, assuming as its denominator the unit, thus allowing the solve of the Fraction Multiplication, as seen below:

Resolve the following operation:


Multiplying fractions by an integer
Source: Education  
September 26, 2019

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