Mixed number: what is it, transformations, examples

mixed number or mixed fraction is the representation of a number composed of an integer part and a fractional part. The representation by a mixed number is done for improper fractions as it has an integer part.

They exist three possible classifications for one fraction, she can be:

• a fraction of its own: when the numerator is less than the denominator;
• an apparent fraction: when, when dividing the numerator by the denominator, the answer is an integer;
• an improper fraction: when the fraction is not apparent and the numerator is greater than the denominator.

Read too: How to solve operations with fractions?

What is a mixed number?

In the Harry Potter movie, the platform they use is a mixed number. [1]

The mixed number or mixed fraction has an integer part and a fractional part. It is represented by the integer part followed by a proper fraction, this representation facilitates the recognition of what is integer and what is fractional in the number.

See some examples:

Fraction types

There are three possible classifications for a fraction, apparent fractions, proper fractions, and improper fractions. To understand how to turn a fraction into a mixed number, we first need to understand each of these classifications. We represent as mixed numbers only improper fractions.

• apparent fraction

A fraction is apparent when it is the representation of a integer, that is, the denominator is divisible by the numerator.

Examples:

We know that 10: 2 = 5, 12: 4 = 3, and -25: 5 = -5, which makes these fractions apparent as they represent whole numbers.

• Own fraction

A fraction is proper when the numerator is less than the denominator.

Examples:

• improper fraction

A fraction is improper when the numerator is greater than denominator and it does not represent an integer, that is, the numerator is not divisible by the denominator:

Examples:

Looking at the three classifications, as the apparent fraction is an integer, and it cannot be represented as a mixed number; in the proper fraction, as the numerator is smaller than the denominator, the division will always generate a result less than 1, that is, there is no integer part. The only fraction that can be described as an integer part and a fractional part is the improper fraction.

See too: Three Common Mistakes in Algebraic Fraction Simplification

How to turn an improper fraction into a mixed number?

To perform the representation of an improper fraction as a mixed number, it is necessary to divide the numerator by the denominator, to know how many whole parts there are. The quotient will be the whole part, and the rest will be the new numerator of the fraction:

Example:

Calculating the 17:3 division, we have:

In this way, we have 5 whole parts and the rest is 2, so the representation of this improper fraction as a mixed number is:

How to turn a mixed number into an improper fraction?

Now doing the reverse process, to turn a mixed number into an improper fraction, just add the integer part with the fractional part.

Example:

solved exercises

Question 1 - Analyzing the improper fraction below, the alternative that contains the representation of the fraction as a mixed number is:

Resolution

Alternative C

To find the mixed fraction equivalent to the improper fraction, let's divide the numerator by the denominator:

So there are 2 integers and the rest is equal to 4, so the mixed number that represents the fraction is:

Question 2 - The following alternative that corresponds to representing the mixed number as a simplified improper fraction is:

Resolution

Alternative E

To find the fractional representation, let's add the integer part with the fractional part of the mixed number:

Image credit

[1] Robert Alford / Shutterstock

By Raul Rodrigues de Oliveira
Maths teacher

Source: Brazil School - https://brasilescola.uol.com.br/matematica/numero-misto.htm