What are Fractions and Proper, Improper, and Mixed Fractions?

What are Fractions and Proper, Improper, and Mixed Fractions?


A fraction is defined as a part of a whole or group of objects in mathematics. A fraction is a part of a given quantity taken from the whole of a specific value or an item. The fraction is represented by a horizontal bar known as a fractional bar. A fraction is a division of numerator upon denominator. A fraction is used to express quantities that are not whole numbers.

 The use of Fractions is important in everyday life from dividing pizza slices to complex engineering problems. Understanding fractions is a basic concept in mathematics. Fractions help in accurate measurement, comparison and ratios. Mastering fractions is an important step in solving advanced mathematics and real-world applications.

It enhances a person problem problem-solving and analytical skills.  A fraction can be simplified using a fraction calculator which can be used in adding fractions and subtracting fractions and can perform all arithmetic functions on it.

Let us look at the fraction using an example.

A chocolate bar is divided into 5 equal parts. Each part of the whole bar represents 1 out of 5 equal parts. The fraction 1/5 is read as '1 by 5'

Types of Fractions

Fractions represent a piece of a whole or the division of two values. There are various kinds of fraction are there which include

Type of Fraction



Proper Fraction

A fraction where the numerator is less than the denominator.


Improper Fraction

A fraction where the numerator is equal to or greater than the denominator.


Mixed Fraction

A whole number combined with a proper fraction.


Proper Fraction:

A proper function is one when the top number is smaller than the denominator of the bottom one. For example, 1/3, 3/7,7/9 are all proper fractions. A proper fraction can be added or subtracted multiplied and divided using a fraction calculator

Improper fraction:

When the numerator is greater than the denominator in a fraction, a fraction is said to be an improper fraction. For example, 5/4, 7/2,11/7 are some examples of improper fractions.

Mixed Number or fraction:

A mixed fraction is defined as the combination of whole and proper fractions. A mixed fraction is written as a whole number followed by a proper fraction. For example, 3 1/2, 4 2/5, 1 2/5 are all examples of mixed numbers.

Equivalent Fractions:

Equivalent fractions are fractions in which the simplified fraction and other fraction represent the same fraction. For example, 1/2, 2/4, and 3/6 are equivalent fractions 2/4 after dividing will give 1/2 and similarly, 3/6 will also give 1/2. They are all comparable fractions since they represent the same amount of a whole.

Like Fractions:

Fractions can also be divided into Like and unlike fractions.  If all the denominators of two or three fractions are the same the fractions are said to be a like fraction. In the case of three examples 3/5, 2/5, and 4/5 they have the same denominator 5 as common so they are said to be like fractions. A fraction calculator helps in solving two or three fractions simultaneously.

Unlike Fractions:

Unlike fractions, they are those fractions with different denominators. It is the opposite of fractions. For example, 1/3, and 2/7 are two unlike fractions as they have different denominators. 3 and 7 respectively.

Reciprocal of a Fraction

A fraction's reciprocal is obtained by swapping the numerator and denominator. The inverse of a number let say 3/5 is 5/3. In general term a/b the reciprocal of it is b/a. 

Unit fraction:

A fraction is said to be a unit fraction if its numerator has 1. For example 1/5, 1/7, and 1/11 are all unit fractions.

Complex Fraction:

If a denominator or numerator of a fraction is in fraction form it is called a complex fraction. If both are in fraction form it can be a complex fraction. For example (2/7)/7, 3/(2/5), (3/4) / (1/2) are complex fractions. The fractions calculator is an online tool that can simplify two or more fractions.

Decimal Fraction

A decimal fraction can be written in the form upon 100 or 10 or 1000 etc. that means the denominator is in power of 10. It can be better understood with example 0.75 can be expressed as 75/100. 

These are some examples of common fractions. Each type has a specific function and is utilized in a variety of mathematical and real-world scenarios.

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