There's a total number of six different types of fractions. The three major types are proper fractions, improper fractions, and mixed fractions. Let's explore the properties of a fraction and define each type.
What Is a Fraction?
A fraction is a number that has a numerator (the top number) and a denominator (the bottom number):
We use the term fraction as a descriptor for parts of a whole. The denominator represents the whole number part of a fraction. The numerator represents the number of equal parts that the whole will be divided into.
If you cut a pizza into four equal pieces, your denominator would be 4. If you wanted to show how much of the pizza one slice is, you'd use the unit fraction. This refers to fractions with a numerator of 1. So here's the fraction that describes each equal slice:
The shaded part below also represents one-fourth of the pizza:
The relationship between each different denominator and each different numerator determines what kind of fraction it is.
Let's take a look at the different types of fractions.
In this type of fraction, the numerator is smaller than the denominator:
The quotient, or division, of a proper fraction will always result in a value less than one.
This is a fraction where the numerator is larger than the denominator:
Because the value of the numerator is larger, the quotient of an improper fraction will always result in a value greater than or equal to 1.
This type of fraction occurs when you combine a natural number and a fraction:
A mixed fraction can be converted into an improper fraction by multiplying the whole number by the denominator and adding the numerator. The resulting number will serve as a numerator over the original denominator:
Because mixed fractions have a whole number part, they are greater than the value of 1.
Like, Unlike, and Equivalent Fractions
The other three types of fractions are like fractions, unlike fractions, and equivalent fractions. Here are definitions and examples of each type:
Like fractions: Sets of fractions that all have the same denominators
Unlike fractions: Sets of fractions all with different denominators
Equivalent fractions: A group of two or more fractions that, when simplified, represent the same value
Why You Need to Know Different Types of Fractions
When you can decide whether a fraction is improper, proper, or mixed, you can determine if its quotient will be greater, less than, or equal to 1. Furthermore, you can group fractions based on their similarities or dissimilarities by determining if they are like, unlike, or equivalent fractions.