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6 Types of Fractions You Need to Know

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):

types of fractions: Example of a fraction

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:

types of fractions: One-fourth

The shaded part below also represents one-fourth of the pizza:

types of fractions: Pizza cut into four slices with one slice shaded

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.

Proper Fractions

In this type of fraction, the numerator is smaller than the denominator:

types of fractions: Example of a proper fraction

The quotient, or division, of a proper fraction will always result in a value less than one.

Improper Fractions

This is a fraction where the numerator is larger than the denominator:

types of fractions: Example of an improper fraction

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.

Mixed Fractions

This type of fraction occurs when you combine a natural number and a fraction:

types of fractions: Example of a mixed 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:

types of fractions: Example of a mixed fraction

types of fractions: Mathematical equation

types of fractions: Mathematical equation

types of fractions: Example of an improper fraction

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

Example of a fraction Example of a fraction Example of a fraction

Unlike fractions: Sets of fractions all with different denominators

Example of a fraction Example of a fraction Example of a fraction

Equivalent fractions: A group of two or more fractions that, when simplified, represent the same value

Example of a fraction Example of a fraction Example of a fraction

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.

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