Fractions. Representation, mixed numbers and operations

22/01/2026

The online fraction simulations on this page will help you better understand the concept of fractions in mathematics. We will discover different ways of representing fractions, mathematical operations with fractions, and what mixed numbers are.

What are fractions in mathematics

Fractions are a fundamental part of mathematics. They are used to represent numbers that are not whole numbers, allowing to express relationships of parts of a whole. A fraction consists of two parts: the numerator and the denominator. The numerator indicates the number of parts that are taken or considered, while the denominator indicates how many parts the whole is divided into. For example, in the fraction 3/4, the numerator is 3 and the denominator is 4.

Representation of fractions in mathematics

Fractions can be represented in different ways. In addition to the common fraction notation, they can be expressed in decimal or percent form. For example, the fraction 1/2 is equal to 0.5 in decimal form and 50% in percent form.

Mathematical operations with fractions

Fractions allow you to perform mathematical operations such as addition, subtraction, multiplication and division. To add or subtract fractions, it is necessary to have the same denominator. If the denominators are different, common denominators must be found using the least common multiple (LCM) technique. To multiply fractions, multiply the numerators together and the denominators together. To divide fractions, multiply the first fraction by the inverse of the second fraction.

Mixed numbers

Mixed numbers are a combination of whole numbers and fractions. They are composed of a whole part and a fraction. For example, the mixed number 3 1/2 is composed of the whole number 3 and the fraction 1/2.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Intro
Builder
Mixed
Matcher
Equality

Introduction

This simulation allows you to select among several functions and represent their derivative. It is possible to check how the derivative is modified by varying the parameters of the functions.

Build a fraction

Build fractions from graphs and numbers to earn stars in this fraction game or explore in the Fractions Laboratory. Test yourself on any level you want – try to collect as many stars as you can!

Mixed numbers

Explore fractions while serving yourself 1 and 1/2 cups of chocolate cake and drinking it with 1/3 cup of water! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the mixed numbers game. Try your hand at any level you like – try to collect as many stars as possible!

Fraction Matcher

Match shapes and numbers to earn stars in this fraction game. Test yourself at any level you like – try to collect lots of stars!

Equality of fractions

Build equivalent fractions with different denominators. Match shapes and numbers to earn stars in the game. Test yourself on any level you like – try to collect lots of stars!