Introducing Fractions

What are Fractions?

Fractions are very commonly used in mathematics. They represent a part of any number that has equal parts (usually a whole number). Fractions are made up of three parts. The numerator (which is the number on top), the division line which separates the two numbers (it is usually horizontal but it can also be at an angle) and the denominator (which is the number on the bottom). The division line has the same meaning as a normal division sign and consequently, a fraction is the same as a division (½ is equal to 1 ÷ 2). This is true for all fractions. Where do we use them? Fractions can appear in almost every mathematical expression. We often use them instead of decimals in problems as they are easier to work with. In algebraic expression, fractions represent division while in other cases they are used as a way to present ratios. Some fractions such as 1/2, 1/3, 1/4 and 3/4 are also used commonly in our everyday life. For example when cutting pie, reading the clock and paying at a shop. The 3 Main Types of Fractions
Proper Fractions Proper fractions are simple fractions such as 1/2 and 1/7 where the numerator is smaller than the denominator and both are integers. They are rational numbers and the denominator can be any integer but zero. When converting a proper fraction into a decimal, the result should be bigger than -1 but smaller than 1. Examples:
Improper Fractions Improper fractions are also simple fractions but their numerator is larger than their denominator. For example, 3/2, 9/4 and 5/3 are improper fractions. Another way to determine whether a fraction is improper or not is to see if the number you get when converting it into a decimal is larger than 1 or smaller than -1. If this is the case, it is an improper fraction. Examples:
Mixed Numbers A mixed number is composed of an integer which is not 0 and a proper fraction. It is created when transforming an improper fraction into a proper fraction. For example, if you transfer 3/2 into a mixed number you get 1 ½. You are basically making the fraction proper by extracting as many whole numbers as possible and then adding them to the proper fraction so that you end up with a number that is not 0 and a proper fraction. Examples:

Shading Fractions

Underneath, there are a few shaded shapes which represent fractions. To test your understanding identify what fraction is shaded and click the image to check your answer (the image will become larger and the correct answer will be displayed on top of the image).
1/3 2/3 1/1
Moving on to some more Challenging Stuff! This page should have taught you the basic principles of Fractions. If you have understood everything, you should move on and start working with fractions. Try simplifying and finding equivalent fractions or even calculating with fractions. Please share this page if you like it or found it helpful!
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Chapter 3.0:  Learning Outcomes Students will know the definition and components of a fraction (numerator, denominator and division line)! Students will know why we use fractions (over decimals)! Students will know and be able to identify the 3 different types of fractions! Students will know how to shade (graphically represent) fractions!
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