Fractions Simplified: the Basics


Basic Fraction Terms

A fraction is made up of two numbers separated by a line.  The bottom number is called the denominator. This number tells you how many parts are in your whole number.  For example, if you divide a candy bar into 6 pieces, your denominator would be 6.  The top number is the numerator.  This number tells you how many pieces of the whole you are talking about or using.  For example if you ate 3 of the pieces of that same candy bar, your numerator would be 3.  Your fraction would then be written as 36.

Types of Fractions

There are 4 main types of fractions that children should be able to work with.

  • Proper fractions – A fraction is proper when the numerator is smaller than the denominator. (Like our example above 36)  This means that you are using less than one whole.
  • Fractions equal to 1 – When the numerator and denominator of a fraction are the same, the fraction is equal to 1.  For example, the fraction 66 is exactly the same as a whole object. (If a candy bar is broken in 6 pieces, and you eat all 6 pieces, you have eaten the whole candy bar!)  Therefore, children should recognize that 66 = 1.
  • Improper fractions – An improper fraction is a fraction that is greater than 1. This means that the numerator is larger than the denominator.  For example 86 is an improper fraction. Because it is larger than a whole, you are actually referring to more than one whole number.  In the case of 86, you are using one whole candy bar (66) and 2 pieces from another candy bar (26).
  • Mixed numbers – Mixed numbers are closely related to improper fractions. In fact, they give you the same information written in a new way.  Mixed numbers include both a whole number and a fraction. The improper fraction 86 can also be written as 126 because it is referring to 1 whole candy bar and 26 more of another candy bar.

Children should be able to recognize and name these types of fractions. You can make it into a game by writing different fractions on sticky notes or index cards and having them sort the fractions under the correct type of fraction.  In our next post, we will talk more about the relationship between mixed numbers and improper fractions.  We will also discuss why children need to understand that relationship. What do you think? Are fractions easy or hard for you to work with?

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