Topic outline

  • Outcomes

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    In this course you will learn about:

    1. Equivalent forms of fractions.
    2. Addition of fractions.
    3. Subtraction of fractions.
    4. Multiplication of fractions.
    5. Division of fractions.

  • What are fractions?

    The real number system is made up of rational and irrational numbers. All rational numbers can be written as an integer over an integer, one word for "integer over an integer" is fraction. But, fractions make more sense when you can "see" them.

    James is about to eat the last biscuit but his friend Simon would really like some of the biscuit too. So, James breaks the biscuit into 2 pieces and shares it with Simon. The action of breaking a whole thing into smaller pieces is what fractions are all about. [edit: I suggest writing the faction labels in the image in lower case]

    Biscuit broken in half

    How fractions work

    Numerator an denominator make up a fraction

    The denominator tells you how many parts the whole was divided into and the numerator tells you how many parts of the whole you have.


    • Equivalent fractions

      Fractions that have the same value are called equivalent fractions. For example, \( \frac{1}{2}=\frac{2}{4} \); by multiplying the numerator and denominator by the same number the fraction keeps the same value, in this case we have multiplied both by 2. To learn more about making fractions equal you can watch the next video. 


    • Types of fractions

      Common fractions or proper fractions are fractions where the numerator is a smaller value than the denominator, for example, \( \frac{1}{4} \).

      In an improper fraction the numerator is larger than its denominator, for example, \( \frac{8}{3} \). 

      A mixed fraction has a whole number part and a proper fraction part, for example, \(1\)\( \frac{3}{4} \).

      In the next video the types of fractions are explained, pause to think about the answers when the video asks you to. 

    • Exercise: "Seeing" fractions

      This "best hands-on fraction exercise" helps you to see the concept of breaking up a whole into smaller parts more clearly. 

    • Fraction apps

      If you would like to explore the basics of fractions a bit more, here are some free apps that you can download from the app store on a smart device. Click on each one to find out more.

      Fraction Mash

      Visual Fractions

      Fractions, by the Math Learning Center



  • Addition of fractions

    To add fractions the denominators of the fractions must be the same. 

    Example

    \( \frac{1}{4} + \frac{2}{4}=\frac{3}{4} \) because the denominators are both \(4\) you can simply add the numerators. 

    In the next video the method of adding fractions is explained using a worked example. 

    • Finding the lowest common denominator

      To add or subtract fractions with different denominators, you must find the lowest common denominator (LCD) sometimes also called the lowest common multiple (LCM). 

      To add fractions with different denominators you must:

      1. Find the lowest common denominator (LCD). 
      2. Rewrite each fraction into an equivalent form using the LCD.
      3. Add the numerators of fractions, keeping the LCD as the denominator.
      4. Simplify the final answer if needed.
      In the next example you will learn the method for finding the LCD. 


      After you have watched the video try the next activity to test your knowledge.
    • H5P icon
      Activity: Add fractions 1 H5P
    • H5P icon
      Activity: Add fractions 2 H5P
    • H5P icon
      Activity: Add fractions 3 H5P

  • Subtraction of fractions

    The method for subtracting fractions is the same as for adding fractions. You can only subtract fractions with the same denominator.

    To subtract fractions with different denominators you must:

    1. Find the lowest common denominator (LCD). 
    2. Rewrite each fraction into an equivalent form using the LCD.
    3. Subtract the fractions, keeping the LCD as the denominator.
    4. Simplify the final answer if needed.
    This method is discussed in detail in the following video. 

  • Multiplication of fractions

    To multiply fractions you multiply numerator by numerator and denominator by denominator. The word "of" is also used to show multiplication in Maths.

    Example

    \( \frac{2}{3} \times \frac{4}{5}= \frac{2 \times4 }{3 \times5} = \frac{8}{15} \)

    Mixed numbers must be changed to improper fractions before multiplying. This is explained in the following video lesson.  

    • Exercise: Multiply mixed fractions

      Practise your skills of multiplying fractions by trying this exercise: Multiply mixed numbers. 

  • Division of fractions

    Dividing by a fraction is the same as multiplying by its reciprocal (where the numerator and denominator change places). 

    Example

    \( \frac{6}{5} \div \frac{2}{3}= \frac{6}{5} \times \frac{3}{2} = \frac{18}{10}= \frac{9}{5}= 1\frac{4}{5} \)

    Mixed fractions must be converted to improper fractions before dividing. The steps for dividing fractions is covered in detail in the following video.