basic mathematics image
 basic mathematics image

Proper and improper fractions. Mixed numbers



A concise but great lesson about improper and proper fractions and mixed numbers.



Improper fractions:

Fractions with a numerator that is bigger than the denominator.

For instance, the following fractions are improper.

9 / 2
   ,  
7 / 4
,and  
8 / 3


Proper fraction:

A fraction with a numerator that is smaller than the denominator.

For instance, the following are all proper fractions.

2 / 3
   ,  
1 / 4
,and  
6 / 8


Mixed number:

A number written as the sum of a whole number and a proper fraction.

For instance,   2 +
1 / 3
  is a mixed number.


The + sign is usually omitted so as to write   2
1 / 3


Mixed numbers can be converted to improper fractions and vice versa.

In our example above,

2
1 / 3
=   
7 / 3


To get  
7 / 3
 multiply 2 by 3 and then add 1. Keep the same denominator.


The above is a shortcut!

To get 
7 / 3
,you will normally add
 
2 / 1
  and  
1 / 3


Using the shortcut however takes less time!

Notice that the denominator for 2 is 1 since 2 =  
2 / 1


Converting to a mixed number

You can also convert an improper fraction to a mixed number

Say you want to convert  
13 / 5
 to a mixed number


Ask yourself, " How many 5 can go into 13? " The answer is 2

2 is your whole number piece of the mixed number

What is the remainder of this division? 5 × 2 = 10 and 13 - 10 = 3

3 is the numerator of the fraction piece

The denominator remains the same, so it will be 5

The mixed number is 2
3 / 5


Another example will make this crystal clear may be

Convert  
25 / 6
to a mixed number


Ask yourself, " How many 6 can go into 25? " The answer is 4

4 is your whole number piece of the mixed number

What is the remainder of this division? 6 × 4 = 24 and 25 - 24 = 1

1 is the numerator of the fraction piece

The denominator remains the same, so it will be 6

The mixed number is 4
1 / 6



Test your knowledge with the quiz below:





Still struggling with fractions? Get rid of your fears and frustrations once and for all!

Buy my ebook. It offers a thorough coverage of fractions!


ebook-image






Page copy protected against web site content infringement by Copyscape





worksheets-banner










Copyright © 2008-2015. Basic-mathematics.com. All right reserved

Are you a fan of this site? Support us     Our awards!     Our partners     About me     Disclaimer     Build your website!     Advertise on my site
    Try our free toolbar     Like us on Facebook     Take our survey     Illustrated fractions     Educational math software     Math jobs     Best Teacher Sites Now     Teachers/Students tools     Search math jobs     Algebra ebook     Fraction ebook     Geometric formulas ebook