Fractions


A proper fraction is a number found between 0 and 1 that is expressed with a numerator on top of a denominator found on the bottom separated by a line,
much like the symbol used in division       ÷

It is useful to see fractions as a part of whole unit


fractions are also a key part of decimals and percentages

for example:   a quarter =   ¼   =  1 ÷ 4  =  0.25  =  25/100  =  100%
                   a half       =   ½   =  1 ÷ 2  =  0.50  =  50/100  =    50%


common fractions can be used as benchmarks for calculations 
     0      ¼       ½        ¾        1 

an improper fraction is when the top (numerator) is larger than the bottom (denominator)
this improper fraction will therefore be a number larger than one
                5
                2
improper fractions can be converted into mixed numbers


a mixed number consists of both a whole number and a fraction
              
mixed numbers can also be converted into improper fractions


This is a great hip-hop video about fractions and their role in decimals & percentages
pay close attention the first half of the video for converting improper fractions to a mix number
(this video is about two and a half minutes long)

When multiplying fractions you simply multiply the numerators with the numerators
and multiply the denominators with the denominators

2    x    4    =     8
3          5          15

This is another great video illustrating the idea of cross cancellation
a process of elimination that can be done prior to multiplying fractions
              this will make later calculations less complicated
                          please note: negatives are used
                      (this video is about a minute and a half)

When dividing fractions you simply switch the division symbol to a multiplication symbol
and then flip the second fraction (a flipped fraction is called its reciprocal)
and now you have a simple multiplication of tops with tops and bottoms with bottoms

4      ÷     2      =       4       x     3    =      12
5             3               5               2            10

Remember how to divide fractions: (1st fraction stays the SAMECHANGE ÷  to  x , FLIP 2nd fraction)


All fractions (proper and improper) can be expressed in their simplest form
this can be done by finding common factors in both the numerator and the denominator.
(What you do to the top, you do the same to the bottom)

12 ÷ 2   =                    15 ÷ 5     =    3                111 ÷ 3     =    37 
10 ÷ 2   =    5                 2÷ 5            4                702 ÷ 3          234



The similarities between fractions can also be seen in the following examples...




1   is in it's simplest form
3


2   can be simplified further
6


 4  is not expressed in it's simplest form
12


Using a common bottom is also an ideal way to compare fractions! (< , > or =) 

When you are adding and subtracting fractions you must first find a common denominator
the best choice is the Lowest Common Multiple (LCM) this denominator does not change for the final answer

4   −    2         =      12     −     10       =       2     
5         3                  15            15               15

a common mistake can be seen in this OOPS!!! video

don't make the same goof when adding and subtracting fractions
                 (this video is about a minute and a half)

Further hints...

Top 3 Rules of Fractions

#1. Remember, what you do to the bottom of a fraction you do the same to the top and vice-versa
what you do the top you do the same to the bottom.

#2. To Add and Subtract fractions you MUST HAVE common bottoms. (Find this using LCM)

#3. You CANNOT Multiply or Divide mixed numbers (change all mixed numbers into improper fractions)

more...
you can add and subtract with mix numbers and improper fractions (provided there is a common bottom) 
and even use the concept of borrowing when needed in subtracting mix numbers

ONLINE TESTS

Test your knowledge of fractions using the following links...

test your general knowledge of fractions at
(there are three levels of difficulty to choose from)

test your skills simplifying fractions (proper and improper) at
(there are three levels of difficulty to choose from)

test your ability to compare and order fractions at
(there are three levels of difficulty to choose from)