Basic Fractions

A fraction is a measure of sharing .

 

Example

What fraction of these counters is yellow ?

   one eighth or one in eight of these counters is yellow

 

Common fractions are written in the form

   

The top number (numerator)  is divided (÷) by
The bottom number ( denominator)

 

 A proper fraction has a smaller numerator
 than denominator.

Examples

3       32     
4       37

 

An improper fraction has a larger numerator, the top is larger than the bottom.
These are often called vulgar or top heavy fractions.

 

 

Examples

13          39     
4           37

Equivalent fractions

Simplifying fractions

To simplify ( or cancel) a fraction, look for a whole number which divides exactly into both
the top number ( numerator) and the bottom number (denominator).
Keep repeating until you cannot continue - remembering that even numbers can always be divided by 2,
and that numbers ending in 5 or 0 can be divided by 5.

 

Examples

           

 

What if you don’t know your tables ?
Try dividing top and bottom by 2, 3, 5, or 10

                       

Alternatively

(This method uses prime factors )

• Divide by each prime number in turn, until you cannot divide exactly by that number. Continue until you reach 1.
• Write the number as the product of its prime factors.
• Cancel out terms
• Multiply

Example

simplify  

 

 

Converting improper  fractions to mixed numbers

Divide the numerator (top) by  the denominator (bottom)
Write the quotient, then put  the remainder over the denominator.
Simplify  if possible.

Example

Examples

Converting mixed numbers to improper fractions

Times the whole number by the denominator (bottom),
Add the numerator (top).
Write this answer on top of the denominator.

Examples

   

 

Calculating fractions of amounts

 

Examples

   

 

Learn

adding/subtracting fractions
multiplying fractions
dividing fractions

Algebraic fractions