Fraction Operations

Adding Fractions

• Make sure the denominators ( bottom numbers) are the same, by finding the Lowest Common Multiple. LCM
• Add the numerators (top numbers)

 Leave the bottom  numbers alone.

• Simplify if possible.
• Convert to a mixed number.

Examples

                                 

 

Subtraction is similar

   

Vedic Method

This is an ancient method from India.
(more information from Vedic Maths.org)

Multiply bottom numbers and put in sign.

Multiply top left by  bottom right
Multiply bottom left by  top right

 Convert to mixed number.

Examples

 

Subtraction is similar

        
 

Examples

 

Multiplying fractions

Simple fractions

1. Multiply Top line
2. Multiply bottom line.
3. Top line over bottom line
4. Simplify if you can.

Examples

 

     If you spot that you can  simplify first:-

• Simplify
• Multiply Top line                      S M M S
• Multiply bottom line.
• Simplify again if necessary.

Examples

 

Multiplying  Mixed number fractions

• Change from a mixed number to an improper  fraction.
• Simplify
• Multiply Top line
• Multiply bottom line.                    S M M S  
• Simplify again if necessary.
• Convert  back to mixed number if necessary.

 

Examples

 

Dividing fractions

 

 The inverse of a number is that number turned upside down.
 The inverse has symbol  .

 

 

     To divide a fraction, multiply it by its inverse.

•  Turn the fraction to the right of the  ÷ sign upside down.
•  Change the ÷ sign to a x. 
• Multiply the fraction as normal.

Examples

 

Alternatively

 

Example

 

So

  

 

 

It also works nicely with algebraic fractions: -