Operations with fractions

1. ADDITION AND SUBTRACTION

To add or subtract fractions we need them to have the same denominator, then we add or subtract the numerators:

                                      

+ = =

 

                                        

+ = =

NOTE: If they haven’t got the same denominator, we reduce to common denominator:

 

2. MULTIPLICATION

To multiply fractions, we multiply the numerators and the denominators:

 

3. DIVISION

The inverse of a fraction is another fraction in which we have exchanged denominator  and numerator:

NOTE: If we multiply the fraction by its inverse, we obtain 1:

To divide fractions:
    - Multiply the numerator of the first fraction by the denominator of the second and write the result in the numerator.
    - Multiply the denominator of the first fraction by the numerator of the second and write the result in the denominator.

  
In another way, we can divide fractions by multiplying the first fraction by the inverse of the second fraction:

 

 

Exercise: calculate:

 

 

Solutions: