Fraction Arithmetic

 
 1  2
3
  +  
 2  3
4
 
=
  (1 x 3 + 2)
3
  +  
  (2 x 4 + 3)
4
Convert fractions to improper form by multiplying the whole number by the denominator and adding the result to the numerator
=
  5
3
  +  
  11
4
Complete the arithmetic to get the fractions to improper form
 
 
Determine the Lowest Common Multiple of the denominators. lcm(3, 4) = 12
=
  5 x 4
3 x 4
  +  
  11 x 3
4 x 3
Scale the left and right fractions such that they have the Lowest Common Multiple as the new denominator
=
  20 + 33
12
The numerators can now be added, as they have the same denominator. Do not add the denominators!
=
  53
12
Complete the arithmetic for the numerator and denominator
=
 4  5
12
Convert the answer to a Proper Fraction by extracting whole numbers from top-heavy fractions.

Fraction Arithmetic

StatsFiddle's fraction arithmetic calculator allows fractions to be added, subtracted, multiplied and divided.

For addition or subtraction of fractions, it is important to find the Lowest Common Multiple of both Denominators. Once the lcm has been determined, scale up the numerators and denominators of both fractions to get a common denominator. Once this is done, the numerators can then simply be added or subtracted from eachother.

For multiplication, convert both fractions to improper fractions (if not already done), and then simply multiply numerator by numerator, and denominator by denominator.

For division, convert both fractions to improper fractions (if not already done), and then simply multiply the left numerator by right denominator (as the result numerator), and left denominator by right numerator (as the result denominator).

As a final step for all types of arithmetic, remember to check the result for Reduction as well as extract any whole numbers if the result is an improper fraction.