• I. Adding fractions.
  
  • a. If both fractions have the same denominators, then simply add their numerators without changing denominator.
    
  • b. If fractions have different denominators, then you can't add them directly. In this case you need to convert fractions to common denominator first. After that you are ready add them like in point (a).
    
• II. Subtracting fractions.
  
  • a. If both fractions have the same denominators, then simply subtract their numerators without changing denominator.
    
  • b. If fractions have different denominators, then you can't subtract them directly. In this case you need to convert fractions to common denominator first. After that you are ready subtract them like in point (a).
    
• III. Multiplying fractions.
  
  • To perform fractions multiplication you have to multiply numerator of first fraction by numerator of second fraction and then denominator of first fraction by denominator of second one.
    
• IV. Dividing fractions.
  
  • a. At the beginning you need to inverse the second fraction. To achieve it - simply swap numerator and denominator in second fraction.
    
  • b. Next, multiply first fraction by inversed second fraction - exactly like in section (III).
    

Simply enter your fractions into form below and Calculla will compute their sum (addition), difference (subtraction), product (multiply) and quotient (division) for you. For each of those operations, Calculla will show you how to get proper result step-by-step:

• I. Remove wholes. In this step we convert mixed number to improper fraction if needed. However, if your fractions have no wholes part, we simply skip this step.
  
  
• II. Perform the appropriate action. This step depends on type of operation we're performing:
  
  • Addition - at the beginning we bring fractions to common denominator, next we add their numerators.
    
  • Subtraction - at the beginning we bring fractions to common denominator, next we subtract their numerators.
    
  • Multiplication - simply we multiply numerator of first fraction by numerator of second one and denominator of first fraction by denominator of second one.
    
  • Division - at the beginning we replace division by multiplication by the inverse, next we follow multiply steps.
    
• III. In this step we already have proper result. However probably not in the simplest form yet, so it may be not yet final.
  
  
• IV. Remove improper fraction. If our result is an improper fraction (i.e. its numerator is greater than denominator) we pull out wholes part before fraction. In this way we create the mixed number.
  
  
• V. Reduction to the simplest form. In this step we reduce the fraction to the simplest possible form.
  

• khanacademy.org: video about adding and subtracting fractions
  
• themathpage.com: tutorial about adding and subtracting fractions
  
• wikipedia: lowest common denominator
  
• mathsisfun.com: .edu.pl: finding common denominator
  
• themathpage.com: multiplying and dividing fractions