Fraction Rules

Operation Explanation Example
Multiply fractions Multiply both numerators and denominators. You don't need the same denominators.
 1     3     1 X 3     3
--- X --- =  ------ = ---
 2     5     2 X 5    10
Fraction addition - Same denominators Just add the numerators. Keep the same denominator.
 1     2     1 + 2    3
--- + --- =  ----- = ---
 8     8       8      8
 Note:Don't add 
      denominators.
Changing denominators Divide the denominator you want by the denominator you have, then multiply by the numerator to get your new numerator.
 3     ?   8/4 = 2;     6
--- = ---            = ---
 4     8   2 x 3 = 6    8
Fraction addition with different denominators If one denominator divides evenly into the other, change to the higher denominator and add.
 1     1     2     1     3
--- + --- = --- + --- = ---
 2     4     4     4     4
If the denominators don't divide evenly, then multiply them together to get your new denominator. Change denominators, then add
  Note: Since 3 doesn't go
  into 5, use 3 x 5 = 15.
 1     3     5     9     14
--- + --- = --- + --- = ---
 3     5     15    15    15
Changing mixed numbers to improper fractions Find the number of unit fractions in the whole number, then add the fractional part of the mixed number.
   2     6     2     8
2 --- = --- + --- = ---
   3     3     3     3
  Note: 2 is 6 thirds.
Changing improper fractions to mixed numbers Divide the numerator by the denominator to get the whole number. Then the fraction is the remainder over the denominator.
     8    8/3 = 2 with a 
For ---   remainder of 2 so
     3    the mixed number 
          is 2 2/3
Dividing fractions To divide one fraction by another, invert (turn upside-down) the second fraction, then multiply.
3/4    3     8    24
--- = --- X --- = --- = 6
1/8    4     1     4
Note: This means there are  
      6 eighths in 3/4.