3        12
     ---  =   ----
      4        16

   As you will recall 3/4 can be transformed to 12/16 by multiplying
   both its numerator and denominator by 4. Whenever you see this
   kind of relationship you are dealing with equivalent fractions.

   CROSS-PRODUCTS: The short-cut way to quickly tell if two fractions
   are equivalent is to multiply the numerator of the first by the 
   denominator of the second (your first cross-product). Then multiply the 
   denominator of the first by the numerator of the second (your second
   cross-product). If the two cross-products are equal then your
   fractions are equivalent.

   Cross-product one: 3 x 16 = 48

   Cross-product two: 4 x 12 = 48

      2          6
     ---   =   ----
      5         15

     Cross-product one: 5 x 6 = 30
    
     Cross-product two: 2 x 15 = 30

     Since the cross-products are equal, the fractions must
     be equivalent.