Definition/Meaning  Word/Phrase 
fraction with fractions in the numerator or denominator 
complex fraction
,
compound fraction

fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on 
continued fraction

fraction whose numerator is larger than the denominator 
improper fraction

fraction with a numerator smaller than the denominator 
proper fraction

cancel common factors in fraction's numerator and denominator 
reduce
