VULGAR FRACTIONS. 59 



VULGAR FRACTIONS. 



Fractions, or broken numbers, are expressions for 

 any assignable parts of an unit ; and are represented by 

 two numbers, placed one above the otber, with a line 

 drawn between them. 



The figure above the line is called the numerator, ^.nd 

 that below the line, the denominator. 



The denominator shews how many parts the integer is 

 divided into, and the numerator shews how many of 

 those parts are meant by the fraction. 



Fractions arc either proper, improper, single, compound, 

 or mixed, 



1. A proper fraction is when the numerator is less than 

 the denominator: as ^, ^^ -|-, &c. 



2. An improper fraction is when the numerator exceeds 

 the denominator : as y, *-^°, &c. 



3. A single fraction is a simple expression for any num- 

 ber of parts of the integer. 



4. A compound fraction is the fraction of a fraction : as 



T of T' i °f h &c. 



5. A mixed number is composed of a whole number 

 and a fraction : as 8-^3 i7tt> ^^* 



Note. — Any whole number may be expressed like a frac- 

 tion by writing i under it : as \. 



6. The common measure of two or more numbers 25 

 that number, which will divide each of them, without :•;. 

 remainder. Thus 3 is the common measure of 12 and 

 T 5 \ and the greatest number, that will do this, is chilled 

 the greatest common measure. 



7. A number, which can be measured by two or more 

 niln.b-r ., is called their common multiple ; and if it be the 



