ARITHMETIC 



353 



ARITHMETIC 



OUTLINE OF DEPARTMENTS OF ARITHMETIC 



I. Notation and Numeration 



(1) Arabic numbers 



(2) Roman numbers 



( 3 ) Notation and numeration of money 

 (4) Use of arithmetical signs 



II. ll:isi<- Processes 



(1) Addition 



(2) Subtraction 



(3) Multiplication 



(4) Division 



III. Common Fraction* 



( 1 ) Notation and numeration of frac- 

 tions 



(2) Reduction 



(3) Addition of fractions 



(4) Subtraction of fractions 



(5) Multiplication of fractions 



(6) Division of fractions 



(7) Complex fractions 



I \ . Factors and Divisors 



(1) Tests of divisibility 



(2) Factoring 



(3) Cancellation 



(4) Greatest Common Divisor 



(5) Least Common Multiple 



V. Decimal Fractions 



(1) Notation and numeration of deci- 



mals 



(2) Reduction 



(3) Addition of decimals 



(4) Subtraction of decimals 



(5) Multiplication of decimals 



(6) Division of decimals 



\ I. Denominate Number* 



(1) Measure 



(a) Of value 



(b) Of wrinht 



(c) Of length 

 l) Of surface 



(e) Of volume 

 <f) Of capacity 

 (g) Of time 



(2) Reduction 



(3) Addition 



(4) Subtraction 



(5) Multiplication 



(6) Division 



(7) Longitude and tlnv 



\li. nelermlimlon of Arras mm* 



\ ..li 



(4) Practical measurements 



(a) Rooflng and flooring 



(b) Plastering and painting 



(c) Masonry 



(d) Lumber measure 



(e) Tanks and bins 



VIII. Percentage 



(1) Principles 



(2) Applications 



(a) Profit and loss 



( b ) Comm ission 



(c) Discount 



(d) Taxes 



(e) Insurance 



(f) Interest 



1. Simple 



2. Compound 



(g) Promissory notes 

 (h) Exchange 



1. Domestic 



2. Foreign 



(i) Stocks and bonds 



IX. Ratio and Proportion 



(1) Ratio 



(2) Simple proportion 



(3) Partnership 



\ Powers and Roots 



( 1 ) Involution 



(a) The square of numbers 



(b) The cube of numbers 



(2) Evolution 



(a) Square root 



(b) Cube root 



(1) Angular measure 



(2) Area of surface* 



(3) Volume of solids 



pletcly dominated by commerce that it waa 

 no longer mentioned in the curricula of even 

 the best schools. 



Among the Romans and the Greeks we find 

 some plea for the study of arithmetic for its 

 culture value. Plato, Aristotle and Pythagoras 

 all set value upon it as a cultural subject. 

 Plato says, "It awakens the soul/' Pythagoras 

 places it with gymnastics and music as the 

 three great educational subjects. He names 

 the subjects in the order gymnastics, music 

 and mathematics. "By the first the pupil waa 

 -. Aliened; by the second, purified; and by 

 the third, perfected and made ready for the 

 society of the gods." A.H. 



ny school-book publishing firm for 

 -tic texts. 



