2 MATHEMATICS 



raised. Thus, 8 2 means that 8 is to be squared; that is, 8X8 

 = 64. Again, 8" means that 8 is to be cubed; that is 8X8X8 

 = 512. 



The radical sign, V , means that some root of the ex- 

 pression under the vinculum is to be found. If it is used 

 without a small index figure, it indicates square root; thus, 

 V64 = 8. The sign ^f~ indicates the cube root; thus, \27 = 3. 



The signs : : : : indicate proportion; thus, 3 : 4 : : 6 : 8 

 is read 3 is to 4 as 6 is to 8. Instead of the sign : : the equality 

 sign = is often used; thus, 3:4 = 6:8. 



The signs ' " mean degrees, minutes, and seconds, respec- 

 tively; thus, 60 15' 15" is read 60 degrees 15 minutes 16 seconds. 



The signs ' " also mean feet and inches, respectively; thus, 

 7' 6" is read 7 feel 6 inches. 



The symbol TC (pronounced pi) means the ratio of the cir- 

 cumference of a circle to its diameter and has a value, near 

 enough for most practical purposes, of 3.1416. 



FRACTIONS 



COMMON FRACTIONS 



The numerator of a fraction is the number above the bar, 

 and the denominator is the number beneath it; thus, in the 

 fraction f , 3 is the numerator and 4 is the denominator. Two 

 or more fractions having the same denominator are said to 

 have a common denominator. By reducing fractions to a com- 

 mon denominator is' meant finding such a denominator as will 

 contain each of the given denominators without a remainder, 

 and multiplying each numerator by the number of times its 

 denominator is contained in the common denominator. Thus, 

 the fractions J, i, and & have, as a common denominator, 

 16; then t = A; i = tl; A = &. 



By reducing a fraction to its lowest terms is meant dividing 

 both numerator and denominator by the greatest number 

 that each will contain without a remainder; for example, in 

 H, the greatest number that will thus divide 14 and 16 is 2; 



14-^2 



so that, - = I, which is jj reduced to its lowest terms. 



16-=-2 





