MATHEMATICS 19 



When several quantities are connected by the various 

 signs indicating addition, subtraction, multiplication, and 

 division, the operation indicated by the sign of multiplication 

 must always be performed first. Thus, 2 + 3X4 equals 

 14, 3 being multiplied by 4 before adding to 2. Similarly, 

 10-J-2X5 equals 1, since 2X5 equals 10, and 10 -J- 10 equals 1. 

 Hence, in the preceding case, if the brace were omitted, the 

 result would be \; whereas, by inserting the brace, the 

 result is 36. 



Following the sign of multiplication comes the sign of 

 division in its order of importance. For example, 5 9-f-3 

 equals 2, 9 being divided by 3 before subtracting from 5. The 

 signs of addition and subtraction are of equal value; that is, 

 if several quantities are connected by plus and minus signs, 

 the indicated operations may be performed in the order in 

 which the quantities are placed. 



There is one other sign used, which is neither a sign of 

 aggregation nor a sign indicative of an operation to be per- 

 formed ; it is ( = ) , and is called the sign of equality; it means 

 that all on one side of it is exactly equal to all on the other 

 side. For example, 2 = 2, 5-3 = 2, 5 X (14 -9) = 25. 



Having described the signs used in formulas, the formulas 

 themselves will now be explained. First, consider the well- 

 known rule for finding the safe load that a rectangular 

 white-oak post will carry, which may be stated as follows: 



From unity subtract 1 one-hundredth of the dividend 

 obtained by dividing the length of the post in inches by the 

 least dimension of its cross-section in inches. Multiply the 

 remainder by 1 ,000 times the area of the post section in square 

 inches. The result is the safe load the post will carry. 



This rule is rather complicated, and it can be greatly 

 simplified by putting it in the form of a formula. 



An examination of the rule will show that three quantities 

 (viz., the area of the section, the length, and the least 

 dimension of the cross-section) are involved. Hence, the 

 rule might be expressed as follows: 



Safe load = 1 ,000 X area of section in square inches 

 length in inches \ 



X 1- 



100 X least dimension of cross-section in inches/ 



