ARITHMETIC. 



of the multiplier are lost in the addition, 

 we omit them. Hence may be inferred 

 the following 



Rule. Place the multiplier under the 

 multiplicand, and multiply the latter suc- 

 cessively by the significant figures of the 

 former, by placing the right-hand figure 

 of each product under the figure of the 

 multiplier irom which it arises; then add 

 the product. 



Example. 



7329 93956 



365 8704 



36645 8758.4 



43974 657692 



21987 751648 



2675085 



817790024 



A number, which cannot be produced 

 by the multiplication of two others, is 

 called a prime number; as 3, 5,7, 11, 

 and many others. A number, which may 

 be produced by the multiplication of two 

 or more smaller ones, is called a compo- 

 site number. For example, ~7, which 

 arises from the multiplication of 9 by 3 ; 

 and these numbers (9 and 3) are called 

 the component parts of 27. 



1. If the multiplier be a composite 

 number, we may multiply successively 

 by the component parts. 

 Example. 



7638 by 45, or 5 times 9, 7638 



45 ' __9 



38190 68742 



30552 5 



343710 



543710 



by repeating the operation, using the 

 multiplier for the multiplicand, and the 

 multiplicand for the multiplier. It may 

 also be proved by division, or by casting 

 out the 9's ; of which afterwards : and an 

 account, wrought by any contraction, 

 may be proved by performing the opera- 

 tion at large, or by a different contraction. 

 The following examples will serve to 

 exercise a learner in this rule. 



Because the second product is equal 

 to five times the first, and the first is equal 

 to nine times the multiplicand, it is obvi- 

 ous that the second product must be five 

 times nine, or forty-five times as great as 

 the multiplicand. 



2. If the multiplier be 5, which is the 

 half of 10, we may annex a cypher, imd 

 divide by 2. If it be 25, which is the 

 fourth part of 100, we may annex two 

 cyphers, and divide by 4. Other con- 

 tractions of the like kind will readily oc- 

 cur to the learner. 



3. To multiply by 9, which is one less 

 than 10, we may annex a cypher, and sub- 

 tract the multiplicand from the number 

 it composes. To multiply by 99,999, or 

 any number of 9's, annex as many cy- 

 phers, and subtract the multiplicand. 

 The reason is obvious ; and a like rule 

 may be found, though the unit place be 

 different from 9. Multiplication is proved 



COMPOUND MULTIPLICATION. 



1. If the multiplier do not exceed 12, 

 the operation is performed at once, be- 

 ginning at the lowest place, and carrying 

 according to the value of the place. 



