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 ARITHMETIC K. 37c 26 for a remainder; which fet below, and proceed to under the common name of faftors; and the number the quarters, faying, i quarter borrowed and 3 make 4, arifing from the multiplication of the one by the other which from 1 you cannot, but from 4, the number of quar- is called the produft, and fometimes the fatt, or the ters in 1 C. and o remains, which o added to 1 in the rettangle. If a multiplier confifts of two or more fimajor gives 1 for a remainder; which fet down, and go gures, the numbers arifing from the multiplication of on to the C. which are integers, faying, 1 C. borrow- thefe feveral figures into the multiplicand, are called pared and 9 make 10, which from 4 you cannot, but ticular, or partial produtts; and their fum is called the total produh. from 14, &c. Multiplication then is the taking or repeating of the multiplicand, as often as the multiplier contains unity. Or, III. The Proof of Subtraftion. Multiplication, from a multiplicand and a multiplier Merchants and men of bufinefs ufe no other proof given, finds a third number, called the produft,. which befides a revifal of the work, or running over it a fe- contains the multiplicand as often as the multiplier concond time ; but it is ufual in fchools to put the learner tains unity. upon proving the operation, by fome of the three me- Hence multiplication fupplies the place of many additions ; for if the multiplicand be repeated or fet down as thods following, viz. 1. The work may be proved by addition; for if you often as there are units in the multiplier, the fum of add the remainder to the minor, the fum will.be equal thefe, taken by addition, will be equal to the product by multiplication. Thus, 5X3 = 15=5 + 5 + 5. to the major, as in the following example. The firft and loweff flrep in multiplication is, to mulExarnp. L. s. d. tiply one digit by another ; and the fairt or number thence major 73 15 10 arifing is called a Jingle produtt. This elementary ftep minor 48 12 6 may be learned from the following table, commonly called Pythagoras's table ofmultiplication : which is conrem. 25 3 4 fultedthus; feek one of the digits or numbers on the head, and the other on the left fide,, and.in the angle of proof 73 15 10 you have their produdt. The learner,, before 2. By fubtradhon; for if you fubtrad! the remainder meeting proceed further, ought to get the table by heart. from the major, the difference will be equal to the minor, he To Pythagoras’s table are here added, on account of as follows. their ufefiilnefs, the produ&s of the numbers 10, 11, 12. L. s, d. 5847 major 73 .15 10 2569 minor 48 12 6 3278 rem. 25 3 4 25-69 proof 48 12 (y 3. By carting our the 9’s;. for the major being equal to the fum of the minor and remainder, if you cart the 9’s out of the major, and place the excefs at the top of the crofs, and then cart the 9’s out of the minor and remainder, as if they were items in addition, and place the excefs at the foot of the crofs, it is plain the figure at the top and foot, if the work be right,.will be the fame. Only, in proving fubtradtion of money, Avoirdupois weight, <bc. care murt be taken to begin with the higheft denomination, reducing always the excefs to the next inferior denomination, as taught in. the proof of addition. See the following example. L. s. d. major 73 15. 10 minor 48 12 6 T rem. 25. 3 4 Chap. IV. Multiplication. I. Multiplication of Integers. In multiplication there are two numbers given, viz. one to be multiplied, called the multiplicand; and another Rule I. Set the multiplier below the multiplicand, that multiplies it, called the multiplier; thefe two go fo as like places may Hand under other, viz. units under r -units,.