Quotient. In the second example, 219).1178410749(.0005380871 the divisor having no deci 2. Divisor. Dividend. 1095.... 834 657 1771 1752 mals, the quotient must have so many as there are in the dividend; wherefore, I have prefixed three ciphers to the left hand of the first quotient figure, before I put on the decimal point. 1907 1752 1554 1533 219 219 Quotient. In the third example, the divi .3719)38.0000(102.178+18 dend, being a whole number, must 3. Divisor. Dividend. 37 19.. 8100 7438 662.0 290 10 29 770 have at least so many ciphers annexed to it as there are decimals in the divisor, and so far the quotient will be whole numbers; then, by annexing more ciphers and continuing the operation, we obtain decimals in the quotient according to the rule. 29 752 Remainder 18 4. Divisor. Dividend. Quotient. .. In the fourth example, there are 125).0000710(.000568 nine decimals in the dividend, includ 1. Find the first quotient figure, as in common division. 2. Let each succeeding remainder be a new dividual, and for every such dividual reject the right hand figure of the preceding divisor. 3. Increase the next subtrahend by adding 1 for every 8 in the product of the omitted figure. 4. When there are not so many figures in the divisor as are required to be in the quotient, continue the operation, as usual, till the number of figures in the divisor and those wanting in the quo tient are equal; then use the contracted method to find the rest. This method of performing division has not appeared in any Arithmetic that I have seen. The operation is the same as in the fourth case of Simple Division, except bringing down the figures from the dividend, which is not done in this case. It is the most concise method I have ever learned, and becomes quite easy with. a little practice. 1. Divisor. Dividend. Quotient. 946)746394(789 84110 850 EXAMPLES. In this example, the first dividual is 7463, which contains the divisor 7 times now I set a dot over the last figure 3, and say 7 times 6 are 42, which I take from 43, and 1 remains; this sum I set down under 3, and say 7 times 4 are 28, and 4 that I carry (for 4 tens which I borrowed) make 32, which I take from 36, and 4 remains; this sum I set down under 6, and then say 7 times 9 are 63, and 3 that I carry (for 3 tens which I borrowed) make 66; this sum I take from 74, and 8 remains, which I set down under 4, and the whole remainder is 841; next 1 set a dot over 9, and the second dividual is 8419: the second quotient figure is 8, consequently I say 8 times 6 are 48;, this sum I take from 49, and 1 remains, which I set down under 9, and say 8 times 4 are 32, and 4 that I carry (for 4 tens which I borrowed) make 36; this sum I take from 41 under 3, and 5 remains, which I set down under 1, and say 8 times 9 are 72, and 4 that I carry (for 4 tens which I borrowed) make 76; this sum I take from 84, and 8 remains, which I set down under 4, and the whole remainder is 851; then I set a dot over the last figure, and the third dividual is 8514: the last quotient figure is 9, of course I say 9 times 6 are 54; this sum I take from 54, and nought remains, which I set down under 4, and proceed on in the same way, and nothing remains all round. 2. Divisor. Dividend. Quotient. The curious and inqui92.41035)2508.9280650510(27.14986 sitive student will please 660 7210100010 79440 550 0 to work this example at large by long division, and he will be convinced of the propriety of using this method in preference to any other, notwithstanding it is too difficult for young begin ners, unless they work their questions at large by the common rule, and set down the several remainders as in the above examples. I learned the above method of performing division of a travelling gentleman, who never authorized me to publish his name.. FEDERAL MONEY. Federal money being purely decimal, is, of course, added, subtracted, multiplied, and divided in the same manner as decimals. NOTATION OF FEDERAL MONEY. 1. In setting down sums of federal money, the cents are placed on the right hand of the dollars, and separated from them by a dot, in the same manner that decimals are separated from whole numbers. 2. If the number of cents be less than 10, a cipher must be put in the ten's place; and if there are no cents in the given sum, two ciphers are placed on the right hand of the dollars. 3. If the dot, which separates the dollars from the cents be removed, the whole sum may be called cents, or decimals of a dollar. Dollars 4. If the sum be cents only, separate two figures from the right hand for cents, and all, on the left hand of the dot, will be dollars, which is fully exemplified in the following 6 5 4 3 2 1. 4 5 6 &c. as in decimals. N. B. In calculations of federal money, we commonly say, so many dollars, cents, mills and decimal parts of a mill; instead of saying, so many eagles, dollars, dimes, cents, &c. Wherefore the above table may be read 654 thousand 321 dollars, 12 cents, 3 mills and 456 decimals of a 'mill. Consequently, any number of dollars, dimes, cents, mills, &c. may be simply expressed in dollars and decimal parts of a dollar. Thus, 21 dollars and one dime are expressed 21 dollars and .1 tenth, or 21 dollars 10 cents. 12 dollars, 4 dimes, 7 cents, 9 mills, are equal to 12 dollars 479 decimals, or 12 dollars, 47 cents, 9 mills. 99 dols. 9 dimes, 9 cents, 9 mills, 9 tenths, are expressed, 99 dols. 9999 decimal parts of a dollar. Place the numbers so that those of like rectly under each other. Then, add them mals. name may stand ditogether as in deci |