shillings, and seven pence three farthings, F, twentyone pounds, fifteen shillings, and five pence halfpenny, G, Hve pounds, six shillings, and seven pence farthing; how much is the debt? Ans. SUBTRACTION OF FEDERAL MONEY. IN Subtraction of Federal Money, proceed as in Simple Subtraction, through the whole, as if it had been all of one denomination ; but observe the separating points, so as to have them in the same place in the remainder, as in the given sums. The proof of this is the same as in Simple Subtraction. Teaches to find the difference between two numbers of diverse denominations. RULE. Place the less under the greater number, so that each may stand under its like denomination ; begin with the lowest denomination, take the lower number from the upper, and set down the remainder underneath ; but if the lower number be greater than the upper, take it from as many of that denomination as make one of the next higher, and to the remainder add the upper number; set their sum underneath, observing in that case to add one to the lower number of the next higher denomination, with which proceed in the same manner, and thus through all the denominations, to the highest, which subtract as in Simple Subtraction. This is proved as Simple Subtraction. Avoirdupois Weight. Ib. oz. dr. Ib. oz. dr. C. qr. 1b. T. C. qr. Ib. oz. dr. 36 7 10 56 10 3 46 1 11 3 11 2 16 10 1 21 9 7 41 912 II 3 21 2 13 3 11 12 14 Apothecaries' Weight. ib. 3 3 5 gr. Ib. 3 3 3 gr. lb. 3 3 + gr. 46 7 4 1 10 27 3 3 0 il 43 5 2 2 14 31 9 2 2 13 19 5 1 2 12 31 9 2 2 15 Pun. ga. An. ga, qt. Tier. ga. qts. T.. Pi. Hhd. ga. qts. qt. 75 36 1 36 59 2 16 8 2 What is the difference of latitude between London, in latitude 51°.32' N. and Boston in Massachusetts, being in lat. 420.23' N. Required the difference of longitude between Boston in longitude 710.03' W. and Cape Sable in Nova Scotia, in longitude, 650.39' W. In these examples the signs, degrees, &c. are counted from r Aries ; or rather from the beginning of Aries, 12 signs making the whole circle of the zodiac; therefore when the signs to be subtracted are a greater number than those from which they are to be taken, borrow 12. See the first example above. Questions to exercise the learner in Compound Subtraction. 1. A man owed £.1136.15.91. has paid £ 735.18.10; how much remains unpaid ? Ans £ 400. 16. 111 2. A man has paid £9.400.16. 11 of a debt of £6.1136. 15.91; how much has he yet to pay ? Ans. £.735. 18. 10. 3. A farm of 200 acres consisted of mowing, pas+ ture, ploughland ; and 20 acres, 3 roods, and 16 perches of it is wood land; how much remains for mowing, pasture, and ploughland ? Ans. 179 acres and 24 perches. 4. A hogshead of tobacco, weighed 5 C. 2 grs. 16 lb. including the weight of the hogshead, which weighed 3 qrs. 27 16. ; what was the net weight of the tobacco ? Ans. 4 C. 2 qrs 17 lb. 5. An English guinea should weigh 5 dwt 6 gr ; a piece of gold weighs 3 dwt. 17 gr.; how much is it short of the weight of a guinea ? Ans. I dwt. 13 gr. 6. A man has travelled 25 miles, 3] furlongs, on a journey of 75 miles ; how far has he yet to travel ? Ans. 50 miles, and 20 poles. DECIMAL FRACTIONS. Decimal Fractions are a part of Arithmetic, in which any thing which is called one, as one pound, one yard, one dollar, one mile, &c. is conceived to be divided into ten equal parts ; and each of those parts into ten other equal parts, and so on by a decimal division, without end ; those fractional parts called decimal fractions are distinguished from whole numbers (called integers) by having a point prefixed, or placed between them and the integers. Thus 2 is a decimal fraction, and is read two tepths ; Also 56,75 is read fifty six, and seventy five hundredths, which will be better understood by the following table of |