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 A R I T II M E T I C K. 393 TABLE I. The Compound Rule of Three in Vulgar ¥radons. Farthings. of a penny. of a /hilling, of af pound. 4 pf -nr 4° TT of-TS Quest. If acre of grafs be cut down by 2 men in -J-of-rVof^nj 4 ofof TV y day, how many acres fhall be cut down by 6 men in 4 tV, 3 f days? Men.: acr.: : men. TABLE II. TABLE III. of a Jh ill. of a pound. of4 a found. day t i 34=* t days. , o+tV 4:4:: V • -nr* or 4 tts+tV Y> °r4 ^4x4x3-4x4-4 Or thus: «u+vV 13 T(J+Tff 4-T<r 13 4 2X2X4X1X3 “2X2X4 “2X2 "‘ “ T TTr+TV* or 4 iix acres. T^T -rer+vV 4+4 -r99, Chap. X. Rules of Practice. vV+tV 4+4 Tnr» °r A v s+nr 4+4+4 When the firft term of a queftion in the rule of three in Table II. become compound frachappens to be unity, the anfwer may frequently be found tionsTheof fractions a pound, by annexing (of to each more fpeedily and ealily than by a formal dating or work- Thus, x d. is y of I.; and 5 d. is of T +fofofthem. ^1. T 5 ing of the rule of three; and the directions to be obfer- 6c. yed in fuch operations are called Rules' of Practice., The variety that occurs in the rules of practice arifes The rules of pradtice naturally follow the dodtrine of chiefly from the different rates, or prices, of one thing, vulgar fractions, the operation being nothing elfe but a as a yatd, pound, an ounce, 6c. and may be reduced multiplying the number whofe price is required, by fuch; to the eighta cafes vis. a fraction of a pound, of a {hilling, or of a penny, as The rate may be,following, 1. Farthings under four. 2. Pence denotes the rate or price of one. twelve. 3. Pence and farthings. 4. Shillings Thus, if the price of 24 yards, at 6 s. 8 d. per yard, under twenty. <;. Shillings, pence, and farthings. 6. be demanded, the anfwer is found by multiplying 24 by under 7 Pounds, {hillings, pence, and farthings. -f, the fraction of a pound equivalent to 6 s. 8d. viz. 8.Pounds. The given number may confift of integers and parts. VX-f^Y^g 1. Hlnce, it is obvious, that to multiply a number by a Case I. When the rate is farthings, under four. fraction whofe numerator is unity, is to divide the faid Rule. Divide the given number by the denominator number by the denominator of the fraction. But if the df the fraction denoting the rate, as contained in Tab. IJ numerator of the fraction be not unity, you muft fird U/z. if the rate be 1 or 2 farthings, divide by 4 or 2, multiply the given number by the numerator, and then the quot will be pence ; and the remainder, in dividing divide- the product by the denominator. Thus, if the by 4, will be farthings, and in dividing by 2, it will be rate be 13 s. 4d.=eyl. the price of 24 yards is found by 1 halfpenny: then divide the pence by 12, the qunt will faying, ^X-|==i61. j or takeof the given num- be {hillings, and the-remainder pence. laftly, divide the {hillings by 20, the quot will be pounds, and the reber twice. When the fraction denoting the rate- happens to be mainder {hillings. But if the rate is 3 farthings, firft compound, the product or anfwer is found by dividing multiply the given number by the numerator 3, and then the given number by one of the denominators of the divide as above directed. compound fraction, the quot by another, and the next Ex. 2. I Ex. 1.. quot by the third, <bc. Thus, if the rate be 2 far8347, at 2 F. 48*9, at t f. things^ of jj'-y of rjJjyl. the price of 1440 yards is found.by faying, s-—^=y.2o, and 7TV)=6o, and 4§=jl. 1214—3 f. 4i73-i + When the rate is expreded by two or more fimple fractions, connected with the fign +, the produCt or ani°|i—2d. 3'17 9dfwer is found by dividing'the given number fucceflively by the feveral denominators, and then adding the quot. L.j 1 2+ ■‘7 7 9i Thus, if the rate be 3 S-—+ the price of 80 yardsia found by faying, •£§ —8, and 4» and 8+4= Case II. When the rate is pence, under twelve. J2I. Divide the given number by the denominator ’ The fractions equivalent to any-number of farthings- of Rule. dendting the rate, as contained in Table nnder 4, to any number of pence under 12, -and to any II. theandfraction you have the anfwer in {hillings; which reduce number of {hillings under 20, are exhibited in the folinto pounds, by dividing by 20. lowing tables. 5G Ex. 1, Vol. I. No. 17. 3
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