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 A R I T H M E T I C K. Ex. 2. 2. When the rate is an odd number of rtullings. Ex. i. £ 5316, at sd. 818, at i d. Ex. 1. Ex. 2. 635, at 1 s. 422, at 3 s. 6|8—2 d. L. 31, 15 s. 42 4 L.44 6 21 2 L-3 Ws/?, The remainders at the firft divifion in the aL. 63, 6 s. bove examples are the fame with the rate. Thus, in Note 1. The reafon of multiplying by half the numEx. 1. every remainder is id. Case III. When the rate is pence and farthings. ber of (hillings in the rate will appear by confidering, Rule. The pence muft be fome aliquot part of a that thefe are the numerators of the fradtions denoting fhiliing ; and, at the fame time, the farthings fome aliquot the rate. Thus, 2 s. is yl. and 4s, is^l. and 6 s. part of the pence; and if they be not fo given, divide is-r^-l. and each unit inx the produdt is two (hillings. the pence into two or more fuch parts, fo as the farthings The divifion by the denominator 10 is performed by cutmay be fome aliquot part of the lowed: divifion of the ting off the right-hand figure of the produdt, and the fipence. Then, beginning with the higheft divifion of gure fo cut off is the remainder ; and as each unit in the the pence, divide by the denominators of the fractions remainder is two (hillings, the double of them is the redenoting the aliquot parts. mainder in (hillings. Note 2. From Ex. 1. we may learn, that when the rate is 2 s. the price is found by doubling the right hand figure of the given number for (hillings, and the other figure or figures are pounds. Note 3. In Ex. 2. the price may alfo be had by taking -f of the given number ; and in this way every remainder will be 4 s. Note 4. By reverfing the operation, from the price and any even rate given, we may readily find the quantity of goods, viz. Multiply the price by 10, that is, to the price annex a cipher, and divide the produdt by half the rate. In Ex. 1. work firft for 1 d.; which being ^ s. di- Ex. 1. How many yards, at 14 s. may be bought vide the given number by the denominator 12, and the for 491. 7)490(70 yards, dnf. quot is (hillings, and the remainder pence ; then, be- Ex. 2. How many gallons, at 8 s. may be bought caufe i farthing is -Jd. divide the former quot by 4, and for 5001. ? 4)5000(1250 gallons. Jnf. the fum of the quots is the price ip (hillings ; which di- Case V. When the rate is (hillings and pence, or vide by 20. (hillings, pence, and farthings. In Ex. 2. the rate i-J d. being an aliquot part of a Rule I. If the rate be (hillings and pence which fhilling, the fecond method is Ihorter and better than the make an aliquot part of a pound, divide the given number by the denominator of the fra&ion denoting the rate ; firft. Case IV. When the rate is (hillings under twenty. the quot is pounds, and each unit of the remainder is eRule. Multiply the given number by the numerator qual to the rate. of the fra&ions contained in Tab. III. and divide the Ex. 1. produft by the denominators. Or, inftead of this ge354, at t s. 8 d. neral rule, take the two particular ones following. 1. If the rate be an even number of (hillings, multiply L.29, 10. the given number by half the number of (hillings in the Ex. 2. rate, always doubling the right-hand figure of the pro443, at 2 s. 6 d. du£t for (hillings, and the reft are pounds.. 2. If the rate be an odd number of (hillings, work; for j 6 the next lefler ev«n number of (hillings, as above; and Rule II. L.IfSithe rate be no aliquot part of a pound,9 for the odd (hilling take ^ of the given number. but may be divided into fucb parts, divide it accordingExamp. i. When the rate is an even number of (hil- ly, work for the parts feparately, and then add. lings. Ex. Ex. 1. 427, at 8 s 540, at 5 s. Ex. 1. Ex. 2.. 6 d. 436, at 2 s. 127, at 4 Si 4 d1 2 6 s. 128 3S.4d. 90 25. 6d. L.43, X2-S. L. 2.5, 8 s. 53 y 6 54 L.144 L.i8i 9 6 394