CASE I. When the tare is so much for the whole. RULE.-Subtract the given tare from the gross weight, and the remainder will be the neat weight. EXAMPLES. 1. What is the neat weight of a cask of raisins, weighing 3 cwt. 2 qrs. 15 lb. tare being 1 qr, 18 lb? cwt. qr. lb. 3 2 15 25 neat weight. 2. What is the neat weight of a barrel of figs, weighing 4 cwt. 3 qrs. 2 lb., tare being 1 qr. 17 lb? Ans. 4 cwt. 1 qr. 13 lb. 3. What is the neat weight of 3 hogsheads of tobacco, weighing 57 cwt. 3 qrs. 16 lb, gross, tare being 4 cwt. 3 qrs. 18 lb? Ans. 52 cwt. 3 qr. 26 lb. 4. A cart load of hay was found to weigh 32 cwt. 3 qrs. 14 lb. including the cart, weighing 15 cwt. qr. 25 lb. ; what did the hay alone weigh? Ans. 17 cwt. 1 qr. 17 lb. CASE II-When the tare is at so much per cask, box, bag, &c. RULE.--Find the neat weight of one cask, box, bag, &c. by the first case, which multiply by the number of casks, &c. and the product will be the neat weight. The value may be found by Practice. EXAMPLES. 1. What is the neat weight of 8 boxes of figs, each weighing 1 cwt. 3 qr. 14 lb. gross, tare or weight of the box alone being 21 lb? 2. Bought 7 casks of sugar, each weighing 5 cwt. 2 qr. 5 lb. gross, tare 1 qr. 18 lb. per cask; what is the neat weight, and its value at 56 shillings per cwt. J 35 cwt, 3 Ans. { qr. £100 12s. 6d. 21 lb. 3. Bought 12 barrels of figs, each 3 cwt. 1 qr. 7 lb. gross, tare 1 qr. 14 lb. per barrel; what is the neat weight, and the cost of the whole, at £3 5s. 4d. per cwt? Ans. { f 35 cwt. 1 qr. £115 3s. CASE III.-When the tare is at so much per cwt., or per cent. RULE. If the tare be any aliquot part of a cwt., divide the gross weight by this aliquot part, and the quotient will be the tare, which subtract from the gross weight, and the remainder will be the neat weight required. When the tare is at so much per cent., that is, so many lb. for every 100 lb., it may be found by the Rule of Three, or by taking aliquot parts. EXAMPLES. 1. What is the neat weight of 10 boxes of soap, each weighing 1 cwt. 1 qr. 23 lb. gross, tare 13 lb. per cwt.? cwt. qrs. lbs. gross 2. Bought 36 casks of treacle, each 3 cwt. 2 qrs. 14 lb. tare per cwt. 8 lb. ; what is the neat weight of the whole, and what will the same cost, at £1 2s. 6d per cwt.? Ans. { 121 cwt. 0 qr. 20 lb. neat weight. £136 6s. 6d. cost. 3. Bought 25 cwt. 3 qr. 12 lb. gross tare 14 lb. per cwt. ; required its neat weight and value, at £2 16s. per cwt.; Ans. 22 cwt. 2 qrs. 14 lb. £63 7s. value. H 4. Required the value of 3600 lb. of wool, at 1s. 8d. per lb., tare being allowed at 4 lb per cent. Ans. £288. CASE IV.-To find the neat weight when tret is allowed with tare. RULE. Find the neat weight as above, and call it tare suttle; which divide by 26, and subtract the quotient from it, and the remainder will be the neat weight. EXAMPLES. 1. Bought 4 hhds. of sugar, each weighing 9 cwt., tare of the whole 2 cwt. 2 qr. 8 lb., tret 4 lb. for 104 lb.; how much neat weight? 0 16 neat weight 2. What is the neat weight of 42 cwt. of sugar, tare in the whole 2 cwt. I qr. 6 lb., and tret 4 lb. in 104, or? Ans. 38 cwt. 0 qr. 19 lb. 3. Bought 4 boxes of soap, each weighing 3 cwt. 1 qr. 27 lb. gross, tare 14 lb. per box, tret as before; what is the neat weight of the whole, and what will it cost, at 37s. 4d. per cwt. ? 12 cwt. 3 Ans. { qr. £24 3s. 4d. 22 lb. 4. Bought 61803 lb. of oil, at £25 10s. per ton, tare 14 tons, tret 4 lb. in 104; what is the neat weight and value? Ans. J 56700 lb. { £637 10s. CASE V.-To find the neat weight, when tare, tret, and cloff are allowed. RULE.-Deduct for tare and tret, as in the last case, and from this result subtract 2 lb. for every 3 cwt., that is the 168th part, and the remainder will be the neat weight required. EXAMPLES. 1. What is the neat weight of 303 cwt 2 qr. 10 lb., tare 15 cwt. 4 lb, tret 4 lb. per 104 lb., cloff 2 lb. per 3 cwt.? cwt. qr. lb. 15 0 4 tare. 26)288 2 6 11 0 11 tret. 168)277 275 1 23 1 2 16 15 oz. cloff. qr. 3 6 1 neat weight. 2. What is the neat weight of 121 cwt. 1 12 lb. gross, tare 10 cwt. 1 qr. 16 lb,, tret 4 lb. per 104 lb., and cloff 2 lb. per 3 cwt.? Ans. 106 cwt. 6 lb. 14 oz. 3. What is the neat weight of 26 casks, each weighing 4 cwt. 2 qr. 7 lb., tare per cask 1 cwt. 1 qr., tret 4 lb. per 104 lb., and cloff as usual? Ans. 82 cwt. 1 qr. 7 lb. 123 oz. VULGAR FRACTIONS. A vulgar fraction, or part of any thing, is expressed by two numbers, one placed above the other, with a line between them; as 3, 4, 10 3 15 &c. The bottom number is called the denominator, and denotes how many equal parts the unit, number, or quantity is to be divided into; and the top number, which is called the numerator, denotes how many of these equal parts are to be taken; that is, if of a unit or quantity be required; here the denominator 4, denotes that the unit or quantity is to be divided into 4 equal parts, and the numerator 3 denotes that 3 of these equal parts are to be taken, and so on for any other fraction. If the numerator and denominator be the same, the fraction is equal to one, as ‡ = 1. If the numerator be greater than the denominator, the fraction is greater than one, as = 1 There are five sorts of vulgar fractions, viz. the proper, the improper, the compound, the mixed, and the complex. 1. A proper fraction is when the numerator is less than the denominator, as 3, 1, 1, &c. 2. An improper fraction is, when the numerator is equal to, or greater than the denominator, as 5 12 49 49 39 &c. 3. A compound fraction is a fraction of a fraction, and known by the word of placed between them, as of, of of &c. 4. A mixed number is composed of a whole number and a fraction, as 21, 31, 127, &c. 5. A complex fraction contains a fractional part in the numerator or denominator, or in both, así 2 3 4, 3, &c. 2 59 NOTE.-A whole number may be expressed as a fraction by placing 1 for its denominator, as 4 The proper and improper fractions are called simple fractions. CASE I. To reduce a given vulgar fraction to its lowest terms. RULE.-Divide the greater number by the less, and this divisor by the last remainder, and so on, till nothing remains; the last divisor will be the greatest common measure, or the greatest number, by which both the numerator and denominator can be divided without a remainder. Divide the numerator and denominator of the given fraction by this common measure, and the quotients will be the numerator and denominator of the new fraction. N. B. The value of a vulgar fraction is not changed by multiplying or dividing both its numerator and denominator by the same number. |