Having the price of any number of yards, &c. to find the price of unity, or one yard. If the quantity do not exceed 12, proceed by setting down the price and dividing it by the quantity, which quotient will be the price of one yard, required: but if the quantity exceed 12, then divide by two such numbers as when multiplied together will produce the quantity, and the last quotient will be the value of 1 yard, required. NOTE. This case proves the first and second cases in Compound Multiplication. EXAMPLES IN OLD LAWFUL AND FEDERAL MONEY. 1. If 9 yards of cloth cost £3 13s. 6d. what is that per yard? 1. If 9 yards of cloth cost $12, 25, what is that per yard? 9)3 13 6 Ans. £o 8 2 OPERATIONS. 9)12,25 $1,36,1,1 187 NOTE. This is performed the same as division of decimals, in all cases. 2. If 7 ells cost £5 17s. 5d. what cost 1 ell? Ans. 16s. 94d. 3. If 11 sheep cost £6 5s. 9d. what did each cost? Ans. £0 11s. 52d, 4. If 12 gallons of rum cost $13,65, what is it per gallon? Ans. $1,13,74. NOTE. When the given quantity (or divisor) is large, and not a composite number, the operation may be performed by long division. CASE II. Having the price of a hundred weight, to find the price of 1. Divide the given price by 8, that quotient by 7, and this quotient by 2, and the last quotient will be the price of 1, required. EXAMPLES. 1. If 1 cwt. of flax cost £2 7s. 8d. what is that per pound? £ 8. d. 8)2 7 .8 7)0 5 111 CASE III. Ans. 74dj Having the price of several hundred weight, to find the price per pound. Divide the whole price by the number of hundreds, which will give the price per cwt. and then proceed as in the last case. EXAMPLES. If 5 cwt. of sugar cost £13 8s. 4d. what is that per pound? CASE IV. Having the price of any number of yards, &c. to find the price of 1 yard. Divide the price by the quantity, beginning at the highest denomination, and if any thing remain reduce it into the next, and every inferiour denominatior, and, at each reduction, divide as before, remembering, each time, to add the odd shillings, pence, &c. if there be any, and you will have the value of unity required. NOTE. If there be,, or of a yard, pound, &c. multiply both the price and quantity by 4, and then proceed as above directed. EXAMPLES. 1. If 954 of figs cost £16 13s. 63d. what are they per pound.? 2. If 147 bushels of rye cost £47 12s. 6d. what is it per bushel! PRACTICAL QUESTIONS. Ans. 6s. 53d, 1. Divide £273 9s. 4d. among 5 men and 4 women, and give the men twice as much as the women. [Carried up.] £273 9 4 proof. 2. Divide £120 17s. 4d. among 7 men and 7 women, and give the women 3 times as much as the men. DUODECIMALS; Or CROSS MULTIPLICATION, is a rule made use of principally by workmen and artificers, in casting up the contents of their work. Dimensions are generally taken in feet, inches and parts, Inches and parts are sometimes called primes, seconds, thirds, and fourths, and are marked thus: inches or primes, (') seconds, (") thirds, (") fourths, (""). This method of multiplying is not confined to twelves, but may be greatly extended; for any number, whether its inferiour denominations decrease from the integer in the same ratio, or not, may be multiplied crosswise; and, for the better understanding of it, the learner must observe, that if he multiplies any denomination by an integer, the value of an unit in the product will be equal to the value of an unit in the multiplicand; but if he multiply by any number of an inferiour denomination, the value of an unit in the product will be so much inferiour to the value of an unit in the multiplicand, as an unit of the multiplier is less than an integer. Thus pounds multiplied by pounds produce pounds; pounds multiplied by shillings produce shillings, &c. shillings multiplied by shillings produce of shillings; shillings multiplied by pence produce of a penny; pence multiplied by pence produce of a penny, &c. General directions abbreviated. 1. Pounds multiplied by pounds produce pounds. 2. Pounds multiplied by shillings, every 20 is one pound, the rest shillings. 3. Pounds multiplied by pence, every 12 is one shilling, the rest pence. 4. Shillings multiplied by shillings, every 20 is one shilling, every 5 is 3 pence, and in each 1 is 2 farthings, and 4 tenths of a farthing. 5. Shillings multiplied by pence, every 5 is a farthing, and each one of a farthing. 6. Pence multiplied by pence every 60 is a farthing, and every 6 one tenth part. The reason is plain in the following diagram. |