3. What will be the cost of 658 lb. of hay, at $7.38 per tun? at $5.25? at $11? - at $8.50? at $12? at $9.00 ? at $9.50? Ans. to the last, $3.948. To reduce shillings, pence, and farthings, to the decimal of a pound, by inspection. There is a simple and concise method of reducing shillings, pence, and farthings to the decimal of a pound, by inspection. The reasoning in relation to it is as follows: 5 of 20s. is 2s.; therefore every 2s. is, or £1. Every shilling is 18, or £05. 100, or £05. Pence are readily reduced to farthings. Every farthing is £ Had it so happened that 1000 farthings, instead of 960, had made a pound, then every farthing would have been, or £·001. But 960 increased by part of itself is 1000; consequently, 24 farthings are exactly 15, or £025, and 48 farthings are exactly 150, or £050. For, add of any number of farthings to the number, and it will be reduced to thousandths of a pound. 25 Wherefore, To reduce shillings, pence, and farthings to the decimal of a pound, by inspection, RULE. Call every two shillings one tenth of a pound; every odd shilling, five hundredths; and the number of farthings, in the given pence and farthings, so many thousandths, adding one, if the number be more than twelve and not exceeding thirty-six, and two, if the number be more than thirty-six. If the farthings be just 12 if 36, they are equal to 0375. 05 of a pound, as above. 01212, they are equal to '0125; 48 farthings=12d.= 1s. equal 1. Find, by inspection, the decimal expression of 9s. 7d., and 12s. 0ąd. Ans. £479, and £603. · 2. Reduce to decimals, by inspection, the following sums, and find their amount, viz.: 15s. 3d.; 8s. 111d.; 10s. 64d.; 1s. 8d.; d., and 21d. Amount, £1.833. To reduce the decimal of a pound to shillings, pence, and farthings, by inspection. Reasoning as before, the first three figures in any decimal of a pound may readily be reduced to shillings, pence, and farthings, by inspection. RULE. Double the first figure, or tenths, for shillings, and if the second figure, or hundredths, be five, or more than five, reckon another shilling; then, after the five is deducted, call the figures in the second and third places so many farthings, abating one when they are above twelve, and two when above thirty-six, and the result will be the answer, within a farthing. Thus, to find the value of £876 by inspection : .8 tenths of a pound 05 hundredths of a pound 026 thousandths, abating 1,25 farthings, 876 of a pound, =16 shillings. = 1 shilling. =0s. 64d. Ans. 17s. 64d. 1. Find, by inspection, the value of £523, and £694. Ans. 10s. 5d., and 13s. 101d. 2. Find the value of £47. NOTE 1.-When the decimal has but two figures, after taking out the shillings, the remainder, to be reduced to thousandths, will require a cipher to be annexed to the right hand. Ans. 98. 43d. 3. Value the following decimals, by inspection, and find their amount, viz.: £785, £·357, £·916, £·74, £•5, £•25, £09, and £008. Ans. £3 12s. 11d. Questions at the discretion of the Teacher. 114. PERCENTAGE. 1. A man owns a farm of 320 acres, 5 per cent. of which is marsh; how many acres are marsh? OPERATION. 320 Ans. 16:00 A. SOLUTION.-Per cent. are Latin words. Cent. is written with a period after it, because it is a contraction of the Latin word Centum, a hundred. The two words together signify, by the hundred. The number 5 with the words per cent. is called the Rate, and signifies how many hundredths are intended to be taken; it is written decimally, 05, thus, 5 per cent. of 320 acres is 05 (5 hundredths) of that quantity; and since of implies multiplication, we multiply 320 by 05, pointing off as in decimal fractions, and get the Ans. 16 acres. The finding of a certain per cent.; or a certain number of hundredths of a quantity, is called Percentage; and it is performed by the following RULE. Multiply the given number or quantity by the rate per cent., written decimally as hundredths, and the product, pointed off as in the multiplication of decimals, will be the percentage sought. 25 per cent. is 25. 50 per cent. is 50. (180, or the whole). 7 per cent. is 07. 100 per cent. is 1.00 125 per cent. is 1.25 1 per cent. is (125, more than the whole). per cent. is a half of 1 per cent. (1⁄2 of 1 hundredth, ⚫01. ·005. or Too of the whole), per cent. is a fourth of 1 per cent., that is, of 10,='0025. per cent. is 3 times per cent., that is, of bo, ='0075. per cent. (of a hundredth, that is, of 10), =·00125. 41 per cent. is 041045 (the 5 expressing 10ths of 100ths), ⚫045. Let the pupil write 2 per cent. decimally; 84 per cent.; 92 per cent.; 10 per cent.; 121 per cent.; 121 per cent.; 133 per cent. EXAMPLES. 2. A farmer gives 10 per cent. of 460 bushels of wheat for threshing; how many bushels does he give? Ans. 46 bushels. 3. A farmer rented ground on which 409 bushels of oats were raised, receiving 30 per cent. for the rent; how many bushels did he receive? Ans. 122-7 bushels. 4. A beef weighs 895 lb., of which 9 per cent. is bone; what does the meat weigh? Ans. 814-45 lb. 5. A schooner, freighted with 725 barrels of flour, encountered a storm, when it was found necessary to throw 28 per cent. of the cargo overboard; how many barrels were thrown overboard, and how many were saved? Ans. to the last, 522 bar. 6. A forwarding merchant agreed to transport 2000 bushels of corn, worth $692.75, from Buffalo to Albany for 12 per cent. on its value; what was the cost of transportation? Ans. $86.593. 7. A farmer had a flock of 639 sheep, which increased 33 per cent. in 1 year; how many sheep had he at the expiration of the year? Ans. 852 sheep. 8. A man owing a debt of $1942-711, pays 163 per cent. of it; how much of it remains due? 9. A man, worth $4861, lost 28 dorsing with his neighbor; how much Ans. $1624.595+. per cent. of it by inof it did he lose? Ans. $1385 385. 10. What is 3 per cent. of $115 ? 11. What is per cent. of $376? 12. A gentleman, worth $4280, spent 15 property in educating his son; how much did tion cost his father? Ans. $3.29. per cent. of his the son's educaAns. $663 40. 13. A merchant has outstanding accounts to the amount of $1960; 22 per cent. of which is due in 3 months, and the remainder in 6 months. What is the amount due in 3 months? in 6 months? Ans. to the last, $1528-80. 14. A merchant who fails in business pays 63 per cent. on his debts; what does a man receive whose demands are $2465 ? Ans. $1552.95. 15. What does another man lose, whose demands are $3615 against the same merchant ? Ans. $1337 55. 16. A young man is left with $5000, and loses 15 per cent. in paying too high a price for a farm, 15 per cent. of the remainder in selling the farm for less than its value; he expends 15 per cent. of what is left in an excursion to the West, 15 per cent. of what he has when he gets back in an unfortunate investment in railroad stocks, and 15 per cent. of the residue in trade; what has he then left? Ans. $2218.526+. NOTE 1.-Under the general subject of Percentage will be considered Insurance, Stocks, Brokerage, Interest, Profit and Loss, Discount, Commission, Bankruptcy, Banking, Taxes, and Duties. Questions at the discretion of the Teacher. 115. Insurance. Insurance is security to individuals against loss of property from fire, storms at sea, &c. Companies incorporated for the purpose, having a certain capital to secure their responsibility, insure property at so much per cent. a year. When any property insured is destroyed by the agent (fire, or other cause) insured against, the company pays to the owner the sum for which it is insured. The sums paid by the several individuals insured make up the losses, and pay the company for doing the business. Premium is the sum paid for insurance. An Underwriter is an insurer, whether it be an incorporated company or an individual. Insurance at sea, called Marine insurance, is usually for a certain voyage. It is sometimes effected by an individual; it is then called out-door insurance. The rate per cent. of insurance is in proportion to the risk. Property is not insured for its entire value, lest it should be fraudulently destroyed. EXAMPLES. 1. What is the annual insurance of $1000 on an academy, at per cent.? Ans. $5. 2. Insured $14500 on a factory, at 12 per cent. per annum; what was the premium? Ans. $253.75. 3. What is the premium for insuring $6000 on a store and goods, at per cent.? SOLUTION.-At 1 per cent., the sum is as many cents as there are dollars, or 6000 cents, which reduced is $60.00, and 2 per cent. is of this, or = Ans. $45. NOTE 1.-In this manner the percentage on any sum at 1 per cent. or less may be calculated with ease. 4. What must be paid for insuring $800 on a farm-house, at per cent.? Ans. $2. 5. The Marine Insurance Company insures $17500 on the cargo of the ship Minerva, from Boston to Constantinople, at 2 per cent.; what is the premium? Ans. $350. 6. Amos Lawrence insures $34000 on the ship Washington and cargo, from Canton to Boston, at 81 per cent.; what does he receive? Ans. $2805. Ans. $21. ;.; 7. The New England Life Insurance Company insures $2000 on a person's life for one year, at a premium of 1 per cent. what is the sum? Life insurance is effected that the heirs of the individual, in case of his death, may receive the sum on which the premium is |