CASE FOURTH. Q. What is the fourth case in reduction of decimals? A, It is to find the value of a decimal in the known parts of the integer. Q. What is the RULE in this case? A. Multiply the given decimal by the parts in the next low. er denomination, (as in reduction descending,) and point off as many figures at the right hand of the product, as there are decimal places in the given decimal; multiply the remainder, or the figures so cut off, by the parts in the next less denomi nation, and cut off as before, and so proceed, till you have brought it to the lowest denomination required; then the sev eral denominations, standing at the left hand of the cut off, will show the value sought. EXAMPLES. 1. What is the value of ,395389 of a ton? Operation. ,395389 Multiply by 1 20 cwt. the next lower denomination. Therefore the answer is 7 cwt. 3 qrs. 17 lbs. 10 oz. 11 dr. Ans. 3 qrs. 14 lbs. Ans. 7 oz. 13 pwt. 4. How many days in,19726 of a year? Ans. 72 ds. nearly. 5. Bring,625 of a yard to qrs. and nails. Ans. 2 qrs. 2 na. 6. How much land in ,6 of an acre? Ans. 2 roods, 16 rods. 7. How many hours in ,2084 of a day? Ans. 5 hours. 8. What is the quantity of,6625 of a mile? Ans. 5 fur. 12 rds. 9. Bring,625 of an ell Fr. to qrs. and nails. Ans. 3 qrs. 3 na. 10. Bring,20635 of a pipe of wine, to galls. Ans. 26 galls. 11. What is the quantity of,046875 of a bushel? Ans. 3 pts. MISCELLANEOUS QUESTIONS IN VULGAR AND DECIMAL FRACTIONS. 1. Add ,,,25, and,125, together, and give the amount in a decimal expression. Ans. 1,108+. 2. What is the amount of ,275, §,,025, and, added together in a vulgar form? 3. What decimal will express the difference between T5' and,745 ? Ans. ,278+. 61 Ans. 1120. 4. If, and be added together, and ,325, and ,4325 subtracted from their sum, what vulgar fraction will show the difference? 3600 Ans. 1373 5. Add of of 12, to 14,0125, and from the sum, subtract of of 16; then multiply the difference by 4,25, and give the result in a vulgar fraction. Ans. 654. 6. Multiply 9, by 1 of § of 71, and divide the product by 9,75, and give the result in a decimal expression. Ans. 4,6274+. 7. Add of a ton, ,75 of a cwt. of a quarter, and ,375 of a pound, and give the result in the known parts of the integer. Ans. 16 cwt. 3 qrs. 14 lbs. 6 oz. 8. Divide ,75 by itself, multiply the quotient by 1, add,625 to the product, then subtract 13, and see if any thing remain. Ans. Nothing. 9. A man bought ,24 of a factory, and sold of his share; what part of the factory did he sell, and what part of the whole does he still own? Ans. He sold, or,08, of the whole factory. He still owns, or,16 of the whole. 10. A man, left an estate to his four sons, worth $16000, in such proportions, that as often as A. had $3, B. had 4, C. 5, and D. 6; what proportion of the estate had each, and what was the amount of each one's share? 11. Reduce,,25, §,,75, 2, ,025, to a common denominator, and give the sum, both in a vulgar and decimal expression. Ans. Reduced to a common denominator, the fraction will appear in the following expressions, viz.: 19200' 19200, 192009 10200, 10800, 1900; the amount in a vular form, 2,20; in a decimal, 2,6583+. 14400 15360 480 9600 4800 6400 12. What will 75§ yards of silk cost, at ,875 of a dollar per yard? Ans. $66,17 cts.,1875. 13. Four men built a ship, which cost $28,000; A. owned such a part of her as cost him $3500; what proportion of the ship did he own, and how much of his share must he dispose of, to sell of the whole ship? Ans. He at first owned part; and must sell of his sharc. 14. I bought of a lottery ticket, and drew $4250; but having sold a certain part of my share, my portion of the money was only $1328,125; how much of my share did I sell, and what part of the whole ticket did I still own? Ans. I sold of my share; and still owned of the whole. FELLOWSHIP. Q. What is to be understood by Fellowship? A. Fellowship is a Rule by which the accounts of several merchants, or other persons, trading together, are so adjusted that each partner may have his share of the gain, or sustain his share of the loss, in proportion to his share of the joint stock. By this rule, also, the estates of bankrupts are divided among their creditors, and taxes assessed on all taxable property, according to its valuation. Q. How many kinds of Fellowship are there? A. Fellowship is of two kinds, single, and compound, or double. SINGLE FELLOWSHIP. Q. What is Single Fellowship? A. It is when the several stocks are continued in trade for an equal term of time. Q. By what RULE do you find each man's gain or loss, according to his stock in trade. A. By the Rule of Three; say, as, the whole stock is to the whole gain, or the whole loss:: so is each man's particu lar stock to his share of the gain or loss. EXAMPLES. 1. A. B. and C. joined their stock in trade; A. put in 300 dollars, B. 450 dollars, and C. 750 dollars; on settling their accounts, they found they had gained 500 dollars; what was each partner's share of the gain? Operation. $300+450+750-$1500 whole stock. Then say, as $1500: 500 :: 300: $100 A.'s gain. Then say, as $1500: 500 :: 450 $150 B.'s gain. Then say, as $1500 : 500 :: 750 : $250 C.'s gain. Or, add together A.'s and B.'s shares, and subtract the sum from the whole gain, and the remainder will be C.'s share. 2. A bankrupt finds he owes to A. $250,18 cents; to B. $114; to C. $645,62 cents; and to D. $354,70 cents; his whole property is sold for only $1023,373 cents; how much can he pay on a dollar, and how much must each creditor receive for his debt? Ans. He can pay 75 cents on a dollar; A. must receive $187,635; B. must receive $85,50; C. must receive $484,215; D. must receive $266,025. 3. Three merchants sent a ship to India, which, with the cargo, cost $30000; A. owned, B. owned, and C. owned the rest; on her return, they found they had gained $12500; what did each one pay out, for the vessel and cargo, and what was each one's share of the gain? Ans. A. paid $6000, and gained $2500; B. paid $12000, and gained $5000; C. paid $12000, and gained $5000. ་ 4. Four house carpenters built a house in company; the lot on which it was built, cost $1000; the lumber, and building materials, of all kinds, cost $6,500; they paid for mason's work, 500 dollars; for painting and glazing, $350. Of these expenses, A. paid, B., C., and D. paid the residue. A. worked on the house 45 days, at $1,50 a day, with three apprentices, who were allowed 75 cents a day, each; B. work. ed 75 days, at $1,75 a day, with two journeymen, who were allowed $1,25 a day, each; C. worked 60 days, at $1,62 a day, with one journeyman, at $1,373, and two apprentices at 87 cents, each; D. worked 90 days, and being the master workman, was allowed $2,25 a day, with two journeymen at $1,75 a day, each, and two apprentices at $1,25 a day, each; having completed the house, they sold it for 2500 dollars more than the cost, labor and all; how much money must each partner receive for his share, in proportion to what he contributed in money and labor, towards the building? Ans. A.'s share $3700,203; B.'s share $3016,044; C.'s share $2450,438; D.'s share $3198,314. N. B. Whole cost $9865; sold for $12365. 5. A. B. and C. traded in company; A. put in $5760, B. put in $2400, and C. put in $1440; on settling their business, they found their gain to be $960; what was each one's share of the gain? Ans. A.'s share, $576. B.'s share, $240. C.'s share, $144. 6. Three merchants entered into partnership; A. put in $6000, B. $4000, and C. $2000; they gained 12 per cent on the whole stock in trade; what was each one's share of the gain? Ans. A.'s gain was $750. B.'s $500. C.'s 250. DOUBLE FELLOWSHIP. Q. What is Double, or Compound Fellowship? A. It is when the several shares of partners are continued in trade for an unequal term of time. Q. What is the RULE for finding each partner's gain or loss? A. First multiply each partner's share, by the time it was continued in trade; then add all these products together, and by the rule of three, say: as the sum of these products: is to the whole gain, or to the whole loss: so is each partner's particular product: to his share of the gain or loss. EXAMPLES. 1. Three merchants joined their stocks in trade; A. put in $600, for 6 months; B. $500, for 9 months: and C. $300, for 12 months; by their speculations they gained $700; what was each man's share of the gain? mo. Operation. A.'s share $600 × 6=3600 A.'s product. 500X 94500 B.'s product. 300×12-3600 C.'s product. B.'s 66 C.'s 86 dolls. Therefore say, as 11700: 700 :: 11700 sum of all the products. 3600 to $215,384+A.'s gain. 4500: to 269,23 B.'s gain. 3600: to 215,384 C.'s gain. 2. Three persons hired a large pasture, for $250, in which to pasture their cattle; on the first of May, each man turned in 40 head; on the first of June, A. turned in 20 head more, but B. took out 15 head of his; July 1st, B. turned in 20 head, and C. took out 20 head of his; August 1st, A. took out 25 head, B. put in 25, and C. put in 30 head; on the first of October, they give up the pasture, and settle the concern; what must each man pay for the use of the pasture? Ans. A. must pay $84,55814. B. $91,91113. C.$73,529. |