WRITTEN PROBLEMS. 5'55 4, and 58 266 MISCELLANEOUS EXAMPLES. 1. What common fraction equals .00096 ? Ans ses 2. Add 11 Ans. 1346 28 8. Add Ans. 247. 178 4. Multiply .0075 cwt. by 4.008. Ans. .03006 cwl. 言 5. Divide 13%tons by 28 Ans. y tons. .7 } .2 1.25 61 Ans. 26273; 1.5341. 2 18 8. Divide 14 square yards by 11 Ans. 113988. 27 134 241 9. Divide £240f by of of of 14. Ans. £285]. 10. What number multiplied by 7f will give 64 for a pro dact? Ans. *4. 11. Divide seven millionths by twelve and a half ten-mil. liontbs. Ans. 5.6. 12. Add 4, 81,.375, and .5, and multiply the sum by 6.24. 36' Ans. 8784 18. Subtract of 12 from s of and divide the remain. der by 4. Ans. 11197 3} 14. Multiply the sum of.5 and by the difference be. 14 84 10 tween and Ans. de 17 263 621 15. Multiply by 25 millionths, and divide the pro 1000 duct by .00121 Ans. .00125. 28 16. The product of two numbers is $, and one of them is of of 2; what is the other ? Ans. Its 17. Add 2.5 cwt., 1.25 cwt., 5 cwt., 4.375 cwt., 1.875 cwt., 8.5 cwt., 1.225 cwt., and 1.275 cwt. Ans. 20 cwt. 18. What number multiplied by $ of 1 of 54 is equal to of 1 of 271? Ans. 8360 19. Divide the sum of six thousandths and six milliontho by their difference, to 6 decimal places. Ans. 1.002002+. 20. From the sum of fr, ß, and ḥ, tako the remainder ob tained by subtracting 34 from its of of 4. Ans. 1886. 54 21. What number must be divided by f of 2f of to 11 if' Ans. 24. 22. John had $225] and earned of 31 times $88f more; having lost part of his money, be found that he had $1867 remaining ; what amount did he lose ? Ans. $978. 23. A ton of iron ore from the mines of Cornwall yields .65 of a ton of pure iron; how much iron will 578.8 tons of ore yield? Ans. 376.22 tons. 24. An oil refiner has on hand 16,745 gallons of coal oil; how many casks, each containing 42.5 gallons, can be filled with it? Ans. 394 casks. 25. How many dress patterns of 12.25 yards each, can be cut from a piece of French percale, containing 50 yards ? Ans. 4+ patterns. 26. An engine pumped 41.25 barrels of 31.5 gallons each from a tank containing 1500 gallons; how many gallons remained ? Ans. 200.625 gal. 27. I bought 3 loads of wood, the firsi containing 1.02 cords, the second 1.05 cords, be third .945 cords; what did it cost at $3.60 a cord ? Ans. $10.854. 28. A dealer bought 1086 bushels of wheat; how many bins, each holding 20.25 bushels, will it fill, and how many bushel-bags can be filled from what remains ? Ans. 53 bing; 12.75 bags. 29. Two speculators bought 4320 acres of Western land. which they divide so that one has .37} and the other .621 of it; how many acres had each? Ans. 1620; 2700. 80. How many lengths of 6-inch stove-pipe can be inade from 87.48 pounds of Norway iron, if one length requires 3.84 pounds? Ans. 27. 31. Mr. Newlin paid $4000 for a truck farm, giving $76.25 an acre for 27.25 acres, and $85.75 for the remainder ; how many acres did he buy? Ans. 49.66+ acres. 32. A man bought 345.75 tons of hay, at $16.25 a ton, } of which he sold at $17.75 a ton, and the rest at cost; how much was the gain ? Ans. $172.875 33. Mr. Hartman bought a lot of wheat and sold .15 of it to one man, and .25 of it to another, and kept 572.85 busbels; how much did he buy? Ans. 954.75 ba. 34. A man devotes .12 of his income to charity, .25 for educating his children, .45 for bousebold expenses, and saves the remainder, which is $284.76; required bis income. Ans. $1582. 35. How many cords of wood, at $5.12. a cord, must I give f'or 91.25 bushels of wbeat, at $1.40 a busbel, and 85 bushels of rye, at $1.25 a bushel ? Ans. 45.66 cords. 36. The circumference of the fore wheel of a wagon is 12.75 feet, and of the bind wheel 14.25 feet; how much oftener does one turn than the other in going 5280 feet, or one mile? Ans. 43.59+ times. 37. A ship whose cargo was worth $25,000, being disabled in a storm, .454 of the whole cargo was thrown overboard; what would a merchant lose who owned .25 of the Ans. $2843.75. 38. A grain dealer expended $6210 for grain, of it being for wheat, at $1.25 a bushel, of it for corn, at $0.75 a bushel, and the remainder for rye, at $1.12a bushel ; how many bushels of each kind did he purchase ? Ans. Wheat, 1656 bu.; Corn, 2070 bu.; Rye, 2300 ba cargo? UNITED STATES MONEY. 211. United States Money, or the currency of the United States, is expressed in the decimal system. 212. The several denominations and their relation to each other are presented in the following table : TABLE. 66 10 mills equal 1 cent. 10 dimes equal 1 dollar. 10 cents 1 dime. 10 dollars 1 eagle. NOTE.-- of a dollar 25 cents; } of a dollar = 50 cents; t of a dollar = 75 cents; of a cent=5 mills. 213. The dollar is the unit and is indicated by the symbol $; the eagle and dollar are read as a number of dollars. Thus $245 is read 245 dollars, instead of 24 eagles, 5 dollars. 214. The dime is one tenth of a dollar, and is expressed as tenths, the decimal point being placed between dimes and dollars. Thus $2.3 expresses 2 dollars and 3 dimes. 215. The cent is one tenth of a dime or one hundredth of a dollar, and is written in hundredths place. Thus $6.75 indicates 6 dollars 7 dimes and 5 cents. Dimes and cents, however, are usually read as a number of cents. Thus 86.75 is read 6 dollars and 75 cents. 216. Since dimes and cents are regarded as a number of cents, when the number of cents is less than 10, a cipher must be written in tenths place. Thus 3 dollars and 4 cents are written $3.04. 217. The mill is one tenth of a cent or one thousandth of a dollar, and is written in thousandths place. Thus $8.375 is read 8 dollars 37 cents and 5 mills. Notes.-1. In checks, notes, drafts, etc., cents are usually written as Fundredths of a dollar in the form of a common fraction, as $1270. % When the final result of a business computation contains mills, if 5 or nuore they are reckoned 1 cent, and if less than 5 they are rejected. Thus $7.187 would be reckoned as $7.19 and $3.162 as $3.16. 3. We used dollars and cents in treating the fundamental rules; we now give a more formal treatment of decimal currency, involving problems that pupils were not then prepared to solve. EXEBCISES IN NUMERATION. Read the following 1. $15.65. 6. $28.05 9. $100.001, 2. $14.753. 6. $10.50. 10. $202.202. 3. $28.284 7. $105.105. 11. $370.037. 4. $132.125. 8. $125.005. 12. $1030.001. EXEBCISES IN NOTATION. Wrice on the slate or board REDUCTION OF UNITED STATES MONEY. 218. Reduction is the process of changing a number from one denomination to another without altering its value. 219. From the explanation given we have the following PRINCIPLES. 1. To reduce cents to mills, annex one cipher. 2. To reduce dollars to cents, annex two ciphers. 3. To reduce dollars to mills, annex three ciphers. 4. To reduce cents to dollars, place the point two places from the right. 5. To reduce mills to dollars, place the point three places from the right NOTE.-In reducing a number of dollars and cents to cents, etc., the separatrix should be removed ; thus, $5.25 = 525 cents, and $8.755 8755 mille. WRITTEN EXERCISES. 1. Reduce 5 dollars to cents. SOLUTION.-In 1 dollar there are 100 cents, and in 5 dollars ther are 5 times 100 cents, or 500 cents, or we annex two ciphers, as soov directed. |