In the next exercises, let the quotient be continued to thousandths, and be expressed by an approximate decimal. 11. Divide 13.29 by 2.8 and .278 by .07. Ans. 4.746' and 3.971'. 12. Divide 2.37 by 93 and .0011 by .09. 13. Divide .737 by 8.9 and .09 by 8.3.. 14. Divide 8.641 by 13 and .643 by 1.05. 15. Divide .023 by .03 and .013 by .074. Another Method of Reducing a Vulgar Fraction to a Decimal. § 153. The quotient of a less integer divided by a greater may be represented by a proper vulgar fraction; thus 3÷4 is 3. If the less integer be then divided by the greater, decimally, ` the vulgar fraction will be reduced to a decimal. 34 3.00 4.75; or 3.75. The application of Rule XXXII to this case, is substantially the same with that of Rule XXVIII. 17 to a decimal. Ans. .266'. to a decimal. 15, or reduce 34, or reduce 120, or reduce to a decimal. Ans. .264'. Ans. .108'. 200 13 to a decimal. Ans. .085. to a decimal. Ans. .073'. to a decimal. Ans. .538'. 19 Ans. .526'. to a decimal. Ans. .173'. 16. Divide 4 by 21. Divide 7 by 121 300 25. Divide 99 by 500, or reduce to a decimal. Ans. .198. 50% 26. How many gallons of wine, at 1 dollar 37 cents per gallon, may be bought for 25 dollars and 50 cents? Expressing the cents in decimals of a $, the number of gallons is the number of times $1.37 cents is contained in $25.5; that is, $25.5-$1.37 $25.5-$2.75. But in the Division of Federal Money, instead of fractions of a cent, it will generally facilitate the operation to take their equivalent decimals. We have then $25.5-$1.375. Ans. 18.545' gallons. 27. What quantity of coal, at 18 dollars and 75 cents per ton, may be purchased for 13 dollars? $13 will buy the same part of a ton that $13 is of $18.75. Ans. .693' of a ton. 28. How many hundred weight of flour, at 2 dollars 183 cents per hundred, may be purchased for 25 dollars? Ans. 11.428' hundred weight. 29. What quantity of land, at the rate of 25 dollars per acre, may be bought for 9 dollars 62 cents? Ans. .3849 of an acre. 30. How many bushels of clover seed, at 5 dollars 182 cents per bushel, may be bought for 30 dollars? 31. How many yards of cloth, at 4 yard, may be purchased for 19 dollars 3 Ans. 5.783' bushels. dollars and 50 cents a 75 cents? Ans. 4.388' yards. dollars and 85 cents per Ans. 25.974' barrels. 32. How many barrels of corn, at barrel, may be bought for 100 dollars? 33. What quantity of bacon, at 8 dollars 314 cents per hundred weight, may be purchased for 5 dollars 64 cents? Ans. .609' of a hundred weight. 34. What quantity of iron, at 45 dollars 50 cents per ton, may be bought for the sum of $7.064+$13.5 ? Ans. .451' of a ton. 35. How many barrels of apples, at 2 dollars 12 cents per barrel, may be bought for $75.832-$20.561? Ans. 26.011' barrels. 36. What should be paid for a ton of hay, when .7 of a ton sells for 13 dollars 12 cents? of If 7 tenths of a ton cost $13.121, 1 tenth would be worth $13.12; and a WHOLE TON, or 10 tenths, would be worth 10 of $13.12; that is, such a part of this sum as is expressed by the reciprocal of 7; or $13.12.7. We may also reason thus. The price of a ton will be such that .7 of the price, or the price X .7, will be $13.12}. Hence $13.12 is a dividend, or product given, and .7 a divisor, or one factor given to find the quotient, which will be the other factor. Ans. $18.750. 37. If 3 cords of wood sell for 12 dollars 75 cents, what is the price per cord? Ans. $3.642'. 38. If 5 yards of broadcloth cost 21 dollars 25 cents, what should be paid for 1 yard of the same cloth? Ans. $4.047'. 39. If of a lot of ground be worth 73 dollars 871⁄2 cents, what is the whole of the lot worth at that rate? Ans. $118.20. 40. If 4 cords of wood come to $9, what is the price per cord? What would 73 cords amount to? Ans. $2; and $15.50. 41. What is the price of wheat per bushel when 25 bushels sell for 37 dollars 683 cents, and what should be paid for 40 bushels at the same rate? Ans. $1.50; and $60. 42. What is the price of butter per pound when 13 pounds sell for 1 dollar 62 cents, and what ought to be paid for 145 pounds of butter at the same price? it sold? Ans. $.12; and $17.40. 43. Bought 50 bushels of salt for $31.25, and sold it at a profit of 25 cents per bushel. At what price per bushel was Ans. $.875. 44. Bought 321 barrels of corn for $81.25, and sold it at a profit of 614 cents per barrel at what price per barrel was it sold, and what was the whole profit made? Ans. $3.1125; and $19.906'. 45. A bought of B 1000 bushels of wheat, at $.871⁄2 a bushel; of which he has sold to C 453 bushels, at $.9 a bushel. At what price per bushel must the remainder be sold to produce a profit of $25 on the 1000 bushels ! Ans. $.90. 46. A person having $300 on hand would disburse it for equal quantities of sugar and coffee. What quantity of each can he purchase, if the sugar be 9 cents and the coffee 15 cents per pound? 9 cents 15 cents =24 cents; then 24 cents will buy 1 pound of each. Ans. 1250 pounds of each. 47. A miller wishes to purchase wheat, rye, and corn, in equal quantities. The prices of these commodities being respectively $1, $.5, and $.37 per bushel, how many bushels of each can he purchase for $500 ? Ans. 266.666' bushels of each. EXERCISES ON CHAPTER VI. 1. What is the value of the expression (3 hundredths +23 thousandths) 9 thousandths? Ans. .000477. 2. What is the value of the expression (8 tenths-75 ten-thousandths)×21 hundredths? Ans. .166425. 3. What is the value of the expression (34 thousandths-+7 hundredths)-3 hundredths? Ans. 3.466'. 4. What is the value of the expression (723 thousandths—9 thousandths)÷8 thousand? Ans. .000089'. 5. What is the value of the expression (34 ten-thousandths+8 hundredths)÷20 thousand? Ans. .000004'. Find the answer to each of the three following questions in a vulgar fraction, in its lowest terms. 6. What is the value of the expression (.25.125+2.5-.05-.005)X.04? Ans. 10. 7. What is the value of the expression (.1+.34+.09+3.2—1.375)÷÷5? Ans. 17%. 8. What is the value of the expression (80-28.5+100-50.4-90.1)÷50? Ans. td. Find the answer to each of the two following questions in an integer and decimal thousandths; employing a mixed or complex decimal to express the exact value. 9. What is the value of the expression (+51+10+.31+2%)—(7+&+51)? Ans. 5.941. 10. What is the value of the expression (253+3.63+16+100})—(41+1+10)? Ans. 130.583. 11. Find the sum 3840+5.123+3.479+31. Ans. 3879.602. 12. Find the sum .7309+ 7834+834.3+.75. Ans. 8669.7809. 13. Find the sum 80.01.1347.9348+3.5. Ans. 14. Find the difference 737.68-7.3473.. 84.5795. Ans. 730.3327. Ans. 756.937. Ans. 339.201 11. Find the amount of a merchant's bill for 3 yards or clot at 7 dollars 684 cents per yard, 124 yards of silk at 1 dolla 314 cents per yard, and 16 skeins of silk thread at 64 cents a skein. Ans. $43.984'. dollars per ton, may be Ans. .636' of a ton. 102 dollars and 50 cents, cents per barrel: at what 12. What quantity of iron at 45 purchased for 28 dollars 62 cents? 13. Bought 20 barrels of flour for and sold the same at a profit of 87 price per barrel was it sold, and what was the entire profit made? Ans. $6; and $17.50. 14. If a ship sail at the rate of 130.75 miles per day, in what time ought she to sail 69.33 miles? Ans. .530' of a day. 15. A merchant bought 25 yards of cloth at 4 dollars 87 cents per yard, and sold it at an entire profit of 50 dollars 68 cents at what price per yard was the cloth sold? Ans. $6.9025. 16. What is the price of sugar per hundred weight when hundred weight costs 6 dollars 37 cents, and what should be paid for 5 hundred weight of sugar at the same rate? Ans. $8.5; and $46.75. 17. A farmer bought a plantation containing 400 acres, at $20 per acre, and sold of it at a profit, on that half, of $213.12. At what rate per acre was the land sold? Ans. $21.565'. 18. If of a yard of silk cost $1.12, what sum should be paid for 15 yards at the same rate? Ans. $27.90. 19. A person wishes to purchase a quantity of coffee, and as much rice. The coffee is at 13 cents, and the rice at 5 cents, per pound; what amount of each can he purchase for $15? Ans. 83.783' pounds. 20. Allowing of a yard of cloth to cost $5.434, what sum ought to be paid for 13 yards at the same rate? Ans. $100.59375. 21. A bought of B 122 bushels of wheat, and of C 75 bushels, at 93 cents per bushel. He made 60 bushels into flour, and sold the flour at a profit of $12.50 if he sells the remainder of the wheat at 814 cents per bushel, what will be his entire profit or loss? Ans. Loss $4.718'. 22. A speculator bought 50 barrels of flour at $4.06 per barrel, and 75 bushels of wheat at $.683 per bushel. Having sold 20 barrels of the flour at $5 per barrel, and the whole of the wheat at $.75 per bushel, at what rate per barrel must the remainder of the flour be disposed of to make his profit $100 on the whole ? Ans. $6.614' per barrel. |