16. 17 18. FRACTIONS AND RELATIONS. 6. Subtract 46031 from 71706. 159 8. If 17 yards of cloth be cut from a piece contain ing 49 yards, how much will be left? 16 3 16 9. A retailer put into a firkin, 28 pounds of butter at one time, 19 pounds at another, and 35 pounds at another, and then sold out 25 pounds. pounds still remained in the firkin? 5 SECTION 17. 1. Suppose a rail-road car to run How many of a mile in 1 minute; what distance will it run in 47 minutes? 2. How many whole ones in 47 times? 3. If of a yard of broad-cloth will make 1 jacket, how many yards will it take to make 18 jackets? 4. How many whole ones in 18 times ?? 5. If of a pound of gunpowder tea cost 1 dollar, how many pounds can be bought for 50 dollars? 6. How many whole ones in 50 times ? SECTION 18. 1. What is the product of 86, multiplied by 9? We multiply by 9 thus, 9 times 964 9 779 is 3; equal to 5. Then we write this under the 4, and carry the 5 to the product of the 6 units. 2. What is the product of 413, multiplied by 7? 3. What is the value of a field, which contains 5 acres, allowing it to be worth 54 dollars per acre? 4 How much is 4 times 3513? 20 5. How much is 9 times 14731 24 6. How much is 28 times 543? 542 28 432 108 182/ 153033 48 ? Here we are obliged to multiply by 8 units and 2 tens separately, and we cannot well bring in the product of the fraction by the 2 tens. Therefore, we first multiply the whole numbers, and then find 28 times, in a separate .operation, which is not here written. 7. How much is 92 times 20511% 8. How much is 100 times 14 ?? 15 ? 9. How many gallons of wine are there in 31 casks, each cask containing 54 gallons? 5 42 100 10. A merchant paid $75,4% apiece, for 47 mules. What did the whole amount to? 11. If a steam-boat run 23615 miles in 1 day, what distance will it run in 16 days? 12. How much is 15 times 27? 49 100 13. What cost 75 books, at 37% of a dollar apiece? 14. If a horse eat 1 of a bushel of oats a day, how many bushels will he eat in 365 days? SECTION 19. 1. If of a chest of tea be worth $6.871, what is the whole chest worth? 2. If of a dollar will pay for travelling 27 miles on a turnpike road, how far can you go for $1? 3. 790 is of what number? 4. If of a kite line be 25 yards in length, what is the whole length of the line? 5. 305 is of what number? 6. If a man can earn 12 cents in of a day, what sum of money can he earn in 1 day? 7. If of a yard of gold wire be worth 15 of a dollar, what is the value of 1 yard of the wire? SECTION 20. 1. A boy having $2, gave of his money for a knife. What fraction of I dollar did the knife cost? 2. of 2 is equal to what part of 1? 3. 6 men divided 5 barrels of flour equally among them, each man taking of the flour in each barrel. What fraction of a barrel did each man get? 4. of 5 is equal to what part of 1? 5. If you should take of a bushel of corn from each of 10 bushels, what fraction of 1 bushel would you obtair? 6. What part of 1 is of 10? 39 7. What part of 1 is of 2? is of 3? is of 4' is of 18 is of 38? 19. 20. 21. FRACTIONS AND RELATIONS. 161 8. A tenant raised 28 bushels of corn, and gave his andlord of it. What improper fraction of a bushel, [how many thirds of a bushel,] did the landlord receive? How many bushels did the landlord receive? 9. of 28 is equal to what improper fraction? Then of 28 is equal to how many whole ones? 10. of 42 is equal to what improper fraction? Then of 42 is equal to what mixed number? 1 11. 13 of 29 is equal to what improper fraction? Then of 29 is equal to what mixed number? 1 12. If $721 should be divided equally among 6 men, how many sixths of a dollar would each man have? many dollars would each man have? How SECTION 21. 1. Suppose a hogshead of brown sugar to be worth $115; what is the value of of the sugar 2. What is of 115? ? 3. 5 men from Connecticut, bought 793 acres of land in Michigan, and divided it into 5 equal farms. How many acres were there in each farm ? The To find of 793 acres, we divide 793 by 5. quotient is 158 acres, and there is a remainder of 3 acres To divide these 3 acres, we take of each acre for each farm. of 3 acres is of 1 acre. 4. What is of 1315?of 530? of 8201? 5. Suppose 12 men to share equally in a prize of $551.20; what is each man's share? 1 6. What is of 55120? 2 of 967? of 700? 7. The Young Ladies' Class Book, which consists of 408 pages of select reading lessons, has been read through by 25 scholars; each reading an equal portion. How many pages did 1 scholar read? 8. of £1 [ of 20s.] is how many shillings, and what fraction of a shilling? 9. Find of £7 in shillings—that is, reduce £7 to shillings, and find of the number of shillings. 10. of 5 shillings is how many pence? 13. 11 men divided 9 hogsheads of molasses equally among them. How many gallons had each man? 14.1 of 7 furlongs is how many rods? 15. of 6 square feet is how many square inches? 16. How many seconds are there in of 10 hours? 17. A trader sold of a hogshead of wine at 37 cents for every of a gallon. What did it amount to? SECTION 22. 1. If 34 barrels of flour be made from 147 bushels of wheat, how much wheat will make 9 barrels of flour? 2. What is 9 times 34 of 147? 3. If 8 yards of broad-cloth cost $38, what will 13 yards cost, at the same rate? 4. What is 13 times of 38? 7 times of 654? 5 times 14 of 270 ? 21 times of 40975 ? 5. If it cost $1.25 to ride 20 miles in a stage, how much will it cost to ride 32 miles? 6. If $16 will pay for 85 pounds of butter, how many pounds will $25 pay for? 7. If 12 cords of wood cost $75, what will be the cost of 19 cords, at the same rate? 8. Suppose 21 cwt. of flour to be worth the same as 65 bushels of salt; how many bushels of salt must be given in exchange for 18 cwt. of flour? 9. If 8 barrels will hold 19 bu. 3pk. 4qt. of corn, how much corn can be put into 15 barrels ? 1. When writing SECTION 23. paper is sold at $5.42 per ream, what is the price of of a ream? 2. If of a ream of paper is worth $1.35, what is of a ream worth? 3. Suppose a hogshead of sugar to be worth $93; what is of it worth? 4. If of a hogshead of sugar is worth $13.284, what is of it worth? 5. What is of 3765? What is 6. How many gallons are there in How many gallons in of a pipe? of 3765? of a pipe of wine? In the following examples, it will be most convenient to multiply by the numerator of the fraction, before dividing by the denominator. See Second Method of operation, exemplified in page 152. 7. The highest point of the Andes, is 21440 feet: Mont Blanc, of the Alps, is as high. What is the height of Mont Blanc ? 8. Virginia contains 66000 square miles: Rhode Island is only How many square miles are there in Rhode Island? as large. 9. If a man's income be $1000 per year, what is his income for 9 months, or of a year? 10. Suppose a man by constant industry can $1.50 per day; what will he earn in 10 days, allowing him to rest of the time? 11. How much must be paid for 13 of a ton of Russia hemp, when the price is $210 per ton? 12. A man having 4 miles to go, rode of the way, and walked the remainder. How many rods did he walk? 13. Suppose 45000 pounds of iron to be sufficient to lay the track on 1 mile of rail-way; how many pounds of iron are required to lay the track on 17 mile? . 14. How much is 4500 plus 7 of 4500? 15. Suppose a rail-way car to run 350 miles a day; what distance will it run in 5 days? 16. How much is 5 much is 5 times 350 and 17. How much is 6 times 350?-That is, how of another time 350? times 91? 84 times 146? 31⁄2 times 244? 124 times 379? 16 times 978 ? PERCENTAGE. The term, per cent., is an abbreviation of per centum, and signifies, by the hundred. 1 per cent. of any number, is of that number; 2 per cent. is 18; 3 per cent. is; 4 per cent. is 13; and so on. 18. What is 5 per cent. of 360 dollars? 360 5 Since 5 per cent. is 156, we multiply by 5, and divide by 100. To divide by 100, we merely point off two figures from the right, as taught in page 116. |