On the opposite page, 30 cities and towns are exhib. ited in their respective situations, relative to each other; and the number of miles, by mail-road from town to town, is noted in figures. 11. Find the distance from Washington, through the intermediate towns, to Augusta, Me....... from Washington to Detroit....... from Washington to St. Louis from Washington to Natchez... from Washington to New Orleans.... from New Orleans to Augusta, Me. ....... 12. Suppose a citizen in each of the places on the opposite page, to start for Washington, and travel 7 miles an hour, 10 hours in each day; how long will each one be in performing his journey? 13. How long would it take you to walk from your school-room to Washington; allowing that you could walk 3 miles an hour, 7 hours in each day? 14. Two men started at the same time- one of them from New Orleans, and the other from Augusta, Me.and travelled towards each other, with equal speed. Between what two towns, and what distance from each of these towns did they meet? 15. Mr. A. went from Portland to Baltimore, travelling 5 miles an hour, and 10 hours a day. Mr. B. performed the same journey; but started 1 day later, and travelled 7 miles an hour. Where did B. pass A.? 16. Divide $1000 among A, B, and C, giving B twice as much as A, and C twice as much as B. 1.7. Gunpowder is composed of 5 parts sulphur, 7 parts charcoal, and 38 parts mitre. How many pounds of each ingredient, in 100 pounds of powder? 18. A and B purchased a cow for $16. A paid $9 of the price, and B paid $7. They sold the cow for $21. What was each one's share of the gain? Solution. Since A paid 1% of the price, and B, A must have of the gain, and B T 19. C and D traded in partnership; C owned $450 of the stock in trade, and D $290. They gained $146. What was each one's share of the gain? 20. Suppose $1000 stock in trade to gain $230; what is the gain on $351 of that stock? 21. E and F purchased 245 acres of land, for $2600. E paid $1200 of the money, and F paid the remainder. How much land should each one have? 22. The national debt of England is not less than $1900 000 000. Allowing 5 per cent. interest to be paid on this sum, how many families would it support, each family spending $400 per annum? 23. If a man can dig a trench in 15 days, and a boy can dig the same trench in 18 days, in what time can they both dig it? (See example 20, Oral sec.) 24. How many days will it take 17 men to perform a piece of work, that 1 man can perform in 95 days? 25. How many days will it take 30 men to perform a piece of work, that 4 men can perform in 50 days? 26. How many days will it take 25 men to perform a piece of work, that 6 men can perform in 40 days? 27. If 15 yards of carpeting, which is one yard wide, will cover the floor of a room, how many yards of carpeting, 3-quarters wide will cover the same floor? Direction. Find the number of square quarters con tained in 15 yards of the wider carpeting; then divide this number, by the number of square quarters contained in 1 yard of the narrower carpeting. 28. Suppose 3 yards of broad-cloth 5-quarters wide, to be made into a cloak; how many yards of silk 3-quarters wide, will it take to line the cloak? 29. How many yards of carpeting that is 5-quarters wide, will cover the floor of a room which is 19 feet in length, and 15 feet in width ? 30. How many bricks will it take to build a wall, 1 foot thick, 5 feet high, and 24 feet long; each brick being 8 inches long, 4 inches wide, and 2 inches thick? 31. If a man can hoef of an acre of corn in a day, and a boy of an acre, how much can they both hoe in a day? In what time can they both hoe 9 acres ? 32. There is a cistern, having 3 pipes; the first pipe will discharge the cistern in 4 hours, the second in 5 hours, the third in 6 hours. What part of the contents of the cistern would all the pipes together let off in 1 hour In what time would they all discharge the cistern? A 33. What is the height of a steeple, whose shadow is 148 feet 4 inches, when a shadow 5 feet 4 inches long is projected from a post 6 feet 4 inches high? 34. A trader failed in business, owing $11000, and having only $5000 to divide among his creditors. How much did he pay on a debt of $95.20? 35. A fox has 50 rods the start of a greyhound, but the hound runs 15 rods while the fox runs 9. How many rods must the hound run to catch the fox? 36. A cubic foot of air weighs 14 ounce. How many pounds of air does a room contain, which is 16 feet long, 14 feet wide, and 10 feet high ? 37. What number must that be, which, being increased by its half, and its third, becomes 88? 38. A and B hired a pasture for $30. A turned in 3 cows, and B turned in 12 sheep. Allowing 5 sheep to be equal to 1 cow, what must each pay? 39. Suppose London to contain 1250 000 inhabitants, New York 203 000, Philadelphia 167000, Baltimore 80 000, and Boston 61000; how many times greater is London, than each of the other cities? EXPLANATION OF CHARACTERS. + This character placed between numbers, shows : that they are to be added together; thus, 6+4 is 10. This character between numbers, shows that the number on the right hand is to be subtracted from the number on the left hand; thus, 9-3 is 6. X This character shows, that numbers are to be multiplied together; thus, 4×5 is 20. This character shows, that the number on the left hand is to be divided by the number on the right hand; thus, 28÷4 is 7. This character shows, that the number on the right is equal to the number on the left; thus, 4+8=12.17 8-3-5. 7×3=21. 32-4-8. 40.1426026+706241+360515=how much? 41.5147+28650-643-426=how much? 42,40673-62-40275×58=how much? 43.872+9516-1430×16÷12=how much? ود 23 DECIMAL FRACTIONS. SECTION 33. A decimal fraction is a fraction whose denominator is 10, or 100, or 1000, &c. The denominator of a decimal fraction is never written: the numerator is written with a point prefixed to it, and the denominator is understood to be a 1, with as many ciphers annexed, as there are figures in the numerator. Thus, .3 is 1; 31 316 .31 is 1; .316 is; 100, 3164. .3164 is 1. 3 1. Write upon the slate, the decimals expressing the following fractions. 10. 10%. 10 100 1000 10000 10000이. 3 708 1642 96041 When a whole number and a decimal are written together, the decimal point is placed between them. Thus, 24.6 is 241; 5.71 is 5100; 48.364 is 71 48364. 2. Write the following mixed numbers, expressing the fractions decimally. 381. 516081052410 10000 It is observable in our system of writing whole numbers, that any figure, wherever it may stand, expresses a quantity to as great as it would express, if it were written one place further to the left. For instance, in the number 1111, the 1 hundred is of a thousand; the 1 ten is of a hundred, or 1이 of a thousand; the 1 unit is of a ten, or 1앙이 of a thousand. In decimals, this system is continued below the place of units. For instance, in the number 1.111, the I next to the right of the unit is 1-tenth, that is, To of a unit; the 1 next to the right of the 1-tenth is 1o of a tenth, or 1-hundredth of a unit; the 1 next to the right of the 1-hundredth, is 16 of a hundredth, or 1-thousandth of a unit. one unit 1.11 1 Ciphers placed on the right hand of decimal figures, do not alter the value of the decimal; because, the figures still remain unchanged in their distance from the unit's place. For instance, .5, 50, and .500 are of equal value, they are each equal to. But every cipher that is placed on the left of a decimal, renders its value ten times smaller, by removing the figures one 5 place further from the unit's place. Thus, if we prefix one cipher to .5, it becomes .05 [100]; if we prefix two ciphers, it becomes 005 [10양이]; if we prefix three ciphers, it becomes .0005 [이양이이]; and so on. 3. Write upon the slate, decimals expressing the following fractions. To이. 이이이 10000 100000 100000이. 4 7 3 8 To read a decimal fraction, Enumerate and read the figures, as if they were whole numbers, and conclude by pronouncing the name of the lowest denomination. 4. Copy upon the slate, the several numbers standing in the following columns, and then read them. 6. Add the following numbers into one sum. 63.75 and 524.0764 and .23 and 261.803. 63.75 524.0764 .23 251.803 849.8594 In arranging decimals for addition, we place tenths under tenths, hundredths under hundredths, &c. We then begin with the lowest denomination, and proceed to add the columns as in whole numbers. 7. What is the sum of 2.164, 870.31, 756, 9.18, 157.0008, 26.104, and .3728? 8. What is the sum of 2706, 58.2, .2065, 6.441, 75, 14.2, and 990.752 ? In Federal Money, the dollar is the unit; that is, dollars are whole numbers; dimes are tenths, cents are hundredths, and mills are thousandths. See page 124. 9. Add together $24.6, $9.07, $5.009, and 5 cents. |