« ΠροηγούμενηΣυνέχεια »
10. Three feet make 1 yard, and 51 yards a rod. How many feet make a rod ? 5 rods? 8 rods?
11. Sixteen and a half feet make a rod, and 320 rods a mile. How many feet in a mile ?
12. Four quarters make a yard, and 5 quarters make an ell English. How many quarters in 5 yards? How many ells English in 20 quarters? How many ells English, then, in 5 yards?
13. Four quarters make a yard, and 6 quarters an ell French. How many quarters in 12 yards? How many ells French in 48 quarters ? .
14. Five quarters make an ell English, and 6 quarters an ell French. How many ells French, then, in 12 ells English ? Solve this question first by multiplication and division, and then by division and subtraction.
15. Four quarters make a yard, 5 an ell English, and 3 an ell Flemish. How many ells English in 15 yards ? and how many ells Flemish in the same ?
16. Twenty shillings make a sovereign, and twenty-one shillings make a guinea. How many guineas in 63 sovereigns ?
Solve this question first by multiplication and division, and then by division and subtraction.
17. One of the fields of a farm is exactly square, being 40 rods long and 40 wide, making 1600 square rods. Another field is only 25 rods wide, yet it contains thc same number of square rods. Is the last named field longer or shorter than the first, and what is its length ?
18. Sixty seconds make a minute, and 60 minutes an hour. How many seconds in an hour ? In 5 hours ? In 25 hours ?
19. Twenty-four hours make a day, and 7 days a week. How many
hours in a week ? In 4 weeks? In 6 weeks? In 14 weeks? In 19 weeks ? [14=15—1; 19=20–1.]
20. Two pints make a quart, 8 quarts a peck, 4 pecks a bushel, and 8 bushels a quarter. How many pints in a quarter ?
21. Eight quarts make a peck, and 4 pecks a bushel. How many quarts in 75 bushels ?
22. Two pints of milk make a quart, and 4 quarts a gallon. How much will a pint cost, at 40 cents a gallon?
1. A FARMER sent his son to market with 24 bushels of potatoes, which he sold at 25 cents a bushel. He bought 16 pounds of sugar, at 64 cents a pound, and 11 pounds of coffee, at 9 cents a pound. How much money did he carry home ?
[The teacher should require his pupils to prove this and the following questions, and explain the process somewhat as follows: 24 times 25 is į of 24X100=600 ; 16 pounds of sugar, at 6 cents, come to 96 cents, and of 16=4, making 100 cents; and 11 pounds of coffee, at 9 cents, come to 99 cents; together 199 cents, which, taken from 600 cents, leave 401 cents to carry home.]
2. A storekeeper sold 3 dozen of eggs, at 10 cents per dozen ; 3 yards of calico, at 121 cents per yard; and 16 pounds of rice, at 5 cents per pound. What did the whole amount to?
3. A man divided $360 dollars between his two sons and two daughters, giving 2 shares to each son, and 1 share to each daughter. How much did each son and daughter get.*
4. At a certain meeting of 280 persons, there were 4 times as many children and twice as many women as men. How many were there of each class?
5. Two brothers, one of whom was twice as rich as the other, calculated their property, and found that together they had $3600. How much did each possess
? 6. The sum of $275 is to be divided among 2 men in such way that for every $4 that one receives, the other is to receive one. How much does each receive ?
* These fractional formulas, or as many as necessary, may be exhibited on the blackboard at the first recitation, but omitted at the review. But neither slate nor paper should be used in any of the exercises in Oral Arithmetic.
7. If a certain number is multiplied by 4, the product is 24. What is the number? By what process is it ascertained ?
8. If a certain number is divided by four, the quotient is 24. What is the number? By what process is it ascertained ?
9. Ten was added to a certain number, and 8 subtracted from it; it was then multiplied by 6 and divided by 4, when the result was found to be 24. What was the number ? Reverse the process. Why?
10. If 4 pounds of brown sugar cost 25 cents, what will 9 pounds cost?
Suggestive Questions. — By what number must the 25 cents be divided to show the price of 1 pound? By what multiplied to show the price of 9 pounds ? Place these numbers so as to indicate such operations; that is, place them in a fractional form, thus, X 25. Why?
11. If 8 pounds of rice cost 56 cents, what will 15 pounds cost? x56. Why? [See note on preceding page.]
12. If 6 pounds of refined sugar cost 75 cents, what will 124 pounds cost ? x 75. Why not 12 ?
13. A man who employed 11 laborers, found that the wages he paid came to $77 a week. He afterwards hired 4 more laborers at the same rate. How much would the weekly wages then amount to ? 15x7. Why?
14. How much is į of 105 ? If, then, the wages for 6 days amount to $105, how much would they amount to for 4 days?
15. If the wages of 15 men amount to $105 for a week of 6 working days, how much would they amount to for 3 weeks and 2 days ? 20=40x105. Why?
16. At $105 for 15 laborers for a week of 6 days, how much does each man earn per day?
17. If a man travel 8 days, when the day is 12 hours long, how many hours does he travel ?
18. If a man travel 360 miles in 6 days, when they are 12 hours long, how far will he travel in 8 days, when they are 10 hours long? 1,0 X 360. Why?
19. At $33 for 6 barrels of flour, what will 32 barrels cost ? 16x11. Why?
20. If wheat rise in price should the 5 cent loaf be made larger or smaller ?
21. If a 5 cent loaf weigh 10 ounces when wheat is 80 cents a bushel, how much should it weigh when it is 100 cents per bushel ? x10. Why?
22. A ship was provisioned for 8 months, at the rate of 15 ounces per day to each person. What must be the daily allowance for each person, in order that the provision may last 12 months ? More or less ? and how much? *x15. Why?
23. A retailer one morning weighed his rice, and found that he had exactly 44 pounds. In the evening he again weighed it, and found that he had remaining 3 times as much as he had sold. How much had he sold ? 4. Why?
24. The same man weighed his raisins in the morning, and found them to weigh 40 pounds. In the evening there remained 8 pounds more than was sold. How many pounds were sold ?
25. Three men purchased jointly a piece of woods, containing 1600 square rods. By agreement the second was to have 200 rods more than the first, and the third 200 rods more than the second. How many square rods was each man to have ? 333}, 533}, 733. Why?
26. There are two numbers whose sum is 96, and their difference 12. What are the numbers ? 96 — 6. Why?
27. Two merchants agreed to trade as follows: The first was to receive $60 a month for carrying on the business; the remainder was to be shared so that the second was to receive double the amount of the first, exclusive of his monthly pay. They gained 600 dollars the first month. How much would each receive ?
Remark. — Interest is an allowance by a borrower for the use of money, or any kind of property lent. Interest is also frequently allowed on unpaid debts. The rate or amount of interest for a given sum differs at different times and in different places. In the state of New York, lawful interest is 7 per cent.; but-in most parts of the United States, it is 6 per cent.; that is, 6 for the use of 100 for one year, whether the money be cents, dollars, pounds, or any other denomination. As 100 cents make 1 dollar, 6 cents is the usual interest for 1 dollar for a year. In reckoning interest, 30 days are considered a month, and 360 days a year.
28. At 6 cents for a dollar for 1 year, what is the interest of 5 dollars for the same time? Of $8? Of $12? Of $15 ? Of $24? Of $100? Of $96 ? Of $125 ? *
* $ is an abbreviation of U.S., and is used to denote dollars, the currency of the U. S.
29. At 6 cents for a dollar for one year, what would be the interest for 2 years ? 4 years ? 5 years?, 7 years?
30. At 6 per cent. (or 6 for 100) for 1 year, what is the interest of $2 for 2 years ? $8 for 2 years ? $6 for 3 years ?
31. As there are 12 months in 1 year, what is the interest of $1 for 6 months, at 6 per cent. ? Interest of $1 for 2 months? Of $6 for 3 months ? Of $6 for 8 months ? $6 for 9 months ? $6 for 11 months ? $6 for 1 month ? $6 for 7 months ?
32. At 6 per cent., what is the interest of $100 for 6 months ? For 8 months ? 9 months ? 1 month? 7 months ? 11 months ?
33. At 6 per cent., what is the interest of $150 for 1 year? Of $200 ? Of 250 ? 226? 500? 750 ? 326 ? 530 ?
34. At 6 per cent., for 12 months, what would be the interest for 2 months, or 60 days ? For 30 days, or one month? For 15 days ? For 45 days ? For 20 days ? For 40 days?
35. At 6 per cent. for 12 months, how much for 2 months, or 60 days ? How much for 1 day? 2 days ? 5 days? 8 days ?
36. At 6 per cent. for 12 months, what is the interest of $100 for 18 months ? For 16 months ? For 8 months ?
37. If the interest of $100 for twelve months is $6, how long must that sum be at interest to produce $9? To produce $12? $4? $1 ?
38. A man was sent on horseback from Boston to Hanover, and went at the rate of 5 miles an hour. After he had been gone 8 hours, another was despatched after him to bring him back. 1. How far was the first ahead when the second started ? The second went at the rate of 8 miles an hour. 2. How much would he gain on the first in an hour ? 3. In how many hours would he overtake him? 4. How many miles would the first have travelled before he was overtaken? Ans. to 3d question, 40. Why?
39. A man sets out on a journey, and travels 30 miles a day. After he had been gone 3} days, his son sets out after him, and travels 45 miles a day? In how many days would he overtake him?
40. A cistern has two pipes. The first can fill it in 3 hours, and the second in 6 hours? How much of it would each of