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This method differs from the 24)16294896(678954, Ans. common way by placing the right14482606
hand figure of every product im181229
mediately under the dividend. 169129
121 8. Divide 3545304 by 47. 9. Divide 45005091 by 57.
Ans. 75432. Ans. 789563.
VI. To divide by any number of 9's, when their number is not less than half the number of places that will be in the quotient, and when there is no remainder.
RULE. — Anner as many ciphers to the dividend, as there are 9's in the divisor. Then write the proper dividend under the number thus found, and subtract it from the number to which ciphers have been annexed; and, as many places of the remainder at the right hand as there were ciphers annexed, are so many figures for the right hand of the quotient ; and, for the remaining numbers of the quotient, a competent number must be taken from the left hand of the above remainder. 10. Divide 123332544 by 999. OPERATION.
By examining the dividend and 123332544000 divisor, we know there will be 6
123332544 places in the quotient. We there123,209211,456
fore take three of these figures from
the right hand of the remainder for 123456 Quotient, Ans. The
lent, Alise the three right-hand figures of the quotient, and the other three we take from the left hand of the remainder. 11. Divide 12332655 by 999.
Ans. 12345. 12. Divide 987551235 by 9999.
Ans. 98765. 13. Divide 9123456779876543211 by 999999999.
MISCELLANEOUS EXAMPLES. 1. What number multiplied by 1728 will produce 1705536 ?
2. If a garrison of 987 men are supplied with 175686 pounds of beef, how much will there be for each man ? Ans. 178 lbs.
3. In one dollar there are 100 cents; how many dollars in 697800 cents ?
Ans. $ 6978. 4. In one pound there are 16 ounces; how many pounds are in 111680 ounces?
Ans. 6980 lbs. 5. A dollar contains 6 shillings; how many dollars are in 5868 shillings?
Ans. $ 978. 6. The President of the United States receives a salary of $ 25,000; what does he receive per month? Ans. $ 20831.
7. A man receiving $ 96 for 8 months' labor, what does be receive for 1 month ?
Ans. $ 12. 8. The distance from Haverhill to Boston is 30 miles; and, if a man travel 6 miles an hour, how long will he be in going this distance ?
Ans. 5 hours. • 9. The annual revenue of a gentleman being $8395, how much per day is that equivalent to, there being 365 days in a year?
Ans. $ 23. 10. The car on the Liverpool railroad goes at the rate of 65 miles an hour; how long would it take to pass round the globe, the distance being about 25,000 miles ? Ans. 384-8 hours.
11. How much sugar at $ 15 per cwt. may be bought for $ 405 ?
Ans. 27 cwt. 12. In 6789560 shillings how many pounds, there being 20 shillings in a pound ?
Ans. 339478 pounds. 13. The Bible contains 31,173 verses ; how many must be read each day, that the book may be read through in a year ?
Ans. 8514: verses. 14. In 123456720 minutes how many hours ?
Ans. 2057612 hours. 15. A gentleman possessing an estate of $ 66,144, bequeathed one fourth to his wife, and the remainder was to be divided between his 4 children; what was the share of each ?
Ans. $ 12,402. 16. A man disposed of a farm containing 175 acres at $ 87 per acre; of the avails he distributed $ 1234 for charitable purposes; $ 197 was expended for the purchase of a horse and chaise; the remainder was divided between 6 gentlemen and 8 ladies, and each lady was to receive twice as much as a gentleman; what was the share of each ?
Ans. $ 627 for a gentleman, and $ 1254 for a lady. 17. If there are 160 square rods in an acre, how many acres are in 1086240 square rods?
Ans. 6789 acres.
18. If 144 square inches make one square foot, how many square feet in 14222160 square inches ? Ans. 98765 feet.
19. What number is that, which being multiplied by 24, the product divided by 10, the quotient multiplied by 2, 32 subtracted from the product, the remainder divided by 4, and 8 subtracted from the quotient, the remainder shall be 2?
20. What is the difference between half a dozen dozen, and six dozen dozen?
Ans. 792. 21. Bought of F. Johnson 8 barrels of flour at $ 7 per barrel, and 3 hundred weight of sugar at $8 per hundred. What was the amount of his bill ?
Ans. $ 80. 22. Sold S. Jenkins my best horse for $75, my second-best chaise for $ 87, a good harness for $31. He has paid me in cash $ 38, and has given me an order on Peter Parker for $ 12. How many dollars remain my due ?
Ans. $ 143. 23. T. Webster has sold his wagon to J. Emerson for $ 85. He is to receive his pay in wood at $5 per cord. How many cords will it require to balance the value of the wagon?
Ans. 17 cords. . 24. Purchased a farm of 500 acres for $ 17,876. I sold 127 acres of it at $ 47 an acre, 212 acres at $ 96 an acre, and the remainder at $ 37 an acre. What did I gain by my bargain ?
Ans. $ 14,702. 25. A tailor has 938 yards of broadcloth; how many cloaks can be made of the cloth, if it require 7 yards to make one cloak ?
Ans. 134 cloaks. 26. Bought 97 barrels of molasses at $ 5 a barrel. Gave 17 barrels to support the poor, and the remainder was sold at $ 8 a barrel. Did I gain or lose, and how much?
Ans. $ 155 gain. 27. There are 12 pence in one shilling; required the number of pence in 671 shillings.
Ans. 8052 pence. 28. Twelve inches make one foot in length ; required the number of inches in 5280 feet, it being the length of a mile.
Ans. 63360 inches. 29. In one pound avoirdupois there are 16 ounces; required the ounces in 1728 pounds.
Ans. 27648 ounces. 30. Required the number of shillings in 8136 pence.
Ans. 678 shillings. 31. It requires 1728 cubic inches to make one cubic foot required the number of cubic inches in 3787 cubic feet.
Ans. 6543936 inches.
Section IX. TABLES OF MONEY, WEIGHTS, AND MEASURES.
- 1 Pound, 21 Shillings sterling "
1 Guinea, 28 Shillings N. E." i Guinea, Note. — One pound sterling is equal to $ 4.44), exchange value.
make i Pennyweight, marked dwt. 20 Pennyweights
OZ. 12 Ounces
20 5760 240
12 = 1 By this weight are weighed gold, silver, and jewels.
Note.-" The original of all weights used in England was a grain or corn of wheat, gathered out of the middle of the ear; and, being well dried, 32 of them were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But in later times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common use; and from hence the rest are com
Ib. 5760 288
= 1 Apothecaries mix their medicines by this weight; but buy and sell by Avoirdupois. The pound and ounce of this weight are the same as in Troy Weight.
AVOIRDUPOIS WEIGHT. 16 Drams
marked oz. 16 Ounces 1 Pound,
lb. 28 Pounds
qr. 4 Quarters
1 Hundred Weight,
cwt. 20 Hundred Weight
Ib. 256 16
qr. 7168 448 28 = 1
112 = 4 = 1 ton. 573440
2240 = 80 = 20 = 1 By this weight are weighed almost every kind of goods, and all metals except gold and silver. By a late law of Massachusetts, the cwt. contains 100 lbs. instead of 112 lbs.
A ton is reckoned at the custom-houses of the United States at 2240 lbs.
LONG MEASURE. 3 Barleycorns, or 12 Lines make 1 Inch, marked 12 Inches
1 Foot, 3 Feet
1 Yard, 6 Feet
1 Fathom, 54 Yards, or 16% Feet
1 Rod, or Pole, “ 40 Rods
1 Furlong, 8 Furlongs
1 Mile, 3 Miles " 1 League "
lea. 69] Miles nearly
« 1 Degree, "6 Deg. or 360 Degrees
66 1 Circle of the Earth.