329217670782 Product, Ans. 12. Multiply 32567895 by 3333. 13. Multiply 876543 by 66666. OPERATION. 87654300000 876543 87653423457 2 Ans. 3)175306846914 58435615638 Product, Ans. 14. Multiply 345678 by 6666666. Ans. V. When the multiplier can be separated into periods, which are multiples of one another, the operation may be contracted in the following manner. 15. Multiply 112345678 by 288144486. OPERATION. 112345678 288144486 674074068 the product by 6. 5392592544 = the foregoing product x by 8 for 48. 16177777632 32355555264 the last product x by 3 for 144. the last product x by 2 for 288. 32371787641631508 Product. - SECTION VII. CONTRACTIONS IN DIVISION. I. To divide by 5. RULE. Multiply the dividend by 2, and the product, except the last figure at the right, is the quotient. NOTE. The remainder will be tenths. 1. Divide 67895 by 5. RULE. OPERATION. 13579,0 Quotient. II. To divide by 25. Ans. 13579. Multiply the dividend by 4, and the product, except the last two figures at the right, is the quotient. NOTE. The two figures at the right are hundredths. 2. Divide 8765887 by 25. OPERATION. Ans. 3506354. 8765887 4 350635,48 Quotient. III. To divide by 33}. RULE. Multiply the dividend by 3, and the product, except the last two figures at the right, is the quotient, and the last two are hundredths. 3. Divide 876735 by 33}. Ans. 2630280. OPERATION. 876735 3 26302,05 Quotient. IV. To divide by 125. RULE.-Multiply the dividend by 8, and the product, except the last three figures, is the quotient, and these last three figures will be thousandths. OPERATION. This method differs from the 24) 16294896(678954, Ans. common way by placing the right 14482606 181229 169129 121 hand figure of every product immediately under the dividend. 121 8. Divide 3545304 by 47. 9. Divide 45005091 by 57. VI. To divide by any number of 9's. Ans. 75432. Ans. 789563. RULE. Let the dividend be divided into periods, consisting each of as many fig ures as there are 9's in the divisor, beginning the division into periods at the left hand. Then write the left-hand period under the second period, the second period under the third, and so on, omitting all the figures which would thus fall to the right of the original dividend, and let this be called a second dividend. Again, write the first period of the second dividend under the second period of the same, its second period under its third, and so continue writing successive dividends, omitting the figures at the right as above, till the first period of the first dividend falls under the last period of the Add together the several dividends thus formed, cutting off as many figures in the sum, as there are 9's in the divisor. Now observe how many units in adding were carried from the right to the left hand figure in the part thus cut off, and add this number of units to the whole. The figures on the left of the separatrix will be the quotient, and those on the right the true remainder. same. 1. What number multiplied by 1728 will produce 1705536 ? Ans. 987. 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. $2083. 7. A man receiving $96 for 8 months' labor, what does he 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 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? Ans. 792. Ans. 15. 20. What is the difference between half a dozen dozen, and six dozen dozen? 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 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. the amount of his bill? 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. $14,402. 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? 27. There are 12 pence in one shilling; ber of pence in 671 shillings. 28. Twelve inches make one foot in number of inches in 5280 feet, it being the Ans. $155 gain. required the numAns. 8052 pence. length; required 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. |