T. 64. To multiply by any number of 9's. 1. Multiply 4789653 by 99999. OPERATION. -965300000 4789653 960510347 Product. Ans. 478960510347. By adding 1 to any number composed of nines, we obtain a number expressed by 1 with as many ciphers annexed as there are nines in the number to which 1 is Thus, 999+1=1000. Therefore, annexing to the multimany ciphers as there are nines in the multiplier is the g as multiplying the number by a multiplier too large by tracting the number to be multiplied from this enlarged ...ill give the true product. -Annex as many ciphers to the multiplicand as there are 9's tiplier, and from this number subtract the number to be mul EXAMPLES FOR PRACTICE. ART. 66. To divide by 33. Ex. 1. Divide 6789543 by 331. OPERATION. 6789543 3 Ans. 20368620. Multiplying the dividend by 3 makes it three times too great; therefore, to obtain the true quotient, we must divide by 100, a divisor three times greater This is done by cutting off two figures on the right. 20 3 6 8 612 9 Quotient. than the true one. RULE. - Multiply the dividend by 3, and divide the product by 100. OPERATION. 9874725 8 789971800 Quotient. Ans. 789978. Multiplying the dividend by 8 makes it eight times too great; therefore, to obtain the true quotient, we must divide by 1000, a divisor eight times greater than the true one. We do this by cutting off three figures on the right. Multiply the dividend by 8, and divide the product by 1000. EXAMPLES FOR PRACTICE. 2. Divide 1728125 by 125. QUESTIONS. Ans. 13825. Art. 66. What is the rule for dividing by 33? Give the reason for the rule. Art. 67. What is the rule for dividing by 125? What is the reason for the rule? § VIII. MISCELLANEOUS EXAMPLES, INVOLVING THE FOREGOING RULES. 1. A BOUGHT 73 hogsheads of molasses at 29 dollars per hogshead, and sold it at 37 dollars per hogshead; what did he gain? 2. B bought 896 acres of wild land at 15 dollars per acre, and sold it at 43 dollars per acre; what did he gain? 3. N. Gage sold 47 bushels of corn at 57 cents per bushel, Which cost him only 37 cents per bushel; how many cents did he gain? 4. A butcher bought a lot of beef weighing 765 pounds at 11 cents per pound, and sold it at 9 cents per pound; how many cents did he lose? 5. A taverner bought 29 loads of hay at 17 dollars per load, and 76 cords of wood at 5 dollars a cord; what was the amount of the hay and the wood? 6. Bought 17 yards of cotton at 15 cents per yard, 46 gallons of molasses at 28, cents per gallon, 16 pounds of tea at 76 cents a pound, and 107 pounds of coffee at 14 cents a pound; what was the amount of my bill? 7. A man travelled 78 days, and each day he walked 27 miles; what was the length of his journey? 8. A man sets out from Boston to travel to New York, the distance being 223 miles, and walks 27 miles a day for 6 days in succession; what distance remains to be travelled? 9. What cost a farm of 365 acres at 97 dollars per acre? 10. Bought 376 oxen at 36 dollars per ox, 169 cows at 27 dollars each, 765 sheep at 4 dollars per head, and 79 elegant horses at 275 dollars each; what was paid for all? 11. J. Barker has a fine orchard, consisting of 365 trees, and each tree produces 7 barrels of apples, and these apples will bring him in market 3 dollars per barrel; what is the income of the orchard? 12. J. Peabody bought of E. Ames 7 yards of his best broadcloth at 9 dollars per yard, and in payment he gave Ames a one hundred-dollar bill; how many dollars must Ames return to Peabody? 13. Bought of P. Parker a cooking-stove for 31 dollars, 7 quintals of his best fish at 6 dollars per quintal, 14 bushels of rye at 1 dollar per bushel, and 5 mill-saws at 16 dollars each; in part payment for the above articles, I sold him eight thousand feet of boards at 15 dollars per thousand; how much must I pay him to balance the account? 14. In 1 day there are 24 hours; how many in 57 days? 15. In one pound avoirdupois weight there are 16 ounces; how many ounces are there in 369 pounds? 16. In a square mile there are 640 acres; how many acres are there in a town, which contains 89 square miles? 17. What cost 78 barrels of apples at 3 dollars per barrel ? 18. Bought 500 barrels of flour at 5 dollars per barrel, 47 hundred weight of cheese at 9 dollars per hundred weight, and 15 barrels of salmon at 17 dollars per barrel; what was the amount of my purchase? 19. Bought 760 acres of land at 47 dollars per acre, and sold J. Emery 171 acres at 56 dollars per acre, J. Smith 275 acres at 37 dollars per acre, and the remainder I sold to J. Kimball at 75 dollars per acre; how much did I gain by my sales? 20. Bought a hogshead of oil containing 184 gallons, at 75 cents per gallon; but 28 gallons having leaked out, I sold the remainder at 98 cents per gallon; did I gain or lose by my bargain? 21. Bought a quantity of flour, for which I gave 1728 dollars, there being 288 barrels; I sold the same at 8 dollars per barrel; how much did I gain? 22. Purchased a cargo of molasses for 9212 dollars, there being 196 hogsheads; I sold the same at 67 dollars per hogshead; how much did I gain on each hogshead? 23. A farmer bought 5 yoke of oxen at 87 dollars a yoke; 37 cows at 37 dollars each; 89 sheep at 3 dollars apiece. He sold the oxen at 98 dollars a yoke; for the cows he received 40 dollars each; and for the sheep he had 4 dollars apiece. How much did he gain by his trade? |