DIVISION OF DECIMALS. 34. DIVISION is the reverse of multiplication. Therefore, processes in division should be the reverse of those in multiplication. As we added the decimal places in multiplication to get the number of places to point off in the product, so we subtract in division to get the number of places to point off in the quotient. Point off as many places in the quotient as the decimal places in the dividend exceed those in the divisor, or add as many ciphers to the quotient as the decimal places in the divisor exceed those in the dividend. NOTE 1. In practice it is not necessary to carry the division farther than the 4th decimal place. If the dividend does not contain figures enough to give this number of places, and the last figure in the dividend gives a remainder in dividing, annex ciphers to the dividend so as to continue the division, and consider the quotient figures arising from the use of these ciphers as so many decimal places in the quotient. NOTE 2. - If the places in the dividend are less than those in the divisor annex enough ciphers to the dividend to make them equal. The quotient arising from the use of all these places will be a whole number. If there be a remainder now annex ciphers so as to continue the division. The quotient arising from the use of these ciphers will be decimal. NOTE 3. - When the dividend is less than the divisor annex ciphers to the dividend in order to divide. The quotient in this case will be entirely decimal. NOTE 4. When the quotient contains less figures than the rule requires to be pointed off make up the lack by prefixing ciphers. MISCELLANEOUS PROBLEMS IN FRACTIONS AND DECIMALS. 35. 1. Sold 4 pieces of carpet. The first contained 314 yds., the second 37 yds., the third 49 yds., and the fourth 44 yds. How many yards were sold in all? 2. A grocer packed in a box for shipment 15ğ lbs. sugar, 19 lbs. coffee, 2 lbs. tea, 173 lbs. ham, and 25 Ibs. bacon. What was the total weight of the contents of the box? 3. I bought 4 bbls. of sugar, the net weight of each being respectively 275 lbs., 285 lbs., 291 lbs., and 269-7 lbs. What was the total net weight? 4. A man inherited of an estate in his own right, and bought the shares of two fellow-legatees who had inherited respectively and of the same estate. What part of the estate did he then own? Y 5. A lady purchased the following goods: 5 yds. of ribbon for $, 14 yds. of lace for $1, and 5 yds. of silk for $15. How many yards did she purchase, and how much money did she spend? 6. Bought of a vessel, then sold. How much do I now own? 7. A farmer bought a cow for $60 and a ton of hay for $171. How much change should he receive out of a $100 note? 8. Paid $331 for taxes, and $125 for one month's rent. How much will I have left out of four $50 bills? 9. If I pay $77 for a barrel of flour, and $14 for some eggs, how much less than $10 is the whole cost? 10. If 3 bushels of apples cost $23, what will be the cost of of 3 bushels? 11. If of a pound of tea cost $1, what is the cost of 31⁄2 times as much? 12. What is the value of 12 cords of wood at $61⁄2 a cord? 13. of 176 V 14. If a pound of coffee is worth $3, what is the value 14. What will 19 dozen eggs cost at 371 cts. per dozen? 15. If 4 tons of hay cost $32, what is the value of 170 tons at the same rate? 16. What is the cost of 25 acres of land at the rate of $750 for 11 acres? 17. If a man can walk 153 miles in 3 hours, how long will it take him to walk 38 miles at the same rate? 18. What is the cost of 114 lbs. of coffee, if 1⁄2 of 4 of 121 lbs. cost 85 cts.? 19. What is the cost of 12 bbls. of flour, if of } of 24 bbls. cost $62? Pexplain explain 20. Bought 50 lbs. of nails at 61 cts. a pound; 15 bolts at 12 cts. a piece; and 3 dozen screws for 371⁄2 cts. What was the amount of my bill? 21. Bought some coffee for $55, and sold it for of its cost, thus losing 9 cts. a pound. How many pounds did I buy? 22. What is the cost of 14 yds. of cloth if 364 yds. cost $119? 23. If 17 bushels of apples cost $93, how many bushels can be purchased for $23? 24. A owes B $30.283, and pays it in 32 yds. of dress goods at 823 cts. a yard, and the remainder in calico at 5 cts. a yard. How many yards of calico should B receive? 25. A farmer's yield of potatoes averaged 98.94 bushels per acre, of oats, 34.65 bushels per acre, and of wheat 13.65 bushels per acre. If 110 acres were planted in potatoes, 252 acres in oats, and 17.8 acres in wheat, what was the total number of bushels harvested? 26. A grocer buys 4 bags of coffee which average 132.08 lbs. each. If 3 of the bags weigh respectively 128.05, 131.75, and 134.15 lbs., what is the weight of the fourth bag? 27. If .34 of a barrel of vinegar cost $3.06, what will 5.3 bbls. cost? 28. A dealer in produce bought 4 wagonloads of wheat, containing respectively 30.015, 31.5, 29.05, and 334 bushels. What was the total cost at $13 per bushel? V 29. From the sum of .163, 3, 9.236, 816, and 11.111 take the difference between 24.621 and 137. 30. A manufacturer finds that the cost of the raw material for a dozen gloves is $93. cost for manufacturing expenses, 1 for boxing and for the profit. ་ 5 To this he adds ¦ of the of the cost for interest, If the cutting and the making, which cost $3.90ğ, be added, what is the selling price? |