72. Reduce 1, 3, 3, 18, 64, 25, and 17 to decimals. 164 A decimal is a fraction, and, if its denominator is written, it will appear as a common fraction. 73. Reduce 0.48 to the form of a common fraction and then to its lowest terms. 0.4848. Ans. 74. Reduce 0.125 to its lowest terms. 100 75. Reduce 0.17 to the form of a common fraction. 84. From 853.078 subtract 563. 85. Multiply 67ğ by 14.5. 86. Multiply 514.85 by 151. 87. Divide 146.25 by 83. 88. Divide 553.7 by 9.25. 89. Divide 1720.8 by 81. 90. Divide 653 by 17.3. 91. Divide 7877 by 7.65. (For Circulating Decimals, see Appendix, page 340.) DECIMAL SYSTEM OF MONEY, WEIGHTS, AND MEASURES. 167. In this currency, the dollar is the unit, cents and mills being decimals of a dollar. Thus, $3.62 represents three dollars and sixty-two cents; $4.085 represents four dollars, eight cents, and five mills; etc. Figures at the right of the third decimal place represent parts of a mill; thus, $5.36275 dollars, 36 cents, 2 mills, and The terms eagle and dime are not much used. of a mill. Eagles and dollars are read together as dollars, and dimes and cents as cents; thus, $47.843 is read 47 dollars, 84 cents, 3 mills. Mills are often written and read as fractions of a cent; thus, $0.12, twelve cents and a half. 168. Reduction is the changing of a quantity to units of greater or less value without changing the value of the quantity expressed. 169. Dollars are reduced to cents by moving the decimal point two places to the right, and to mills by moving the decimal point three places to the right. Thus, $6= 600 cents =6000 mills. 170. Cents are reduced to dollars by moving the decimal point two places to the left. Mills are reduced to dollars by moving the decimal point three places to the left. Thus, 3789 cents $37.89; and 3789 mills $3.789. 171. Oral Exercises. 1. Reduce $ 47 to cents. 2. Reduce $34.56 to cents. 3. Reduce $3.456 to mills. 4. Reduce $483 to cents; to mills. 5. Reduce $6.84 to cents; to mills. 6. Reduce $1.876 to mills. 7. Reduce 564 cents to dollars. 8. Reduce 3692 mills to dollars. 9. Reduce 87694 cents to dollars. 10. Reduce 76843 mills to dollars. Write the answers to these ten examples. 11. If to pay for a knife at $2, a pocket-book at $ 3, a lot of paper and envelopes at $1.25, I have only a ten-dollar bill, how much change ought I to receive back? 12. If I had $75, and paid out of it three 10's, four 5's, two 2's, and 62 cents, how much should I have left? 172. When a decimal can be reduced to a common fraction with not more than one figure as its denominator, instead of multiplying by the decimal, it is often easier to use this common fraction as a multiplier. Thus, in United States currency, instead of multiplying by the number expressing the number of cents, in practice we often use the common fractions in the following 13. What cost 64 yards of cloth at $0.87 a yard? = Solution. $0.87 of a dollar. If a yard is worth of a dollar, 64 yards would be worth 64 times of a dollar, or of 64 dollars, or $56, Ans. 173. Price is the assigned value of a unit of any article; cost is the assigned value of the whole, or of a number of units, of the quantity. 174. The rules given for operations in decimals apply to operations in United States Money. 14. Bought a hat for $4.50, a coat for $18.75, a vest for $5.25, and a pair of boots for $5; what did I pay for all? 15. If apples are worth $2.50 a barrel, what are 3 barrels worth? 16. When 8 cords of wood are worth $ 44, what is the value of 1 cord? 17. At $6 a ton how many tons of coal can I buy for $ 24? Solution. I can buy as many tons as $6 is contained times in $ 24 ; $24 ÷ $6=4; hence, I can buy 4 tons. 18. What cost 48 barrels of apples at $1.37 a barrel? Solution. $1.371⁄2 = $13. 48 barrels at $1 a barrel would cost $48. of a dollar more on each barrel would be g of 48 dollars, or $18; $48 +$18-$66, Ans. 19. What cost 48 pounds of raisins at 12 cents a pound? 20. What cost 54 yards of muslin at 163 cents a yard? 21. What cost 74 bushels of apples at 33 cents a bushel? 22. What cost 40 pairs of gloves at 50 cents a pair? 23. How many pounds of cheese at 12 cents a pound may be bought for 3 bushels of corn at 87 cents a bushel? (First find how many pounds for 1 bushel.) 24. Paid $87.50 for a horse, $145.25 for a pair of oxen, $14.25 for a wagon, and $ 45.75 for a cart; what did I pay for all? 25. A man who owed $699.60, paid $164.67; how much did he still owe? 26. Bought a farm for $3684.75, and stock and tools for the farm for $1476.25; how much more did I pay for the farm than for the stock and tools? 27. If 12 gentlemen have $7497.84 apiece, what sum have they all? 28. If 45 persons deposit $ 346.25 each in a savings-bank, how many dollars do they deposit? 29. Divide $69345.36 equally among 18 men. |