43. A miller owned of a mill and sold of his share; what part of the mill did he still own? 44. A and B own a farm. the remainder. A owns of it, and B B sells of his share to A; what part of the farm does each own? 45. A man sold a watch for $62.50, which was of the cost of a new one. price of the two watches. 46. Reduce its denominator. Find the difference in the to an equivalent fraction having 7 for 47. A can do twice as much work as B; how many times B's work can both do? 48. B can do 5 times as much work as C; how many times C's work can both do? 49. If A can do 2 times as much work as B, what part of A's work can B do? 50. A and B together do a piece of work in 12 days; what part of the work do both do in 1 day? If A does 3 times as much as B, how many times B's work do What part of the whole work does B What part of the whole work does A they both do? do in one day? do in one day? How long will it take B to do the work alone? How long will it take A to do the work alone? 51. Two men do a piece of work in 18 days. If the first man works 3 times as fast as the second, in how many days can each do the work alone? 52. How much greater, or less, is of 4 than of 43? 6 13 53. Reduce (2 × 51) ÷ (41 × 51) to simplest form. 54. How much will 17 umbrellas cost, if 6 cost $14.371? 55. of a pound of indigo cost 12 cents, what must be paid for 13 pounds at the same rate? 56. What is the value of 3 bales of cotton, each weighing 440 pounds, when 1 pound sells for 131 cents? 57. 720 bushels of oats are worth 120 bushels of wheat. What is the value of the oats, if wheat is worth 90 cents a bushel? 58. 37 yards of brussels carpet are worth 225 bushels of potatoes at 25 cents a bushel. What is the price per yard? 59. A father left a fortune to his three children. The oldest was to have of it, the second was to have of it, and the youngest was to have the rest. By this arrangement the oldest received $10000 more than the youngest. Find the value of the estate, and the amount each received. 60. Add of of 7 and 2 of 5 of 7, and divide 용 1 the sum by of § of 34 of 9. 3 10 61. Twice of of 91 is of how many times of six times of 171? DECIMAL FRACTIONS. 157. Decimal fractions are fractions whose denominator, usually understood, is ten, or some power of ten. 158. A decimal fraction always expresses a certain number of tenths, hundredths, thousandths, etc., of a unit. Thus .5, which is read five-tenths. .05, which is read five-hundredths. .005, which is read five-thousandths. NOTATION OF DECIMALS. 159. The decimal point (·) determines the denomination of the fraction. 160. The denominator of a common fraction may be any number whatever, and is always expressed. The scale in decimal fractions is the same as that in whole numbers. This is shown below in writing the following num 1st. That the local value of a digit is only one-tenth as great in the fourth as it is in the fifth place at the left of the point. 2d. That the local value of a digit is only one-tenth as great in the third as in the fourth place at the left of the point. 3d. That the local value of a digit is only one-tenth as great in the second as it is in the third place at the left of the point. 4th. That the local value of a digit is only one-tenth as great in the first as it is in the second place at the left of the point. 5th. That the local value of a digit is only one-tenth as great in the first place at the right of the point as it is in the first place at the left of the point. GENERAL LAW. Finally. While numbers increase in a ten-fold ratio from the point toward the left, they decrease in a tenfold ratio from the point toward the right. WRITING DECIMALS. RULE. Write as in whole numbers, and place the decimal point so as to express the denomination required. 162. In decimals, as in whole numbers, each digit used in expressing a number may have a simple or a local value. 163. The local value of any digit depends upon its position with reference to the decimal point. RULE. READING DECIMALS. Read as in whole numbers, giving the name of the lowest denomination in the decimal read. NOTATION AND NUMERATION OF DECIMALS. How many places are required — 3. To express three hundred and thirty-three units? 5. To express thirty-three tenths? 6. To express three hundred and thirty-three tenths? 7. To express thirty-three hundredths? 8. To express three hundred and thirty-three hundredths? 9. To express thirty-three thousandths? 10. To express three hundred and thirty-three thousandths? 11. To express thirty-three ten-thousandths? 12. To express three hundred and thirty-three tenthousandths? 13. To express three tenths? 14. To express three units and three tenths? Analyze and write 1. Thirty-three thousand. 2. Thirty-three hundred. 3. Three hundred and thirty-three units. 4. Thirty-three units. 5. Thirty-three tenths. 6. Three hundred and thirty-three tenths. 7. Thirty-three hundredths. 8. Three hundred and thirty-three hundredths. |