adding the same number to both of its terms? By subtracting the same number? (Illustrate, taking .)

50. How is the value of an improper fraction, greater than 1, affected by adding the same number to both of its terms? By subtracting the same number? (Illustrate.)

WRITTEN PROBLEMS.

51. Add,, of 2, and 31.

10

52. From of 1 take of 14.

53. From the sum of 273 and 203 take their difference. 54. Multiply by 35; 35 by 13; 13 by 10; 31 by 21. 55. Divide by 32; 32 by 1; 19 by 7; 41 by 31. 56. 1+15 what? -? 11 × 7? 11 ÷ 7? 57. Multiply 2045 by 35; 806 by 843; 301 by 163. 58. Divide 347 by 15; 692 by 215; 194 by 163.

59. A farm is divided into five fields, containing respectively 21 A., 343 A., 457 A., 565 A., and 29 A.: how many acres in the farm?

60. There are 30 sq. yd. in a square rod: how many square rods in 786 sq. yd.?

61. A man travels 5 miles an hour: how long will it take him to make a journey of 75% miles?

62. At $8 a ton, how many tons of hay can be bought for $108!?

63. If of an acre of land cost $68, what will 12 acres cost?

64. If of a yard of velvet cost $84, how many yards can be bought for $1964?

65. If a number be diminished by of 2 of itself, the remainder will be 69: what is the number?

66. A pedestrian walked of his journey the first day, of it the second day, and then had 24 miles to travel : how long was the journey?

67. A man pays $350 a year for house rent, which is of his income: what is his income?

68. A man bequeathed to his wife $4860, which was of his estate: what was the value of the estate?

69. A graded school enrolls 208 boys, and of the pupils are girls: how many pupils are enrolled in the school?

70. A man owning of a ship sells of his share for $3480: at this rate, what is the value of the ship?

71. A owning of a mill, sold of his share to B, and of what he then owned to C for $460: what was the value of the mill at the rate of C's purchase?

72. A owns of a section of land; B, of a section; and C, as much as both A and B: what part of a section does C own?

73. A bought his share to B, and Idid A then own?

of a factory for $21840, and sold of

of it to C: what part of the factory

74. A and B together own 396 acres of land, and 3 of. A's farm equals of B's: how many acres does each own? 75. A stock of goods is owned by three partners, A owning, B, and C the remainder; the goods were sold at a profit of $6160: what was each partner's share?

76. of a stock of goods was destroyed by fire, and of the remainder was damaged by water, and the uninjured goods were sold at cost for $5280: what was the cost of the entire stock of goods?

77. A man paid of his money for a farm, of what remained for repairs, of what then remained for stock, of what then remained for utensils, and then had left $650: how much money had he at first?

78. A merchant tailor has 67 yards of cloth, from which he wishes to cut an equal number of coats, pants, and vests : how many of each can he cut if they contain 33, 27, and 14 yards respectively?

79. An estate was divided between two brothers and a sister; the elder brother received of the estate, the younger

, and the sister the remainder, which was $450 less than the elder brother received: what was the value of the estate? What was each brother's share?

SECTION IX.

DECIMAL FRACTIONS.

NUMERATION AND NOTATION.

1. If a unit be divided into ten equal parts, what is one part called?

2. If a tenth of a unit be divided into ten equal parts, what is one part? What is of it?

3. If a hundredth of a unit be divided into ten equal parts, what is one part? What is of ?

4. What part of a tenth is a hundredth? a hundredth is a thousandth?

What part of

5. How do the fractions, 10, and 10 compare with each other in value?, 10, and 1000?

106. Since the fractional units, tenths, hundredths, thousandths, etc., decrease in value tenfold, they are expressed, like the orders of integers, on a scale of ten. This is done by extending the orders to the right of units, and calling the first fractional order tenths, the second hundredths, the third thousandths, etc. A period is placed at the left of the order of tenths. Thus, is written .5; 1 is written .05; 1000 is written .005, etc.

12. How many tenths and hundredths in .25? In .45?

.63? .78? .84? .69? .39?

C.Ar.-7.

13. How many tenths, hundredths, and thousandths in .325? In .246? .307? .405? .056?

14. How many tenths, hundredths, and thousandths in .045? In .407? .008? .065? .607? .325?

15. How many hundredths in 15?

100

00

In 18? .34? .42? 16. How many thousandths in 15? In 125? .325?

.065? .205? .008? .046 ?

25 000

1000

107. When the right-hand figure of a decimal denotes hundredths, the whole decimal denotes hundredths, and when the right-hand figure denotes thousandths, the whole decimal denotes thousandths. Thus, .25 is read 25 hundreths; .325 is read 325 thousandths.

108. When fractions denoting tenths, hundredths, thou

sandths, etc., are expressed like integers, on the decimal scale, they are said to be expressed decimally.

27. What is the name of the third decimal order? The fourth? The fifth? The sixth?

28. What does each significant figure of .0034 denote? Of .00275? Of .03405? Of .000325? Of .030056

109. When a decimal fraction is expressed decimally, the right-hand figure is written in the order indicated by the name of the decimal. Thus, is written .00325.

325 180000

40. Four hundred and seven thousandths.

41. Ninety-five ten-thousandths.

42. Six hundred and forty-four ten-thousandths.

43. Seven thousand and eighty-two ten-thousandths. 44. Fifty-seven hundred-thousandths.

45. Seven hundred and eight hundred-thousandths.