51. Find the product of the two factors .04 and .7. 52. The product of two factors is .028, and one of the factors is .7. What is the other factor?

53. How many ciphers in the product of the denominators of any two decimal fractions? Decimal places in the product of any two decimals?

54. The dividend is the product of what two factors? The dividend contains as many decimal places as what two factors?

55. How many decimal places in the product of tenths multiplied by ones? Tenths by tenths? Hundredths by tenths? How many decimal places are there always in the product of any two decimals?

56. How many decimal places in the quotient of tenths divided by ones? Tenths by tenths? Hundredths by tenths? Thousandths by tenths? How many decimal places are there always in the quotient?

57. If a grocer sells A sugar at $.10 a pound, how much will 3 pounds cost? 5 pounds? 7 pounds? 10 pounds? 58. If a boy sells 4 papers of gum-drops for $.80, how much does he receive for one paper?

59. At $.06 a pound, what will 10 pounds of nails cost? If $.35 are paid for 5 pounds, what is the price per pound? 60. At $.24 a dozen for eggs, what must be paid for .5 of a dozen? For 1.5 dozen? .25 of a dozen? 1.25 dozen? 61. In 1 rod are 5.5 yards. How many yards long is a chain that measures 5 rods? 8 rods?

62. If 2.5 yards of linen cost $1.25, what is the price per yard? If .25 of a yard of cloth cost $1.25?

63. What is the product of 5 multiplied by 5 thousandths? Of 25 hundredths by 4 thousandths? Of $.005 by .10? 64. If a pound of tea costs $.75, what is the cost of .5 of a pound? Of .25 of a pound? Of 2 pounds? 2.5 pounds?

65. If 4 quarts of cranberries are sold for 60 cents, what part of a dollar does one quart cost? 5 quarts cost what decimal part of a dollar? 8 quarts?

66. I paid $.75 fare on a railroad, at an average of 3 cents a mile. How far did I travel?

67. A housekeeper paid $5.25 for 100 pounds of flour. What price per pound did she pay? Find the cost of 6 pounds.

68. If 2 pounds of sugar cost $.333, what will 9 pounds cost? 69. Frank bought 6 quires of paper at $.25 a quire, and had $.50 left. How much money had he at first?

70. Harry bought 7. melons at $.18 each, and had but a dollar and nine cents in his pocket. How much did he need to pay for them?

71. A lady paid $.75 for oranges at $.05 each. After giving away 10 of them, how many had she left?

72. I had $10 in my pocket, and paid all but $2.25 for 5 yards of cloth. What was the price of the cloth per yard?

Find the product of

73. .5 times .25 of a ton.

74. $.005 multiplied by 100.

Find the quotient of

77. $7.25 divided by 100.

78. 1.44 dozen divided by 12.

75. .25 times .05 of a gallon. 79. $1.50 divided by $.03. 76. $.125 multiplied by 80.80. .875 of a ton divided by .25.

259. Principles.

I. Only similar orders of decimal units can be added or subtracted.

II. The number of decimal places in the product equals the number of decimal places in both factors.

III. The number of decimal places in the dividend equals the number of decimal places in the divisor and the quotient together.

Exercises.

1. From the product of .5 times .25 take .05.

260. Model. 5 times 25 are 125; and since hundredths multiplied by tenths produce thousandths, the product must contain three decimal places, or as many decimal places as are in both factors, giving .125.

Now 125 thousandths less 5 hundredths, or 50 thousandths, are 75 thousandths, or .075, the result required.

2. To the quotient of .025 divided by .5 add .5.

261. Model. - 25 divided by 5 equals 5; and since thousandths divided by tenths produce hundredths, the quotient must contain two decimal places, or as many decimal places as are in the dividend less the number in the divisor, giving 05.

Now 5 tenths, or 50 hundredths, added to 5 hundredths are 55 hundredths, or .55, the result required.

Find the value of

1. (.05 + .75) X 50. 5. (.125 ÷ .5) × 40

2. (.005+.07) X 12. 6. 500 X (.05÷.25). 3. (.125 X80) +.25.7. (.075 X 1.1) X 80.

9. 100 X .05 + 50. 10. (50 + .05) X 10.

11. 1.25 (7

4. (75 X .001) + .5. 8. .008 ÷ (4 × .25). 12. (601⁄2 × .5)

2

+1.25).

- 25.

3. Give your reasoning for fixing or placing the decimal point in the result of each of the preceding examples.

CHAPTER IV.

DENOMINATE NUMBERS.

1. Notation and Numeration.

262. A Denominate Unit is one of any name or denomination.

Thus, 1 yard is a denominate unit; so, also, is 1 ton, 1 mile, etc. 263. A Denominate Number is one or more units of denomination.

any

Thus, 1 foot is a denominate number; so, also, is 3 quarts, etc.

264. A Simple Denominate Number is a number expressed in units of only one denomination.

Thus, 5 yards is a simple denominate number; so, also, is 7 feet. 265. A Compound Denominate Number is a number expressed in units of two or more denominations of the same nature.

Thus, 5 yards 2 feet is a compound number; also, 8 gallons 3 quarts. 266. Compound Denominate Numbers are generally called Compound Numbers.

MEASURES.

267. A Measure is a fixed unit used in comparing or determining quantity.

Thus, 1 foot is a measure of length; 1 pound is a measure of weight; 1 dollar is a measure of value.

Measures may be divided into six classes:

1. Measures of Extension. 2. Measures of Capacity.

3. Measures of Weight.

4. Measures of Money.

5. Measures of Circles.

6. Measures of Time.

MEASURES OF EXTENSION.

268. Extension may be a line, a surface, or a solid. A Line is that which has length only.

A Surface is that which has length and breadth.

A Solid, or Body, is that which has length, breadth, and thickness.

269. Measures of extension are of three classes: measures of lines, measures of surfaces, and measures of solids.

I. LINEAR MEASURES.

270. Linear Measures are used in measuring lines and distances.

The units or denominations of linear measures are inch, foot, yard, rod, and mile.

In measuring cloth, or goods sold by the yard, the linear yard is divided into halves, quarters, eighths, and sixteenths.

II. SURFACE MEASURES.

271. A Square is a surface having four equal straight sides, and four equal corners or angles.

A Square Inch is a surface 1 inch long and 1 inch wide. A Square Foot is a surface 1 foot long and 1 foot wide. 272. Surface Measures, or Square Measures, are used in ascertaining the extent of surfaces; as of boards, plastering, land, etc.

The units or denominations of surface or square measures are square inch, square foot, square yard, square rod, acre, and square mile.