57. What is the weight of 56 sacks of salt if each weighs 12 pounds?

58. If a barrel holds 2 bushels of apples, how many barrels will hold 132 bushels?

59. A man earns $2 a day: in how many days will he earn $150?

60. If a man's steps are 2 feet each, how many steps will he take in walking 250 feet?

61. Two brothers paid $4250 for a mill, one paying of the cost and the other: how much did each pay? 62. A man bequeathed of his estate to his wife, of it to each of his two sons, and the rest to his daughter: what part did the daughter receive?

63. A primary school enrolls 240 pupils; of the pupils are in the first grade, in the second grade, and the others in the third grade: how many pupils in each grade?

64. A fruit-dealer bought 80 barrels of apples, each containing 2 bushels, at $2 per barrel, and then sold the apples at $1 per bushel: how much did he gain?

65. A man who owned & of a newspaper sold of his share to his brother and of it to his sister: what part of the paper did each buy? What part did the man then own?

66. A man divided 180 acres of land among three sons, the eldest receiving of it, the second son of it, and the youngest son what remained: how many acres did each son receive?

67. Two men start from the same place and walk in opposite directions, one 24 miles an hour and the other 3 miles an hour: how far apart will they be in 1 hour? In 4 hours? In 10 hours?

68. A grocer bought 4 crocks of butter, weighing respectively 31 pounds, 28 pounds, 27 pounds, and 30 pounds, and the weight of the empty crocks was 221 pounds: what was the weight of the butter? What was its cost at 33 cents a pound?

DECIMAL FRACTIONS.

NUMERATION AND NOTATION.

1. IF a square be divided into ten equal parts, what is one part?

2. If a tenth of a square be divided into ten equal parts, what part of the square is one of these parts? How much is of?

100

3. If a hundredth of a square be divided into ten equal parts, what part of the square is one of these parts? How much is

of?

4. How many tenths in a unit? How many hundredths in one tenth? How many thousandths in one hundredth?

The division of a unit into tenths, tenths into hundredths, hundredths into thousandths, etc., is called a decimal division, and the fractions arising from such a decimal division of the unit is called a decimal fraction. Thus, five tenths, fifteen hundredths, forty-five thousandths, etc., are decimal fractions.

Decimal fractions may be expressed by figures by writing the numerator over the denominator; as, fo, 100, 1000, etc. When a decimal fraction is thus expressed it is written in the common form, i. e., the form common to all fractions.

Since 10 thousandths equal 1 hundredth, 10 hundredths 1 tenth, and 10 tenths 1 unit, decimal fractions may also be expressed, like integers, on a scale of ten, called the decimal scale. This is done by writing the tenths in the first order at the right of units, the hundredths in the second order, the thousandths in the third order, etc., and placing a period, called the decimal point, at the left of the

15

order of tenths. Thus, may be written .5; 10%, .15; 1850, .045, etc. This is called the decimal form of writing decimal fractions.

45

5. How many tenths in .3?. In .6? .7? .8? .9? 6. How many hundredths in .02? In .04? .07? 7. How many tenths and hundredths in .24? .36? 8. How many thousandths in .005? .008? .006? 9. How many tenths, hundredths, and thousandths in .356? In .523? .603? .041? .406? .007?

The decimal .3 is read three tenths; .24 is read twentyfour hundredths; and .205 is read two hundred five thousandths.

10. Read .6; 7; 8; 25; .36; .45; .125; .244. 11. Read .06; .008; .045; .04; .014; .503.

NOTE. A decimal fraction expressed in the decimal form is read precisely as it would be if written in the common form.

63.63; 10009

12. Read 1,9; 36, .63; 50%, .503; 16, .024.

When decimal fractions are written in the decimal form they are expressed decimally, and they are then called briefly decimals.

Write decimally the following fractions:

The fourth decimal order is ten-thousandths; the fifth, hundred-thousandths; and the sixth, millionths.

The decimal .0205 is read two hundred five ten-thousandths; .02005 is read two thousand five hundred-thousandths; .000024 is read twenty-four millionths. The name of a decimal is the name of its right-hand order.

Copy and read the following decimals:

29. Four hundred twenty-two thousandths. 30. Seven hundred five ten-thousandths.

31. Fifteen millionths.

100000

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1000000

32. Four hundred fourteen hundred-thousandths.

An integer and a decimal united as one number is a mixed decimal. Thus, 5.4 and 25.24 are mixed decimals.

The orders on the left of the decimal point are integral orders, and those on the right are decimal orders. Decimal orders are also called decimal places.

When a mixed decimal is expressed in words the integer and the decimal are connected by and. Thus, 45.14 is read forty-five units and fourteen hundredths, or, omitting " units," forty-five and fourteen hundredths.

33. Read 12.6; 15.045; 25.03; 7.009
34. Read 27.305; 6.0346; 504.35; 2.003

35. Read 400.04; 5000.004; 400.0012; 300.006 36. Write decimally 25; 6180; 461330; 600130. 37. Forty-five units and fifty-two hundredths.

38. Forty units and forty-five thousandths.

39. Two hundred units and seventy-nine millionths. 40. Two hundred seventy-nine millionths.

41. Five thousand units and sixty-six millionths.

42. Five thousand sixty-six millionths.

43. Fourteen units and fourteen hundred-thousandths. 44. One thousand eighty-seven millionths.

45. Eight hundred forty-two ten thousandths.

A Decimal Fraction is one or more of the decimal parts of a unit.

The decimal parts of a unit result from its division into tenths, tenths into hundredths, hundredths into thousandths, etc., called the decimal division.

The denominators of decimal fractions are 10, 100, 1000, 10000, etc. When a decimal fraction is expressed in the decimal form, the denominator is not written.

The successive decimal orders decrease in value from left to right and increase from right to left in the same manner as integral orders.

The following table gives the names of six integral and six decimal orders:

Integral Orders.

Decimal Orders.