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40. A farmer has 300 sheep. He sells of them at $31 each, and the remainder at $4 each. How much does he get for all?

41. If 6 dozen oranges cost $26, how much will 24 dozen cost?

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44. A blackboard is 21 feet long and 31 feet wide. The width is what part of the length?

of an

45. I paid $4000 for 21 acres of land, and after taking § of an acre for streets divided the remainder into lots of acre each. I sold the lots at $150 each. Find the gain.

46. I spent 1, 4, and How much had I at first?

of my money and had $20 left.

47. Compare 42 and 28. If 28 men earn $56 in a day, how much will 42 men earn in the same time?

48. What is the distance around a lot 60 feet front and 121 feet deep?

49. How many times can I fill a pail holding a gallon from a 12-gallon tank that is full?

50. Frank is 16 years old, and of his age is of John's age. How old is John?

51. Find the product of 1048 × 24.

52. Find the cost of the following articles: 12 yd. velvet @ $2.25; 12} yd. suiting @ 50; 7 yd. of dimity @ 20¢.

53. A carpenter worked 4 days one week, 5 days the next week, and 5 days the next week. How many days did he work in the three weeks?

54. If he received $3.50 a day, how much did he earn?

55. A merchant sold 20 pounds of sugar at 5 cents a pound, 121 pounds of tea at 36 cents a pound, 161⁄2 pounds of rice at 8 cents a pound, and 12 dozen oranges at 40 cents a dozen. Find the amount of the sale.

56. A dealer bought 80 bushels of apples at $ a bushel, 60 bushels at $ a bushel, and 40 bushels at $ a bushel. How much did the apples cost?

57. He retailed of them at $1 a bushel, of them at $1% a bushel, and the remainder at $ a bushel.

he gain?

How much did

58. From a piece of cloth a tailor cut 6 garments, each containing 4 yards, and there remained 4 yards. How many yards did the piece contain at first?

59. A grocer sold 1 pounds of butter to one customer, 21 pounds to another, 34 pounds to another, and 5 pounds to another. How much butter did he sell?

60. I have $30 in gold, $18 in silver, and the remainder in paper money. The gold is what part of the silver and the paper money?

61. A gardener raised 20 bushels of beans. He sold of them at $1.80 per bushel and the remainder at $1.65 per bushel. How much did he get for the crop?

62. A real estate dealer bought a plan of 12 lots for $1800. He sold of them at $200 each, of the remainder at $180 each, and the remainder at $160 each. How much did he gain?

DECIMALS

DECIMAL DIVISIONS OF A UNIT

Any unit may be divided into 10ths, 100ths, 1000ths, etc. A decimal fraction is any number of tenths, hundredths, thousandths, etc., of a unit. When expressed with a decimal point, without a written denominator, it is usually called a decimal. Thus and .5, 150 and .05, 1‰o and .005 are decimal fractions, but the term decimal is usually restricted to the forms .5, .05, .005, etc. To write or express a number decimally, however, means to write it with the decimal point.

5

25

35

2 355

1. Express decimally: 0, 1800, 10, 1000.

2. In 5.55, the figure in tenths' place equals how many times the figure in hundredths' place? The figure in ones' place equals how many times the figure in tenths' place?

In any decimal or whole number 10 units of any place = 1 unit of the next place to the left.

The decimal point is used to separate the units and parts of units. It is always placed at the right of ones' place and before tenths' place.

A mixed decimal is an integer and a decimal united; as, 4.5. 3. What is the first place to the right of a decimal point called? the second place? the third place?

4. What is the largest decimal division of any unit? the second largest? the third largest ?

NOTATION AND NUMERATION OF DECIMALS

Observe the table of places and the names of integral and decimal units.

3, 7 4 5, 5 5

2 6 8

7

Read a

Name the decimal places, beginning at tenths.

decimal as though its denominator were expressed; thus, .045 is read forty-five thousandths.

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10. We read 2.005, 2 and 5 thousandths. What word stands for the decimal point? In reading a mixed decimal, what must we always call the decimal point?

NOTE. Pupils should receive a thorough blackboard drill in reading decimals and mixed decimals. Special care must be taken not to read and except between ones and tenths.

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32. What does the last place in enumerating the decimal always tell? What is the decimal unit in .5? in .05? in .005?

33. Five thousandths calls for how many decimal places? 5 must be written in what decimal place? How many naughts must be prefixed to 5?

34. Tenths means how many decimal places? hundredths? thousandths?

millionths?

ten-thousandths ?

hundred-thousandths?

In writing a decimal, write the last figure of the decimal in the place called for. If the significant figures do not occupy all the decimal places, prefix the necessary naughts.

35. Express decimally five tenths; five hundredths; five thousandths; six and four tenths; ten and twenty-four thousandths; sixty-five ten-thousandths; eight and eight thousandths: six hundred and four ten-thousandths.

36. Five millionths; twenty-five hundred thousandths; six and seven thousandths; eight hundred and five tenths.

Equivalents of common and decimal fractions.

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3. §=100; 1= 100; = 100?

4. 12=100; 12 = 180; 8 = 180?

5. Give the decimal equivalents for: 1,,,, §, 1, 12,

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