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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 $27o, how much will 24 dozen cost?
Find the amount of the following bills: 42. 61 yd. of ribbon @ 104. 43. 121 lb. of sugar @ 64.
124 yd. of muslin @ 8%. 21 lb. butter @ 28%. 11} yd. silk @ 984.
44 lb. of lard @ 16€. 10] yd. lace @ 20%.
3.1 qt. beans @ 10%. 44. A blackboard is 21 feet long and 31 feet wide. The width is what part of the length?
45. I paid $4000 for 24 acres of land, and after taking of an acre for streets divided the remainder into lots of 16 acre each. I sold the lots at $150 each. Find the gain.
46. I spent 1, 4, and } of my money and had $20 left. How much had I at first?
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 601 feet front and 121 feet deep?
49. How many times can I fill a pail holding 1 a gallon from a 12-gallon tank that is full?
50. Frank is 16 years old, and / of his age is iz of John's age. How old is John?
51. Find the product of 1044 x 24.
52. Find the cost of the following articles : 12 yd. velvet @ $2.25; 12; yd. suiting @ 50¢; 78 yd. of dimity @ 20%.
53. A carpenter worked 41 days one week, 54 days the next week, and 54 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 51 cents a pound, 121 pounds of tea at 36 cents a pound, 161 pounds of rice at 8 cents a pound, and 14 dozen oranges at 40 cents a dozen. Find the amount of the sale.
56. A dealer bought 80 bushels of apples at $f a bushel, 60 bushels at $z a bushel, and 40 bushels at $y a bushel. How much did the apples cost?
57. He retailed I of them at $1 a bushel, 1 of them at $10 a bushel, and the remainder at $4 a bushel. How much did he gain?
58. From a piece of cloth a tailor cut 6 garments, each containing 41 yards, and there remained 4 yards. How many yards did the piece contain at first?
59. A grocer sold 11 pounds of butter to one customer, 24 pounds to another, 34 pounds to another, and 51 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 2 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, 1 of the remainder at $180 each, and the remainder at $160 each. How much did he
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, 16g and .05, 1ooo 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.
1. Express decimally: Po, 1 186, o 3586
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.
Name the decimal places, beginning at tenths. decimal as though its denominator were expressed ; thus, .045 is read forty-five thousandths.
7. .5005 8. .0007 9. .2002
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.
Read : 11. 25.005 12. 600.45 13. 800.5
17. 98.7405 18. 400.0504 19. 305.0209
1000 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? naughts must be prefixed to 5?
34. Tenths means how many decimal places? hundredths? thousandths ? ten-thousandths ? hundred-thousandths ? millionths ?
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.
5. Give the decimal equivalents for: 1, f, g, h, j, k, Pay 13, s.