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11. The product of two factors is .35, one of which is .5; what is the other?

12. The product of two factors is .035, one of which is .07; what is the other?

13. Divide .6 by .3;

.42 by .6; .025 by .05; .0072 by .12. 14. Divide .14 by 7; .48 by .04; .0060 by .012.

How many decimal places in the quotient when tenths are divided by units? Tenths by tenths? Hundredths by tenths?

See Drill Table, page 269, 404.

PRINCIPLE.-The quotient must contain as many decimal places as the number of decimal places in the dividend exceeds those in the divisor.

The number of decimal places in the dividend must first be made equal to the number in the divisor before the division is possible.

WRITTEN

155. 1. Divide .952 by .7.

EXERCISES.

EXPLANATION.-Divide as in fractions (124, Ex. 4). .7) .952 Thus, .952÷.7=18%÷10=108%×40=188=1.36. Or, Divide as in integers, and since the dividend contains

1.36

three decimal places, and the divisor one, the quotient must have two

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If the number of figures in the quotient is less than the excess of the decimal figures in the dividend over those in the divisor, supply the deficiency by prefixing ciphers.

If there is a remainder, the division may be continued, the ciphers annexed being so many decimals of the dividend.

The quotient carried to four decimal places is sufficiently exact for most business transactions.

To divide by 10, 100, 1000, etc., remove the decimal point in the dividend as many places to the left as there are ciphers in the divisor (137, 404).

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23. If 125 bushels of oats cost $62.50.
24. If 35 pounds of sugar cost $2.80.
25. If 144 bushels of wheat cost $168.48.
26. If 100 acres of land cost $31561.
27. If 9 turkeys cost $7.874.

28. If 396 pounds of sugar cost $44.748.
29. If 2500 pounds of butter cost $625.
30. If 2450 pounds of pork cost $153.
31. If 894 pine-apples cost $80.46.

18. .084÷8.

19. $6832.
20. 44.4.
21. $27÷371.

22. 100.001.

32. How many coats can be made from 32.4 yards of cloth, allowing 2.7 yards for each coat?

33. If 125 bushels of potatoes cost $821, how many barrels, each containing 24 bushels, can be bought for $224.40 ?

34. A man bought 26 sold them at $3.90 a box.

boxes of lemons at $44 a box, and How much did he lose?

35. At $.311 a bushel, how many bushels of potatoes can be bought for $9 ?

36. If 18.24 yards of cloth cost $27.36, what will 7.25 yards cost? 9 yards? 153 yards?

37. If 4 tons of coal cost $32.3, what will 93 tons cost?

Find the value

38. Of 1.12 x 5÷÷÷14.

39. Of $15.5÷8 × 100.

40. Of 7.1 x 8.2-342.5.

41. Of 25x.5 × 12+20÷100.

42. A merchant bought 14 boxes of tea for $560; it being damaged, he was obliged to lose $106.75 on the cost of it; how much did he receive a box?

43. A man bought 4 yards of cloth at $3.20 a yard, and 37 pounds of sugar at $.08 a pound; he paid $6.80 in cash, and the remainder in butter at $.16 a pound; how many pounds of butter did it take?

44. A farmer sold 40 bushels of barley at $.75 a bushel, 50 bushels of oats at $ a bushel, 5 tons of hay at $15 a ton, for all of which he received $102.75 in money and 5 barrels of flour. What was the cost of the flour a barrel?

For additional exercise in decimals, treat each set of numbers in both the double columns as follows:

First, add the four numbers on every line of the two double columns; thus, 324+.324 + 7.75 + 5.5 = 337.574. Then take the first set of two numbers, 324 and .324, find their difference, their product, and the quotient of the first divided by the second. All processes and results should be in decimals.

In like manner, treat each set of two numbers in each double column.

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Find the second member of the following equations:

61. (1.008 18+ 63÷4000 x 100) — = ?

62. (714.714) (.34.034 x .25 of 6) = ? 63. (.48 ÷ 800 × 10000 + 6.4 ÷.08) ÷ .125 = ?

64. ($262.64 ÷ $.56) × .0084 + .024 × 100 = ? 65. ($1260 × 3.49) $10.47 $850 $6.80 ? ÷ · =

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156. 1. What will be the cost of 18 pounds of butter, at 25 cents a pound?

ANALYSIS. Since 1 pound cost 25 cents, or $1, 18 pounds will cost 18 times $1, or $15, equal to $41, or $4.50. Or,

At $1 a pound, 18 pounds will cost $18, and at $ a pound, of $18, which is $43, or $4.50.

2. What will 24 table books cost, at 12 cents each? At 16 cents each? At 20 cents each?

3. What will be the cost of 15 bushels of oats, at 33 cents a bushel? At 50 cents a bushel?

4. At 16

cents each, what will be the cost of 12 slates? Of 20 slates? Of 24 slates?

5. What will be the cost of 16 pounds of rice, at 64 cents a pound? At 83 cents? At 10 cents?

6. How many pounds of raisins, at 16 cents a pound, can be bought for $5?

ANALYSIS. Since 16 cents are $1, $5 will buy as many pounds of raisins as $ is contained times in $5, which are 30 times.

7. At $.50 a bushel, how many bushels of oats can be bought for $15? For $16? For $25?

8. What is the cost of 40 pairs of shoes, at $1.25 a pair? ANALYSIS.-At $1 a pair, the cost would be $40; but since the price is $1+$1, the whole cost is $40+ of $40, or $50.

9. At $1.50 each, what is the cost of 48 chairs?

10. What is the cost of 60 yards of cloth, ot $1.124 a yard?

At $1.16? At $1.25? At $1.334? At $2.50?

11. At $2.25 a pair, what is the cost of 12 pairs of shoes? Of 16 pairs? Of 18 pairs? 20 pairs? 25 pairs?

157. Quantity, in commercial transactions, is the amount of anything bought or sold.

158. Price is the value of a unit of any commodity.

159. Cost is the value of the entire quantity bought or sold.

160. An aliquot part of a number is one of the equal parts of a number; or, it is an exact divisor of a number. Thus, 3, 5, and 71 are aliquot parts of 15; 2, 21, 3}, and 5, of 10.

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1. Price x quantity = cost.

GENERAL FORMULAS: 2. Cost ÷ quantity = price.

3. Cost price quantity.

=

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162. To find the cost of a quantity, when the price is

an aliquot part of one dollar.

1. What cost 951 bushels of oats, at $.33 a bushel?

EXPLANATION.-Since 33 cts.

is $1,951 bushels cost 951 times $, or $251, or $317.

Or, the cost is as many dollars as there are bushels, and of 951 is 317.

$3951 $251= $317.

=

Or, 951÷÷÷3 = 317, or $317.

Price x quantity:

= cost.

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