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divided into twelve other equal parts called thirds, and each third into twelve equal parts called fourths; and so on

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20736 of a foot, &c.

It is usual to distinguish inches by one mark, thus (') seconds by two marks, (") thirds by 3 marks, (''') fourths by 4 marks, ("") &c. These marks are called indices. Twelve of each of the less denominations are equal to one of the next greater, as in the following

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Hence they are added and subtracted in the same man

ner as compound numbers.

MULTIPLICATION OF DUODECIMALS

Is used in finding the contents of surfaces and solids. (Note. F stands for feet, and I or for inches.)

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That is, the product of any two denominations will al ways be of that denomination denoted by the sum of thei indices.

RULE.

1. Write the multiplier under the corresponding denominations of the multiplicand.

2. Multiply each denomination in the multiplicand by the highest denomination in the multiplier, carrying 1 to the next higher for every 12 in the lower denomination.

3. Multiply each denomination in the multiplicand by the second denomination in the multiplier, and set the result of each denomination one place removed to the right of the

former products; and so on for each of the other denominations of the multiplier, always placing the product by a smaller denomination one place farther to the right than that of its superior denomination.

EXAMPLES

1. How many square feet are contained in a board 6 feet 7 inches long, and 2 feet 5 inches wide?

Operation.

F

6

7

2

5

13

2'

2

8' 11"

Illustration. We first multiply the multiplicand, beginning with the inches, by the two feet in the multiplier; thus, 7 x2F=14′=1F 2in. We place the 2' under the inches, and carry the 1 to the feet; 15 10' 11′′ thus, 6FX2F=12, and 1 to carry =13F. We then multiply by the 5′ in the multiplier; thus, 7'x5' 35′′-2′ 11′′; we set the 11" one place to the right, and carry the 24 to the next; thus, 6F × 5'30', and 2' to carry make 32' 2F 8', which we set down in their proper places, and the products added together give the answer, 15F 10' 11", or 15F 1011 inches.

2. How many square feet are contained in a board 15 feet 5 inches long, and 1 foot 8 inches wide?

5'

15F

[blocks in formation]

3. How many solid feet in a block 2ft. 6 inches long, 1ft. 9 inches wide, and 1ft. 5 inches thick?

2ft. 6' length

1 9 breadth

[blocks in formation]

4. How many square feet are contained in a floor 16ft. 9 inches long, and 12ft. 4 inches wide? Ans. 206ft. 7in. 5. How much wood in a pile 6ft. long, 3ft. 9in. high, and 4ft. 6in. wide? Ans. 101ft. 3in.

6. How many square feet are contained in 15 boards, each 18ft. 5in. long, and 1ft. 7in. wide? Ans. 437f. 4′ 9′′. First find the square contents in 1 board which multiply by 15, using the factors.

7. Multiply 16ft. 9in. by. 7ft. 11in. 8. Multiply 10ft. 4' 3" by 2ft. 8'.

Ans. 132ft. 7 in.

Ans. 27ft. 77 4.

9. How many square feet in a board 36ft. 8in. long, and

2ft. 4' 9" wide?

Ans. 87ft. 10′ 2′′. 10. How much wood in a load 8ft. long, 4ft. 5′ high, and 3ft. 9' wide? Ans. 132ft. 6'=1 cord, 4 ft

MISCELLANEOUS QUESTIONS FOR EXERCISE IN THE

FOREGOING RULES.

1. What is the sum of 1948 added to itself?

Ans. 3896.

2. There are three numbers, their sum is 2302, the first is 311, and the second 695, what is the third?

Ans. 1296. 3. What is the difference between 31 eagles, and 3099 dimes?

Ans. 10cts.

4. If the minuend be 3441, and the remainder 365, what is the subtrahend? Ans. 3806. 5. What number being multiplied by 5, will make just as nuch as 25 multiplied by 49?

Ans. 245. 6. What number is that which being divided by 96 the quotient will be 128? Ans. 12288.

7. There are 6 chests of drawers, each containing 18 drawers-in each drawer is 6 divisions, and each division contains $36. How many dollars in all? Ans. $23328.

A line or vinculum drawn over several numbers, denotes that the numbers under it are to be taken jointly, or as one whole number.

8. 5+8X9-2=91.

9. 12-3+585-7=How many?

10. 407-15X12-3+7-How man?

Ans. 84.

Ace 512..

11. A man being asked his age replied, I have 7 sons, the difference between whose ages is just 2 years-I was 34 years old when my oldest son was born, and that is now the age of my youngest. What was his age?

12. If from a staff 8 feet in length, A shadow, 5 is made,

Ans. 80 years.

What is that steeple's height in yards,

That's 90 feet in shade?

Ans. 48 yards.

15

Ans. 2÷20

13. What number, being multiplied by 15, the product will be? 14. What number is that which being divided by 15, the

product will be ?

Ans. X15-117. 15. What number is that, to which if you add, will be ? Ans. -=23 16. What number is that, from which if you subtract the remainder will be?

Ans..

17. B and C traded together and gained $100; B put in $640, C put in so much that he must receive $60 of the gain. How much did C put in? Ans. $960.

18. Divide $356 between B and C, so that the shares shall be in proportion to each other as 3 to 5.

3+5 8 356; 3: $133 B's part..

{5:2221 C's part.

19. Bought cloth at $1,25 per yard, and lost 25 per cent by the sale of it. How was it sold per yard?

Ans. $93,7 m.

20. Thomas sold 150 pine apples at 33 cts. apiece, and received as much money as Harry received for a certain number of watermelons which he sold for 25 cents apiece. How much money did each receive, and how many melons had Harry?

Ans. each received $50, and Harry had 200 melons. 21. B and C depart from the same place and travel in opposite directions, B goes east 23 miles a day, and C travels west 35 miles a day. How far will they be apart at the end of 6 days, and how many miles will each have traveled?

Ans. 348 miles. B will have traveled 138m. and C 210. 22. A certain pasture will last 936 sheep 7 weeks.—

!

How many must be turned out, so that it will be sufficient to last the remainder 9 weeks?

Ans. 214. 23. A merchant bought a quantity of flour for $137, and sold it again for $143, what did he gain per cent?

Ans. 4

per cent. 24. Said Henry to Richard, my purse and money are worth $43,75. But the money is thirty-four times as much as the purse. I demand how much the purse was worth, and how much money it contained?

Ans. $1,25 and it contained $42,50.

25. A young man received £210, which was of his elder brother's portion, now three times the elder brother's portion was half the father's estate. What was the value of the whole estate?

Ans. £1890 26. What is the interest of $256 from January 1st, 1833, to Sept. 16th, 1835, at 6 per cent?

Ans. 41,60. 27. A note dated April 15th, 1828, for $756,20 was paid July 10th, 1836. What was the amount paid, interest being computed at 6 per cent per annum?

Ans. $1129,88c. 8m.+ 28. What is the difference between the interest of $500 at 5 per cent for 12 years, and the discount of the same sum at the same rate and for the same time?

Ans. $112,50. 29. What is the yearly insurance of a Cotton Factory, valued at $35640, at 25 per cent premium? Ans. 935,55. 30. What is the cost of $1500 Bank Stock, at 8 per cent advance, or at 108 per cent? Ans. $1625.

31. Suppose 2 men start from the same place and travel in opposite directions, one at the rate of 5 miles an hour, and the other as fast. How far apart would they be at the end of 13 hours? Ans. 108 miles.

32. A hare starts 40 yards before a grey hound, and is not perceived by him until she has been up 40 seconds; she scuds away at the rate of 10 miles an hour, and the dog makes after her at the rate of 18 miles an hour. How long. will the course hold, and what space of ground will be run over from the place where the dog started?

Ans. 60sec, and 530yds. space. 33. Three persons purchase a sloop, towards the pay

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