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Q. What is the produet of 5" (seconds) multiplicd by 7" (secuads)!
A. 35', that is, 35 fourths.
Q. How may the value of the product always be determined?

A. By placing as many marks or accents at the right of the product as there are marks at the right of both multiplier and multiplicand counted together.

Q. What, then, would gonn (fifths) multiplied by 8:9" (sixths) pro
A. 56" , that is, 56 elevenths...
Q. What would 7" (seconds) multiplied by 5'" (thirds) produce
A. 35, that is, 35 fifths.
Q. What would 8" multiplied by 3'' produce !
A. 24", (fourths.)

R. From the preceding, what appears to be the value of feet mulsiplied by primes or inches ? or what do feet mulriplied by primes give !

A. Primes.
Q: What do primes multiplied by primes give ?
A. Seconds.
Q. What do primes multiplied by seconds give ?
A. Thirds.
Q. What do seconds multiplied by seconds give ?
A. Fourths."
Q. What do seconds multiplied by thirds give ?
X. Fifths.
Q. What do thirds multiplied by thirds give?

A. Sixths. Note. This might be extended in the same manner to any indefinito longda the following table contains a few of those denominations.

Repeat the

TABLE. 12" (fourths). ..... make 1" (third.) 12" (thirds) ...... mako 1" (second.) 12" (seconds) ..... make 1 (inch or prime.) 12 (inches or primes) make 1 foot. Q. How may duodecimals be added and subtracted !

A. In the same manner as compound numbers ; 12 of a less denomination always making I of a greater, as in the foregoing table.

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MULTIPLICATION OF DUODECIMALS.
Q. What are duodecimals used for ?

A. For measuring any thing respecting which length and breadth, also depth, are considered.

?. How many square feet in a board 10 ft. 8 in. long, and -t. 5 in. broad?

We have seen how such an example may be performed by common decimale : so will now perform it by duodecimals.

OPERATION.
Length, 10 ft. 8.

8 inches or primes=1% of a - Breadth, 1 5

foot, and 5' (primes) = ing of a 4 5 4"

foot; then, x B=ty of

a foot, that is, 40" (seconds) 10 8

3' (inches) and 41 (seconds) :

we now write down 4" at the Ans. 15 1' 4" I right of the inches, reserving

the 3' to be carried to the inches. in multiplying 10 feet by the 5', we say 19 X = 4 or 501 (inches), and the 3' we reserved makes 53', 4 feet and 5', which we place under feet, and inches in their proper places. Then, multiplying 10 ft. 8'' by 1 ft. makes 10 ft. 8', which we write under the X ft. 5'. We now proceed to add these two products together, which, by carrying 12, after the inanner of compound rules, make 15 ft. 1 (inch) 4" (seconds), the

Answer.

It will be found most convenient in practice to begin by multiplying the mnl. tiplicand first by the foet, or bighost denomination of the multiplier, then by the inches, &c., thus :

1X8'=&, and I ft. x 10 ft. = 10 ft. Then 50 x OPERATION

8 = 401 =3, (to carry,) and 4il, (to write down); 10 st. 8

10 x 5 = 501 + 3(10 carry)=53' = 4 it, and 5, which we write down underneath the 10 and 8. Then, the sum of these two products, auderl together

as before, is 15 t. 11 4 Ans., thu saino result as the 10 g

other.

Nute. Had we been required to multiply 15 it. 4 5 411 14H by feet and inches again, we shoukl have pro

ceeded in the suine inanner, carrying " (Thirds) one

place farther towns the rigt, and HII (fourths) 15 1' 4": 1

another place still, and so on.
. From these examples we derive the following

RULE.
Q. Ilow do you multiply in duodecimals ?

A. Begin with the highest denomination of the multiplier and the lowest denomination of the

multiplicand, placing the first figure in each prod. act one place farther towards the right than the former, recollecting to carry by 12, as in com. r pound rules.

More Exercises for the Slate. 2. How many feet in a board 2 ft. 6' wide, and 12 ft. 3' long?

A. 30 ft. 7'6" 3. In a load of wood 8 ft. 41 long, 2 ft. 64 high, and 3 ft. 3 wide, how many solid feet? A. 67 ft. 8' 6!!.

Note.Artificers compute their work by different measures. Glazing and mason's flat work ate computed by the square foot; painting, paving, plaster ing, &c. by the square yard; flooring, roofing, tiling, &c., by the square of 103 feet; brick work by the rod of 16feet, whose square is 2721; the contents of bales, cases, &c., by the ton of 40 cubic feet; and the tonnage of ships by the son of 95 foot.

4. What will be the expense of plastering the walls of a room 8 ft. 61 high, and each side 16 ft. 3' long, at $,50 per square yard? $30,694 +.

5. How many cubic feet in a block 4 ft. 3' wide, 4 ft. 6 long, and 3 ft. thick? A. 57 ft. 4! 67.

6. How much will a marble slab cost, that is 7 ft. 4' long, and 1 ft. 31 wide, at $1 per foot ? A. $9,161

7. How many square feet in a board 17 ft. 7 long, 1 ft. 5 wide, A. 24 ft. 101 11".

8. How many cubie feet of wood in a load 6 ft. 71 long, 3 p 6 high, and 3 ft. 8' wide ? A. 82 ft. 5' ghl 4!.

9. A man built a house consisting of 3 stories; in the upper story there were 10 windows, each containing 12 panes of glass, each pane 14 long, 12' wide; the first and second stories contained 14 windows, each 15 panes, and each pane 16' long 12' wide : how many square feet of glass were there in the whole house ? A. 700 sq. ft.

10. What will the paving of a court-yard, which is 20 R long, and 56 ft. 4! wide, come to, at $,20 per square ?

A. $788,663 11. How many solid feet are there in a stick of timber 70 Å long, 15 thick, and 184 wide ? A. 131 ft. 3.

Questions on the foregoing. 1. How many pence are there in 1 s. 6 d.? How many cents ?

2. What will 4 yards of cloth cost, in cents, at 1 s. 68 per yard? At 38. per yard? At 4 s. 6 d.? At 6 &? N Oss 19,92,?

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23. If 30 bushels of oats cost $10, what is that a bushel? What will 5 bushels cost? What will 20 bushels ?

24. If 3 men mow a field in 8 days, how many men will mow the same in 2 days? In 1 day? In 4 days?

25. Two men, A and B, hired a pasture; A paid $3, and B $5; what fractional part of the whole did each pay? The profits from the pasture were $16; what was each man's share of the gain?

26. Three men, A, B, and C, are engaged in trade; A puts in $4, B $5, and C $6; they gained $60: what is each one's share of the gain?

27. Two men, Å and B, hired a pasture for $12; A put in I cow 4 months, and B 2 cows 3 months; what ought each to pay ?

28. A merchant, having purchased a piece of broadcloth for $2 per yard, wishes to make 20 per cent on it; what price pust he ask for it?

29. William has } of a dollar, Thomas t', and Harry }; how many cents have they in all ?

30. A merchant sold calico at $,22 per yard, and thereby gained 10 per cent. ; what did it cost him per yard ?

31. Harry, having i ot' an orange, gave to Thomas, who graves of his part to his little brother, and kept the remainder himself; what part did he keep? How much is of ? How much does of of from leave?

32. How much is 1 x š of ?-1. How much is 1 x 1 of ?

33. What is the quotient of divided by ?
84. How much does exceed ,75?
35. How much does exceed 11?

36. How many strokes does a regular clock strike in 2 hours? 3 h.? 4 h.? 5 h. ? 6 h.? 7 h.? 8 h.? 9 h.? 10 h.? 11 h.? 12 h.? 24 h. ?

37. How many square feet in a board 12 inches wide, and 48 inches long? 36 in. long? 72 in. long?

38. What part of an acre of land is there in your father's garden, allowing it to be 4 rods long and 2 rods wide? 4 Bods wide ?

39. How many cord feet of wood are contained in a load 8 feet wide, 2 feet high, and of the usual length ? How many feet in a load 6 feet high and 3 feet wide ? 2 feet tiga and 6 feet wide? 4 feet high and 24 feet wide?

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