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terms together, and divide the product by the third ; the quotient will be the answer, in the same denomination as the middle term was reduced into.

If there be fractions in your question, they must be ftated as before directed ; and if they be vulgar, invert the third term : Then multiply the three terms con. tinually together, and the product will be the answer.

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1,

EXAMP How much shalloon, that is $ yard wide, will line 61 yards of cloth, which is 14 yard wide ? rd. yds. gr.

qrs.

grs. qrs. As 11:04 :: 3

As 5 27 :: 3 4 4

5
5 27

3)135
4)45

540

11% yds. Ang The same by Vulgar Fractions. First. 1=1, 51=1, and 3qrs.= }, then yds. yds. yd.

5 X 27 X4 As I :*::* And IX*X=

4X4X3 4 =11; yds. Ans.

The same by Decimal Fractions. 1= 1,25, 61=6,75, and 3qrs.=,75, then

yd. yds. yd. As 1,25 : 6,75 :: 175 1,25

What length of board

7 inches wide, will make a 3375

square foot ? 1350

In., br. In. len. In, br. In. len. 675

:: 7 : 19 Ant ,75)8,4375(11,25 yds. Ainf.

2.

As 12

:

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3. How many yards of carpet, 2 feet wide, will cover a floor, which is 18 feet long and 16 feet wide ?

ft. ft. ft. ft. yds.

As 16:18 :: 21x3 : 341: Ang. Note, I multiply 2 by 3, because 3

feet=1 yd. 4. Suppose I lend a friend £350 for 5 months, he promising the like kindness ; but, when requested, can spare but £125 ; how long may I keep it to balance the favour?

& Mo. £ Mo.

As 350 : 5 :: 125 : 14 Anf.
5. Suppose 450 men are in a garrison, and their pro.
visions are calculated to last but

5
months ;

how

many must leave the garrison, that the same provisions may be sufficient for those who remain, 9 months ?

Mo. Men. Mo. Men. Men.
As 5 : 450 :: 9 : 250, & 450-250=200 Men. Anf.

6. If a man performs a journey in 15 days, when the day is 12 hours long ; in how many will he do it, when the day is but 10 hours ?

b. d. h. d.

As 12 : 15 :: 10 : 18 Answer. 7. If a piece of land, 40 rods in length, and 4 in breadth, make an acre ; how wide must it be, when it is but 19 rods long to make an acre ?

Leng. Br. Leng. Br. ft. in.

As 40 : 4 :: 19 : 8 6 117 Ans. 8. lf, when wheat is 6s. per bushel, the two penny loaf weighs 9,60%. what ought it to weigh, when wheat is 75. 6d. per bushiel ?

s. d. oz. pwt. gr.
As 6: 9,6 :: 76:7 13 14,4 Answer.
9. If a piece of board be 30 inches in length ; what
breadth will make i} square foot ?

in. in.
As 1,5 : 1 :: 30 : 7,2 Answer.

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59.f. in.

10.

mo.

mo,

II.

many men must

теп.

A3 12 :

I 2.

If 9 men can build a house in 5 months, by working 14 hours per day ; in what time will the same number of men do it, when they work only 19 hours per day?

h.

h.
A6 14 : 5 :: 10 : 7 Answer. ,

A wall which was to be built 24 feet high, was raised 8 feet by 6 men, in 12 days ;

how be employed to finish the wall in 4 days?

ft. men. ft. As 8 : 6 :: 24-8 : 12 to finish it in 12 days. And days. men. days, men.

12 :: 4 : 36 to finish it in 4 days.

There is a cistern having a pipe, which will empty it in 6 hours ; how many pipes, of the same capacity, will empty it in 20 minutes ?

ho. pi.

min. pi. As 6 : 1 :: 20 : 18 Answer. 13. What number of men must be employed, to finish in 9 days, what 15 men would be 30 days about?

da. men. As 30 : 15 ::9; 50 Answer. 14: If a field will feed 6 cows 91 days ; how long will it feed 21 cows ?

d.

d. As 6: 91 :: : 26 Answer. 15. How much in length, that is 84 inches broad, will make a foot square ? in. in,

in. As 144 ; } :: 8. : 16% Answer. 16. How much in length, that is 13 poles in breadth, will make a square-acre ? ро. ро.

po.
::: 137 :1114 Answer.

da. men.

COWS.

COWS.

21

in.

po.

As 100

1

17. A regiment of soldiers, consisting of 745 men, is to be clothed, each suit to contain 31 yards of cloth, which is it yard wide, and lined with shalloon yard wide ; how many yards of shalloon will line them?

18.

As 745X31 : 1 :: 5 : 4097; yds. Ans.

If a suit of clothes can be made of 45 yards of cloth, 1 yard wide ; how many yards of coating, f of a yard wide, will it require for the same person?

yd.yds. yd. yds. gr. n.
As i} : 45 :: 5:6 1 34 Answer.

A B BREVIATION S.

To know whether a fraction, when abbreviated, be equiva

lent in all respeëls to the original given fraction.

RULE.-As the numerator of the fraction, in its lowest terms, is to its denominator ; so will the nume. rator of the original fraction be to its own denomi. nator.

Or, as one numerator is to the other ; so will one denominator be to the other, &c.

A owes B £75 135. 6d. now £100 of A's money is equal to £140 of B's ; what must A pay to satisfy the faid debt?

to d. 198= therefore, 75 13

5

13 6

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£54 Ion Anf: Now, to prove whether {be equal to 140 Num. Den. Num. Den. Num. Num. Den. Den. As 5 : 7 :: 100: 140_Or, as 5 : 100 :: 7 : 140.

و

COMPOUND

COMPOUND PROPORTION,

OR,

DOUBLE RULE OF THREE, Teaches to resolve such questions as require two, or more ftatings, by simple proportion ; and that, whether direct, or inverse :-It is composed (commonly) of 5 numbers to find a fixth, which, if the proportion be direct, muft bear such proportion to the 4th and 5th, as the 3d bears to the ist and 2d: But if inverse, the 6th number must bear such proportion to the 4th and 5th, as the ift bears to the 2d and 3d.

Always place the three conditional terms in this order : That number, which is the principal cause of gain, loss or action, possesses the first place ; that which denotes the space of time or distance of place, the second ; and that, which is the gain, loss or action, the third ; this being done, place the other two terms, which move the question, under those of the same name, and if the blank place, or term fought, fall under the third place, then the question is in direct proportion ; therefore,

RULE 1.-Multiply the three last terms together, for a dividend, and the two first for a divisor : -But if the blank fall under the first or second place; then, the proportion is inverfe; therefore,

RULE 2.--Multiply the first, fecond and last terms together for a dividend, and the other two for a divisor, and the quotient will be the answer.

If £100 gain £6 in a year ; what will £400 gain in 9 months ? £.P. Mo. f. Int.

:: 6 Terms in the supposition, or conditional terms. 9

Terms which move the question. Here, the blank falling under the third place, the question is in direct proportion, and the answer must be found by the first rule ; therefore,

I.

12

100 : 400 :

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