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RULE. Take two figures or factors, whose product ex mes nearest, though short of the multiplier, and multiply by them as in case second. Then multiply the given sum by the number which will make up the deficiency; then add this last product to the sum produced by the two factors, and their sum will be the answer.

EXAMPLES.

1. What will 17 bushels of wheat come to, at 10s. 6d. per bushel?

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pence per yard?

Ans. £8 18s. 6d. DEM.-It is plain, from the preceding case, by multiplying the price of one by 5, and then that product by 3, that we have the price of fifteen'; and it is then evident, if we inultiply the price of one by 2, and add the product to the price of fifteen, we must have the price of 17 bushels, which was required.

2. What will 23 yards of cloth come to, at 4 shillings 7 Ans. £5 5s. 5d. 3. What is the worth of 47 pounds of butter, at 9 pence 2 farthings per pound? Ans. £1 17s. 2d. 2qrs. 4. How many cwt. are contained in 19 kegs of tobacco, each weighing 56lb.? Ans. 9cwt. 2qrs. 5. What is the weight of 17 hogsheads of sugar, each weighing 8cwt. 3qrs. 14lb.? Ans. 150cwt. 3qrs. 14lb.

6. What is the weight of 23 chests of tea, each weighing 3cwt. 1qr. 21lb.? Ans. 79cwt. Oqrs. 71b. 7. What will 19 yards of cambrick come to, at 11s. 6d. per yard? Ans. $10 18s. 6d. 8. What will 52 pounds of tea come to, at 5 shillings 9 pence per pound? 9. If one pound of coffee cost 2 shillings 3 pence; what must be paid for 26 pounds? Ans. £2 18s. 6d.

Ans. £14 19s.

10. If one yard of lasting cost 7 shillings 10 pence; what will 65 yards cost? Ans. £25 9s. 2d.

CASE IV. To find the value of a hundred weight, by having the price of one pound given.

RULE.-If the price be farthings, multiply 2 shillings 4 pence, by the farthings in the price of one pound, and the product will be the

price of lewt., or 112 pounds. If the price be in pence, multiply 9 shillings 4 pence by the price of one pound, and the product will be the price of lcwt. or 112 pounds.

EXAMPLES.

1. If one pound cost 2 farthings, what cost lcwt?

S. d.

2 4

2

Ans: 4s. 8d.

Ans. 4s. 8d. DEM. The reason of our taking 2 shillings 4 pence for a multiplicand, is evident, when we recollect that in 112 farthings there are 2 shillings 4 pence, the prict of lcwt., at one farthing a pound; then it is plain, at 2 farthings a pound, it must be twice as much; consequently we multiply the price, at one farthing, by 2, which gives us the price of lcwt., at 2 farthings per pound? 2. What will lcwt. of rice cost, at 21d. per pound?

s: d. 2 4

10 farthings=2a.

Ans. £1 3s. 4d.

Ans: £1 3s. Ad.

Ans. 11s. 8d.
Ans. 16s. 4d.

3. What will lcwt. cost, at 1d. per pound?
4. What will lcwt. cost, at 13d. per pound?
5. What will lcwt. come to, at 3 farthings per pound?

6. What will 1cwt. cost, at 4d. per pound?

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9

4

4

Ans. £1 17 4

Ans. 7s.

Ans. £1 17s. 4d,

DEM.-The reason of our setting down 9s. 4d. for a multiplicand is plain, because 9s. 4d. is the price of lcwt. or 112 pounds, at 1 penny per pound, for 112 pence make 9s. and 4d. It is then plain, it must be four times as much, at four pence per pound, as at one penny per pound, consequently we multiply the price of lewt., at 1 penny per pound, by 4, which must give us the price of lcwt., at 4d. per pound; because at 4d. per pound, lcwt. must cost 4 times as much, as at one penny per pound. 7. What is the value of Icwt., at 3 pence per pound?

Ans. £1-85.

8. What is the value of 1cwt., at 7 pence per pound?

Ans. £3 5s. 4d.

9. At 9 pence per pound, what is the value of 1cwt. ?

Ans. £4 4s.

10. At 8 pence per pound, what is the value of 1cwt.?

K

Ans. £3 14s. 8d

PRACTICAL QUESTIONS

1. What is the worth of 42 bushels of peas, at 4 shillings 6d pence per bushel?

Ans. £9 9s.

2. What is the worth of 42 bushels of apples, at 2 shillings 6 pence per bushel?

Ans. £5 5s, 3. What is the worth of 49 yards of broadcloth, at 18 shillings 4 pence per yard?

Ans. £44 18s. 4d.

4. What is the weight of 8 hogsheads of sugar, each weighing 7cwt. 3qrs. 191b.?

Ans. 63cwt. 1qr. 12lb.

5. What is the weight of 6 chests of tea, each weighing 3cwt. 2qrs. 8lb.? Ans. 21cwt. 1qr. 20lb.

6. How many yards in 12 pieces of cloth, each containing 18 yards, 2qrs. Ina.? Ans. 222yds. 3qrs.

7. What is the weight of 2 dozen silver spoons, each weighing 2oz. 12pwts. 5grs.? Ans. 5lb. 2oz. 13grs.

8. How many cords of wood in 9 piles, each containing 26 cords, 98 feet? Ans. 240 cords, 114 feet.

9. In 35 pieces of cloth, each measuring 27 yards; how many yards in the whole? Ans. 953 yds. 3qrs. 10. How much land in 4 fields, each of which contains 12 acres, 2 roods, 16 rods? Ans. 50 acres, 1 rood, 24 rods. 11. What is the value of 20 cords of wood, at 9s. per cord? Ans. £9. 12. What are 18 yards of shirting worth, at 2 shillings 6 pence per yard? Ans. £2 5s. 13. What is the worth of 25 bushels of wheat, at 10 shìllings per bushel ? Ans. £12 10s.

COMPOUND DIVISION,

Is finding how often one number or sum is contained in another of different denominations, or how often it may be subtracted from another.

RULE.-Divide the left hand denomination the same as in simple division; and if any thing remains, reduce it to the next inferiour denomination, adding to the product whatever you have in the given sum of the next less denomination; then divide as before, and again reduce the remainder to the next inferiour denomination, and thus continue the work, till the whole is finished.

Proved by compound multiplication. Multiply the quotient by the divisor, and if the product equal the multiplicand the work is right..

CASE I.

1. Divide £32 16s. 8d. equally among 4 persons.

d.

£ S.
4)32 16 8

Ans. 8 4

Ans. £8 4s. 2d. the share of each.

DEM.-It is plain, if £32 16s. 8d. be divided into 4 parts or shares, that one part or share is a fourth part of the whole; and by dividing the whole sum by 4, our quotient must be a fourth part of the whole, which plainly appears from the quotient itself, because each quotient figure is one fourth part of a like denomination in the dividend.

2. If 5 bushels of clover seed cost £11 3s. and 4d.; what did it cost per bushel? Ans. £2 4s. 8d.

£ S. d. £ S. d.
3 4 (2 4 8

5)11

10

20

23

20

3

12

40

40

5 Proof. £11 3 4

0 remainder.

DEM.-It is plain, that the quotient must be in each place of the same kind or denomination of that part of the dividend which produced it, hence by dividing the pounds of the dividend by the divisor (5,) our quotient is 2 pounds; and we have one pound remaining, which we multiply by 20, because it equals 20 shillings, and to the product, we add the 3 shillings of our dividend, and divide the 23 shillings by 5, the divisor, which gives 4 for a quotient; which is shillings, because the shillings of the dividend produced it; we now have 3 shillings for a remainder, which we reduce to pence, by multiplying by 12, and adding the four pence of the dividend to the product; we now have 40 pence, in which we find 5 contained 8 times, which gives us 8 pence in the quotient without a

NOTE. The student will recollect, that compound division is exactly the reverse of compound multiplication. In compound multiplication, we have the price of one pound, one yard, &c. given to find the price of a quantity. In compound division, we have the price of a quantity given to obtain the price of one. And since this rule is exactly the reverse of multiplication, the student will discover, that our remainder, in each place, is produced by the carriage in multiplication; therefore, when any thing remains in pounds, it is as many times 20 in shillings, because in multiplication, we divide the shillings by 20 and carry the quotient to the pounds, which becomes the remainder in division; and for the same reason, when any thing remains in shillings, it is so many times 12 in pence, and so on.

3. A box containing 36 hats cost £48; how much was that per hat? Ans. £1 6s. 8d.

6 8

6

£

£

s. d.

36) 48 36

( 1

12

8

20

240 £48

216

24.

0 0

6

Ο 0

DEM. It is plain, that one hat must cost one thirty-sixth part as much as 36, and when we divide the whole sum by 36, our quotient is one thirtysixth part of the whole sum, as plainly appears by the proof; because when we repeat the quotient 36 times, we find that the product equals the dividend or whole cost. In the proof, it will be noticed, by multiplying by 6, and then that product by 6, is the same as directly multiplying by 36; because the two multipliers are the component parts of 36, for 6 times 6 are 36.

12

288

288

0

NOTE. In addition to the illustration of this rule already given, the student has only to keep in mind one thing, that is, to obtain the price of one yard, one pound, &c.; we must divide the price of the quantity by the quantity, and the quotient will be the price of one yard, one pound, &c. Or if the weight of a number of hogsheads, bales, bags, or boxes, be given, to obtain the weight of one; divide the weight of the whole quantity or number by the number of hogsheads, bales, bags, or boxes, and the quotient will be the weight of one.

4. Three cows cost £22 3s. 9d.; what was the cost of each? Ans. £7 7s. 11d. 5. If £12 9s. 8d. be divided equally among 4 men; how

much will each receive? Ans. £3 2s. 5d. 6. If 7 Ells cost £5 17 shillings 5 pence; what cost 1 ell? Ans. 16s. 91d. 7. If 8 horses cost £185 17s. 6d.; what was the cost of one horse? Anş. £23 4s. 8d. 1qr. 8. If 10 bushels of wheat cost £3 6s. 8d.; what cost one bushel? 9. A man paid £2 10s. for 15 bushels of corn; what did he pay per bushel ?

Ans. 6s. 8d.

Ans. 3s. 4d.

10. A merchant paid £105 for 50 barrels of flour; what did he pay per barrel? Ans. £2.2s.

CASE II-When the divisor exceeds 12, and is a composite number, it sometimes shortens the work to divide by the component parts of the divisar.

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