PRACTICAL QUESTIONS.

1. What is the worth of 42 bushels of peas, at 4 shillings 6 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? 12. What are 18 yards of shirting worth, at 2 shillings 6 pence per yard? Ans. £2 5s.

Ans. £9.

13. What is the worth of 25 bushels of wheat, at 10 shillings 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.

Ꭶ .

£ d. 4)32 16 8

Ans. 8 4 2

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 ?

£8. d. £ s. 5)11 3 4 (2 4

10

1 Proof. £11 3

20

23

20

3

12

40

40

0

remainder.

d.

8

5

4

Ans. £2 4s. Sd.

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 multitiplication, 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, 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.

d.

£

S.

6

8

36 ) 48 ( 1

36

12

8

20

240 £48

216

24

12

288

288

6

0 0

6

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 thirty sixth 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.

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.

4 men; how Ans. £3 2s. 5d.

5 If £12 9s. 8d. be divided equally among much will each receive?

6. If 7 Ells cost £5 17 shillings 5 pence; what cost 1 ell? Ans. 16s. 94d. 7. If 8 horses cost £185 17s. 6d. ; what was the cost of .; one horse ? Ans. £23 4s. 8d. 1qr. 8. If 10 bushels of wheat cost £3 6s. 8d.; what cost one bushel? Ans. 6s. 8d. 9. A man paid £2 10s. for 15 bushels of corn; what did

he pay per bushel ?

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 divisor.

RULE. Divide first by one of the component parts of the divisor, and then that quotient by the other; and the last quotient will be the

d.

£ s. 0 (43

84

3

20

70

63

7

12

84

$4

0

d. 4

Here we find that the same result is produced, and the reason is obvious from the principles of multiplication, which are

exactly the reverse of those in division.

2. A man bought 36 bushels of apples for £2 14s.; what did he pay per bushel? Ans. 1s. 6d. 3. Bought 28 cords of wood for £16 16s.; how much was paid per cord? Ans. 12s. 4. Bought 72 bushels of wheat for £41 8s.; what was paid per

bushel?

Ans. 11s. 6d. 5. Sold 81 barrels of flour for £147 16s. 6d.; how much was that

per barrel?

Ans. £1 16s 6d.

6. Bought 42 ploughs for £128 9s.; how much is that Ans. £3 1s. 2d.

per plough?

EXAMPLES

Of Weights, Measures, &c.

1. If 24 pieces of cloth contain 426yds.; how many yards

in one piece?

Ans. 17yds. 3qrs. 2. If 6 chests of tea weigh 21cwt. 1qr. 26lb. ; what is the weight of 1 chest?. Ans. 3cwt. 2qrs. 91b.

3. If 7 hogsheads of sugar weigh 69cwt.; what is the weight of 1 hogshead? Ans. 9cwt. 3qrs. 12lb. 4. If 11 pieces of cloth contain 163 yds. 2qrs. 2na.; how much in each, suppose they contain equal quantities?

Ans. 14yds. 3qrs. 2na. 5. Divide 219 acres, 1 rood, 8 rods, into twelve equal Ans. 18 acres, 1 rood, 4 poles:

parts.

6. If 174yds. 1qr. 2n. be divided equally among 5 persons, what will be the share of each ? Ans. 34yds. 3qrs. 2n. 7. Divide eighteen gallons equally among one hundred and forty four soldiers. Ans. 1 pint apiece..

PRACTICAL QUESTIONS

In Compound Multiplication and Division.

1. If one bushel of corn cost 45 cents; what will 8 bushels cost? Ans. $3,60 cents.

2. If 8 bushels of corn cost $3,60 cents; how much was per bushel? Ans. $0,45 cents.

that

3. A man received $19,50 cents for 30 day's labour; how much was that per day? Ans. $0,65 cents.

4. A gentleman wishes to put 130 bushels of apples into barrels, containing 3 bushels and one peck each; how many barrels does he need?

Ans. 40. 5. The Prince of Wales receives a salary of 150 thousand pounds a year; how much is that per day?

Ans. £410 19s. 2d. 6. A piece of calico containing 29 yards, cost $8,70 cents; what was that per yard? Ans. $0,30 cents.

7. A privateer took a prize of $30,000, of which the owner took one third, and the officers one fourth; the remainder is equally divided among 125 seamen; how much must each seaman receive? Ans. $100.

8. One hundred and sixty three men took a prize worth $1811,16 cents, of which the captain had four shares, and the first lieutenant three shares, the second lieutenant two shares; what was the share of each officer, and each private? Ans. Captain's share $42,12 cents; first Lieutenant's share $31,59 cents; second Lieutenant's share $21,06 cents; and a private's share $10,53 cents.

9. Divide £136 14 shillings 6 pence among two men and three women, and give each man three times as much as a woman; what will each man, and each woman receive? Ans. £45 11s. 6d. 1 man's share. 10d. 1 woman's share.

£15 3s.