V. The quotient will in most cases require to be reduced to a higher denomination; if there be a remainder, it will be of the same denornination which the second term was brought into, and must be reduced into the next lower denomination, and then divided by the first term, and the quotient will be of this latter denomination; and if there be still a remainder, it must be reduced lower and divided, and so on until you get to the lowest denomination the second term admits of.

Method of proof. Reverse the question thus; say as the third term is to the fourth, so is the first term to a fourth, or answer, which will come out exactly the same as the second term in the original question, when the work is right: or, to be more plain, make the third term the first, the answer the second, and the first term the third, and, working according to the rule, the answer will be the same as the second term of the question.

EXAMPLES.

1. If 2 yards 3 quarters of muslin cost 1l. 5s. 8d. what is the value of 4 yards 3 quarters 2 nails of the same?

Divided by the 1st. 44)24024 ( 546 quotient in pence.

220 20)45 6

78

-2156 12)

-2184 12)

terms multiplied toge

Divided by the 1st. 78)24024 (308 quotient in pence,

234 20)2 5 8

624 11. 5s. 8d. Ans. or 4th term.

624

Explanation.

Of the three terms given in the question, the odd term is money, viz. 1. 5s. 8d. which (being of the same kind as the answer required) I put in the second place. The two remaining terms are of the same kind, viz. both muslin; these occupy the first and third places; the term of supposition, 4yd. 3qr. in the first, and the term of demand, 4yd. 3qr. 2n. in the third. 1 reduce both these terms into nails; the result of the first being 44, and of the third 78. I also reduce the second, 17. 5s. 8d. into pence, and the result is 308. I then multiply 308 and 78, viz. the second and third, together, and divide the product 24024 by 44, the first. The quotient 546 is of the same name which the second term was in when I multiplied it by the third, namely, pence; I therefore divide 546 by 12 and 20 successively, and it gives 27. 5s. 6d. the

answer.

For the proof. I take the third term of the question and make it the first ; the fourth term, or answer, I make the second; and the first term of the question I make the third; and, working exactly the same as before, the answer comes out 17. 5s. 8d. which is the same as the second term of the question, and thereby shews that the operation is truly performed.

2. If 5lb. of powder-blue cost 10s. 5d. how many pounds can 1 buy for 21. 16s. 3d.?

3. If 3 ounces of tea cost 1s. 7d., what cost 1cwt. 1qr. 2lb.? Ans. 611. 10s. 8d. Stated thus; 3oz.: 1s.7d.:: 1cwt. 1gr. 2lb. 4. If 11 pounds of sugar cost 13s. 6d.4, what cost 2cwt. 3qr. Ans. 191. 3s. 6d.

4lb.?

Stated thus; 11lb. : 13s. 6d. :: 2cwt. 3qr. 4tb.

5. If 7 yards of cloth cost 127. 7s. 4d. what will 12yd. 2qr. 2n. cost? Ans. 221. 6s. 1d.

Stated thus; yd.: 121. 7s. 4d. :: 12yd. 2qr. 2n.

6. If 15 pounds of cheese cost 16s. 3d. what is that per cwt.? Ans. 61. 1s. 4d. Stated thus; 15lb.: 16s. 3d. : : 112lb. 7. If hops sell for 31. 18s. 6d. per cwt. what sum will buy 8cwt. 3qr. 14lb. ? Ans. 341. 16s. 8d.4.

Stating; 112lb. : 3l. 18s. 6d. :: 8cwt. 3qr. 14lb.

8. A Rear-Admiral's half-pay is 17s. 6d. per day, how much is that per year? Ans. 3191. 7s. 6d.

Stating; 1 day 17s. 6d. :: 365 days.

9. A person owes 12347. but being unable to pay the whole, his creditors agree to accept 16s. 6d. in the pound; what sum do they receive in all? Ans 10201. 12s. 5d.

Stating; 11. 16s. 6d. : : 1234l.

:

10. What sum will purchase 20 reams of paper, when 6s. 5d. will buy seven quires? Ans. 181. 6s. 8d.

Stating; 7quires: 6s. 5d. :: 20 reams.

11. A person having 3751 Venetian ducats, agrees to sell them at the rate of 40 ducats for 9l.; how much English money does he receive for the whole? Ans. 8431. 19s. 6d.

Stating; 40duc.: 9l.: 3751duc.

12. A bankrupt who owes 2500l. has effects amounting to 4371. 10s.; how much in the pound will he be able to pay his creditors? Ans. 3s. 6d. Stating; 2500l.: 4371. 10s. : : 1l, 13. If a gallon of wine cost 12s. 4d. what is the value of a pipe? Ans. 771. 14s.

14. If 13 yards of cloth cost 21. Os. 1d. what must be given for 75 yards? Ans. 111. 11s. 3d.

15. If a quarter of wheat cost 51. 4s. 10d. what will 11qr. 3bu. cost? Ans. 591, 12s. 5d..

16. What is the value of 30ch. 12bu. 2pk. of coals, at 6s. 6d. per sack? Ans. 1181. s. 1d.

129. When the second term is a compound number, it will in

many cases be convenient to use Compound Multiplication and Division, whereby the trouble of reducing both the second term and the answer will be saved.

17. If 3 cwt. of tallow cost 5l. 10s. 9d., what is the value of 16 cwt.?

18. If 12 ounces of silver cost 31. 7s. 6d. what cost 35 ounces? Ans. 91. 16s. 10d..

19. If 15 loads of hay sell for 127. 12s. 11d. what sum will be sufficient to purchase 28 loads at the same rate? Ans. 231. 12s. 1d.4, 5 rem.

20. If 27 fother of lead cost 1717. 15s. 9d. what sum will buy 35 fother? Ans. 2221. 13s. 9d.

21. Sold $1 pounds of tobacco for 14l. Os. 1d.; what must be charged for 64 pounds? Ans. 11l. 1s. 4d.

22. Bought 99 reams of

foolscap for 1261. 4s. 6d. ; what will 137 reams cost at that rate? Ans. 1741. 13s. 6d.

130. When the first term will divide the second without

remainder.

RULE. Divide the second term by the first, and multiply the

quotient by the third; the product will be the answer.

23. Paid 41. 178. 6d. for the reaping of 10 acres of wheat; what must be paid for the reaping of 124 acres at that rate?

24. If 8 years' rent of a farm be 52321. what sum will 11 years' rent amount to? Ans. 71947.

25. If 9 bushels of wheat sell for 4l. 19s. 9d. what is that per load? Ans. 221. 3s. 4d.

26. If 41. be charged for a year's interest of 100l. what sum must be lent to gain 500l. in the same time? Ans. 12500.

27. If 10 ounces of gold be worth 401. 15s. what will be charged for a cup of the same metal, weighing 2lb. Soz.? Ans. 1301. 8s.

131. When the first term will divide the third without remainder.

RULE. Divide the third term by the first, and multiply the quotient by the second, or the second by the quotient; the product will be the answer.