15. From a piece of cloth containing 64 yards 2 na. a taylor was ordered to make 9 soldiers' coats, which took one third of the whole piece; how many yards did each coat contain ? Ans. 2yds. lar. 2nd.

PRACTICAL QUESTIONS.

1. If 9 yards of cloth cost 4l. Ss. 7d. what is that per yard ?

s. d. gr.

94 S 7 2

9 $ 2 Answer.

Ans. £2 1s. 10d.

2. If 11 tons of hay cost 231. Os. 2d. what is that per ton ? 3. If 12 gallons of brandy cost 41. 15s. 6d. what is that per gallon? Ans. 7s. 11d. 2qrs. 4. If 84 lbs. of cheese cost 1l. 16s. 9d. what is that

Ans. 54d.

per pound? 5. Bought 48 pairs of stockings for 11. 2s. how much a pair do they stand me in?

Ans. 4s. 73ds

6. If a reckoning of 5l. 8s. 104d. be paid equally among 13 persons what do they pay a-piece? Ans. 8s. 4d.

7. A piece of cloth containing 24 yards, cost 181. 6s. what did it cost per yard?

Ans. 15s. Sd.

8. If a hogshead of wine cost SSI. 128. what is it a gallon? Ans. 10s. 8d. 9. If 1 cwt. of sugar cost 3. 10s. what is it per pound? Ans. 7 d. 10. If a man spends 71l. 14s. 6d. a year what is that per calendar month? Ans. £5 19s. 6d. 11. The Prince of Wales' salary is 150,000l. a year, what is that a day? Ans. £410 19s. 2d.

12. A privateer takes a prize worth 12465 dollars, of which the owner takes one half, the officers one fourth, and the remainder is equally divided among the sailors, who are 125 in number; how much is each sailor's part? Ans. $24 93cts.

13. Three merchants, A, B, and C, have a ship in company. A hath, B, and C, and they receive for freight 2281. 16s. 8d. It is required to divide it among the owners according to their respective shares.

Ans. A's share £143 0s. 5d. B's share £57 4s. 2d. C's share £28 12s. 1d.

14. A privateer having taken a prize worth $6850, it is divided into one hundred shares; of which the captain is to have 11; 2 lieutenants, each 5; 12 midshipmen, each 2; and the remainder is to be divided equally among the sailors, who are 105 in number.

Ans. Captain's share $753 50cts. lieut's. $342 50cts. a midshipman's $137, and a sailor's $55 88cts

REDUCTION,

TEACHES to bring or change numbers from one name to another, without altering their value.

Reduction is either Descending or Ascending.

Descending is when great names are brought into small, as pounds into shillings, days into hours, &c.-This is done by Multiplication.

Ascending is when small names are brought into great, as shillings into pounds, hours into days, &c. This is performed by Division.

REDUCTION DESCENDING.

RULE.

Multiply the highest denomination given, by so many of the next less as make one of that greater, and thus continue till you have brought it down as low as your question requires.

PROOF. Change the oruer of the question, and divide your last product by the last multiplier, and so on.

EXAMPLES.

1. In 251. 15s. 9d. 2grs. how many farthings?

NOTE. In multiplying oy 20, I added in the 15s.-by 12 the 9d.-and by 4 the 2qrs. which must always be done in like cases.

2. In 31l. 11s. 10d. 1gr. how many farthings?

Ans. 30329

3. In 46l. 5s. 11d. 3qrs. how many farthings?

Ans. 44447 4. In 611. 12s. how many shillings, pence and farthings P Ans. 1232s. 14784d. 59136grs. 5. In 841. how many shillings and pence ? P

Ans. 1680s. 20160d.

6. In 18s. 9d. how many pence and farthings?

Ans. 225d. 900grs.

7. In 312l. 8s. 5d. how many half-pence?

Ans. 149962

8. In 846 dollars at 6s. each, how many farthings?

Ans. 243648

9. In 41 guineas at 28s. each, how many pence? Ans. 13776 10. In 59 pistoles, at 22s. how many shillings, pence, and farthings?

Ans. 1298s. 15576d. 62304qrs. 11. In 37 half-johannes, at 48s. how many shillings, six-pences, and three-pences ?

Ans. 1776s. 3552 six-pences. 7104 three-pences. 12. In 121 French crowns, at 6s. 8d. each, how many pence and farthings? Ans. 9680d. $8720grs.

REDUCTION ASCENDING.

RULE.

Divide the lowest denomination given, by so many of that name as make one of the next higher, and so on through all the denominations, as far as your question requires.

PROOF. Multiply inversely by the several divisors. {

EXAMPLES.

1. In 224765 farthings, how many pence, shillings and

pounds?

Farthings in a penny

4)224765

Pence in a shilling

= 12)56191 1

Shillings in a pound

= 20)468|2 7d.

£234 28. 7d. 1qr.

Ans. 56191d. 4682s. 2341.

NOTE. The remainder is always of the same name as

the dividend.

2. Bring 30329 farthings into pounds?

3. In 44447 farthings, how many pounds?

Ans. £31 11s. 10d. 1gr.

Ans. £46 5s. 11d. Sqrs.

4. In 59136 farthings, how many pence, shillings, and pounds ? Ans. 14784d. 1232s. £61 12s. 5. In 20160 pence, how many shillings and pounds? Ans. 1680s. or £84.

6 In 900 farthings, how many pounds?

Ans. £0 188. 9d.

7. Bring 74981 half-pence into pounds?

Ans. £156 4s. 21d.

8. In 243648 farthings, how many dollars at 68. each?

Ans. $846.

9. Reduce 13776 pence to guineas, at 28s. per guinea. Ans. 41

10. In 62304 farthings, how many pistoles, at 228. Ans. 59.

sach ?

11. In 7104 three-pences, how many half-johannes, at 48s. ?

Ans. 37.

12. In 38720 farthings, how many French crowns, at

Cs. 8d. ?

Ans. 121.

Reduction Ascending and Descending.

1. MONEY.

1. In 121l. Os. 94d. how many half-pence?

Ans. 58099

2. In 58099 half-pence, how many pounds? Ans. 121. Os. 94d. 3. Bring 23760 half-pence into pounds. Ans. £49 10s. 4. In 214l. 1s. 3d. how many shillings, six-pences, three pences, and farthings? Ans. 4281s. 8562 six

pences, 17125 three-pences, and 205500 farthings. 5. In 1371. how many pence, and English or French crowns at 6s. 8d. each ? Ans. 32880d. 411 crowns. 6. In 249 English half-crowns, how many pence and pounds? Ans. 9960d. and £41 10s. 7. In 346 guineas, at 21s. each, how many shillings, groats and pence? Ans. 7266s. 21798 gr'ts and 87192d. 8. In 48 guineas, at 28s. each, how many 4d. pieces? Ans. 3584

9. In 81 guineas, at 27s. 4d. each how many pounds? Ans. £110 14s. 10. In 24396 pence, how many shlings, pounds and pistoles ? Ans. 2033s. £101 13s. and 92 pistoles.

9s. over.

11. In 252 moidores, at 36s. each, how many guineas at 28s. each ? Ans. $24. 12. In 1680 Dutch guilders, at 2s. 4d. each, how many pistoles at 22s. each ? Ans. 178 pistoles, 4s. 13. Borrowed 1248 English crowns, at 6s. 8d. each, how many pistareens, at 14 d. each will pay the debt? Ans. 6885 pistareens and 74d. 14. In 50l. how many shillings, nine-pences, six-pences, four-pences, and pence, and of each an equal number? 12d.+9d.+6d.+4d.+1d. =32d. and £50 == 12000d.+32=375 Ans.