NOTE. In multiplying by 20, I added in the 15s.-by 12 the 98,-and by 4 the 2 qrs. which must always be done in like cases.

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

Ans. 30329

3. In 461. 5s. 11d. 3qrs. how many farthings?

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

Ans. 1680s. 20160d.

6. In 188. 9d. how many pence and farthings?

Ans. 225d. 900grs.

7. In 3121. 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. 12988. 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. 38720grs.

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 =2|0)468|2 7d.

£234 2s. 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?

and pounds?

Ans. £31 11s. 10d. 1qr.

Ans. £46 5s. 11d. 3qrs.

4. In 59136 farthings, how many pence, shillings, 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 18s. 9d.

7. Bring 74981 half-pence into pounds?

Ans. £156 4s. 21d. 8. In 243648 farthings, how many dollars at 6s. each? Ans. $846.

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

Ans. 41.

Ans. 59,

10. In 62304 farthings, how many pistoles, at 225.

each?

11. I 7104 three pences, how many half-johannes,

Ans. 37.

at 48s.? 12. In 38720 farthings, how many French crowns, at 6s. 8d.?

Ans. 121.

Reduction Ascending and Descending.

1. MONEY.

1. In 1211. Os. 94d. how many half-pence?

Ans. 58099.

2, In 58099 half-pence, how many pounds? Ans. 1211. 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 sixpences, 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. 21793gr'ts, and 87192d. 8. In 48 guineas, at 28s. each, how many 44d, pieces? Ans. 3584.

9. In 81 guineas, at 27s. 4d. each, how many pounds? Ans. £110 14s.

10. In 24396 pence how many shillings, pounds and pistoles? Ans. 2033s. £101 13s. and 92 pistoles.

9s. over.

11. In 252 moidores, at 363. each, how many guineas at 28s. each ? Ans. 324. 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 144d. each, will pay the debt? Ans. 6885 pistareens and 74d. 14. In 50l. how many shillings, nine-pences, six-pences, fourpences, and pence, and of each an equal num. ber? 12d.+9d.+6d.+4d. X1d.=32d. and £50== 12000d.32=375 Ans.

REDUCTION OF FEDERAL MONEY.

1 Reduce 2745 dollars into cents. 2745 dollars

100

Ans. 274500

Here I multiply by 100, the cents in a dollar; but dollars are readily brought into cents by annexing two cyphers, and into mills by annexing three cyphers. Also, any sum in Federal money may be written down as a whole number and expressed in its lowest denomination; for, when dollars and cents are joined together as a whole number, without a separatrix, they will show how many cents the given sum contains; and when dollars, cents, and mills are so joined together, they will show the whole number of mills in the given sum.--Hence, properly speaking, there is no reduction of this money; for cents are readily turned into dollars by cutting off the two right hand figures, and mills by pointing off three figures with a dot; the figures to the left hand of the dot are dollars; and the figures cut off are cents, or cents and mills.

2. In 345 dollars, how many cents and mills?

Ans. 34500 cts. 345000 mills 3. Reduce 48 dols. 78 cts. into cents. Ans. 4878

Ans. 2508

4. Reduce 25 dols. 8 cts. into cents. 5. Reduce 54 dols. 36 cts 5m. into mills, Ans. 54365 6. Reduce 9 dols. 9 cts. 9m. into mills. Ans. 9099

7. Reduce 41925 cents into dollars. 8. Change 4896 cents into dollars. 9. Change 45009 cents into dollars. 10. Bring 4625 mills into dollars.

$cis. Ans. 419 25 48.96 450 08

4 62 5

2. TROY WEIGHT.

1. How many grains in a silver tankard, that weighs

1 lb. 11 oz, 15 pwt.?

&

2. In 246 oz. how many pwts. and grains?

Ans. 4920pwt. 118080grs.

Ans. 8.

3. Bring 46080 grs. into pounds. 4. In 97397 grains of gold how many pounds? Ans. 16lb. 10 oz. 13pwt. 5grs. 5. In 15 ingots of gold, each weighing 9 oz. 5 pwt how many grains? Ans. 66600. 6, In 4 lb. 1 oz, I pwt. of silver, how many tablespoons, weighing 23 pwt. each, and tea spoons, 4 pwt. 6 grs. each can be made, and an equal number of each sort? 23pwt.+4pwt. 6grs.=654grs. the divisor; and 4lb 1 oz. 1pwt. 23544grs. the dividend. Therefore 23544 654-36 Answer.

3. AVOIRDUPOIS WEIGHT.

In 89 cwt. 3 qrs. 14 lb. 12 oz. how many ounces?

4

359 quarters.

[Carried up.