26. If the Federal Debt, which is 42 million dollars, be equally divided between the 13 States: What will be the share of each? Ans. 3230769 dollars. 27. If 9000 men march in a column of 750 deep: How many march abreast?

12 Ans. 28. What number, deducted from the 32d part of 3072, will leave the 96th part of the same?

64 Ans.

29. What number is that, which, multiplied by 3589, will pro-duce 92050672 ? 25648 Ans. 30. Suppose the quotient arising from the division of two numbers to be 5379, the divisor 37625: What is the dividend, if the remainder came out 9357? 202394232 Ans.

31. There is a certain number, which being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 being subtracted, and 30 added to the remainder, the half sum shall make 35: Can you tell me the number?

700 Ans.

32. A sheepfold was robbed three nights successively; the first night, half the sheep were stolen, and half a sheep more; the second half the remainder were lost, and half a sheep more; the last night they took half what were left and half a sheep more ; by which time they were reduced to 30: How many were there at first?

Begio with 30, and, reckoning back from the last night to the first, you will find that 31 were stolen the 3d night, 62 the 2d, and 124 the first. Ans. 247.

33. Two boys, A and B, had 850 chesnuts between them; but A had 150 more than B: How many had each. 850-2 425 half sum, and 150-275 half diff.; then 425-75 500 A's, and 425-75-350 B's.

34. What number added to the 27th part of 6615, will make 570 ?

325 Ans

REDUCTION

TEACHES to bring numbers of one denomination to others of different denominations, retaining the same value.

It is of two sorts, viz. Descending and Ascending.

REDUCTION DESCENDING

Teaches to change numbers from a higher to a lower denomi nation. It is performed by multiplication.

RULE.*

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

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

Note. From this rule and Case VI. of Simple Multiplication, it appears, that Federal Money is reduced from higher to lower denominations by annexing as many cyphers as there are places from the denomination given, to that required; or, if the given sum be of different denominations, by annexing the several figures of all the denominations in their order, and continuing with cyphers, (if necessary,) to the denomination required; or, what amounts to the same thing, by reading the whole number from the left to the required denomination, as one number in the required denomination.

EXAMPLES.

1. In 3 eagles 2 dollars, how many mills? 2. In 91 dollars 75 cents, how many cents? 3. In 50 eagles, how many dollars?

Ans. 32000 m.

Ans. 9175 c.

4. In 44 dollars, 1 cent, 4 mills, how many mills? 5. In 9 dollars, 31 cents, 7 mills, how many mills? 6. How many cents in 39 dollars 5 cents?

7. In 28 dollars 17 cents, 5 mills, how many mills? 8. In £27 15s. 9d. 2qrs. how many farthings?

Ans. 500 D

Note. In multiplying by 20, I added in the 15s. by 12, the 98. and by 4, the 2qrs. which must always be done in like cases. To prove the above question, change the order of it, and it will stand thus: In 26678 farthings how many pounds?

The reason of this Rule is exceedingly obvious; for pounds are brought into shillings by multiplying them by 20; shillings into pence by multiplying them by 12; and pence into farthings by multiplying them by 4; and the contrary by division; and this will be true in the reduction of numbers consisting of any denomination whatever. The rule for Reduction ascending is simply the reverse of this, and equally evident.

4)26678

12)6669 2qrs.

2/0)55/5 9 d.

Answer, £27 15 9 2

Ans. 35177.

Ans. 91751.

Ans. 345358.

Ans. 9744.

9. In £36 12s. 10d. 1qr. how many farthings? 10. In £95 11s. 5d. 3qrs. how many farthings? 11. In £719 9s. 11d. how many half pence? 12. In 29 guineas, at 28s. how many pence? 13. In 37 pistoles, at 22s. how many shillings, pence, and farthings? Ans. 814s. 9768d. 39072qrs. 14. In 49 half johannes, at 48s. how many sixpences? Ans. 4704. 15. In 473 French crowns, at 6s. 8d. how many threepences? Ans. 12613. 16. In 53 moidores, at 36s. how many shillings, pence and farthings? Ans. 1908s. 22896d. 91584qrs. 17. In £29 how many groats, threepences, pence, and farthings? Ans. 1740 groats, 2320 threepences, 6960d. 27840qrs. 18 Reduce 47 guineas and one fourth of a guinea into shillings, sixpences, groats, threepences, twopences, pence and farthings. Ans. 1323 shillings, 2046 sixpences, 3969 groats, 5292 threepences, 7938 twopences, 15876 pence, and 63504 qrs.

REDUCTION ASCENDING

Teaches to change.numbers from a lower to a higher denomination. It is performed by division.

RULE.

Divide the lowest denomination given, by so many of that name, as make one of the next higher, and thus continue till you have brought it into that denomination which your question requires.

Note. From this rule and the note under Case II. of Simple Division, it appears, that Federal Money is reduced from lower to higher denominations by cutting off as many places as the given denomination stands to the right of that required; the figures cut off belonging to their respective denominations.

EXAMPLES,

1. How many eagles in 42000 mills?
2. In 3175 cents, how many dollars?
3. In 500 dollars how many Eagles?
4. In 4414 mills, how many dimes?
5. In 9317 mills, how many dollars?
6. How many dollars in 28175 mills?

Ans. 4 E $2 Ans. $31 75 c. Ans. 50

7. In 547325 farthings, how many pence, shillings, and pounds }

Farthings in a penny

4)547325

Pence in a shilling = 12)136831 1 qr.

Shillings in a pound = 20)11402 78.

£570 2s. 7d. 1 qr.

Ans. 136831d. 11402s. and £570.

Note. The remainder is always of the same name as the dividend. 8. Bring 35177 farthings into pounds.

9. Bring 91751 farthings into pence, &c.

10. Bring 345358 half pence into pence, shillings, and pounds. 11. Reduce 9744 pence to guineas, at 28s. per guinea.

12. In 39072 farthings, how many pistoles, at 22s.

13. In 4704 sixpences, how many half johannes?

14. In 12613 threepences, how many French crowns, at 6s. 8d.? 15. In 91584 farthings, how many moidores, at 36s. ?

16. In 27840 farthings, how many pence, threepences, groats, shillings and pounds?

17. In 63504 farthings, how many pence, twopences, threepences, groats, sixpences, shillings and guineas?

Note. The preceding questions may serve as proofs to those in Reduction descending.

REDUCTION DESCENDING AND ASCENDING.

1. MONEY.

1. In £97 how many pence and English or French crowns, at 6s. 8d.? Ans. 23280d. and 291 crowns. 2. In 947 English crowns, at 6s. 8d. how many shillings and English guineas? Ans. 6313s. 4d. and 225 guineas 13s. 4d. 3. In 519 English half crowns, how many pence and pounds? Ans. 20760d. and £ 86 10s. 4. In 1259 groats, how many farthings, pence, shillings, and guineas? Ans. 20144qrs. 5036d. 419s. 8d. and 14 guin 27s. 8d. 5. In 75 pistoles, how many pounds? Ans. £82 10s. 6. In 735 French crowns, how many shillings and French guineas, at 26s. 8d.? Ans. 4900s. and 183 guin. 24s. 7. In 5793 pence, how many farthings, pounds, and pistoles? Ans. 23172qrs. £ 24 2s. 9d. and 21 pistoles, 20s. 9d. 8. In £99, how many shillings, and half johannes, at 48s.? Ans. 1980s. and 41 half joes. 12s. Ans. 127 guin. 24s. Ans. 191 moid. 24s.

9. In £ 179, how many guineas? 10. In £345 how many moidores? 11. In 59 half joes, 37 moidores, 45 guineas, 63 pistoles, 24 English crowns, and 19 dollars; how many pounds, half joes, moidores. guineas, pistoles, English crowns, dollars, shillings, peace, and farthings?

Ans. £354 43. 147 half joes, 28s. 196 moidores, 28s. 253 guineas, 322 pistoles, 1062 English crowns, 4s. 1180 dollars, 4s, 7824 shillings, 85003d. and 310032qrs.

When it is required to know how many sorts of coin, of different values, and of equal number, are contained in any number of another kind; reduce the several sorts of coin into the lowest denomination mentioned, and add them together for a divisor; then reduce the money given, into the same denomination, for a dividend, and the quotient, arising from the division, will be the number required.

Note. Observe the same direction in weights and measures. 1. In 275 half johannes, how many moidores, guineas, pistoles. dollars, shillings and sixpences, of each the like number?

A moidore is 36s.

275 half joes.

that is

72 sixpences.

48 shil. in a johan.

One shilling has

2 do. 187)26400(141 of each and 33 sixp. or
1 do.
16s. 6d. over, the answer.

Divisor 187 sixpences.

2. A Gentleman distributed £37 10s. between 4 poor persons, in the following manner, viz. that as often as the first had 20s. the second should have 15s. the third, 10s. and the fourth, 5s. What did each person receive? Ans. The first man £15, second

£11 5s. third £7 10s. fourth £3 15s.

2. TROY WEIGHT.

1. How many grs. in a silver bowl, that weighs 3lb. 10 oz. 13

pwt.?

Proof. 24)22368 grains, answer.

20)932

12)46—12 pwt.

3-10 oz.