CASE

When different denominations are divided, by any number not exceeding 12.

RULE.

Divide the highest denomination first. The remainder, if any, must be brought to the next lower denomination; and, after adding it to the next lower denomination, divide the sum by your divisor and proceed thus, with all the denominations, till the work is finished.

£.

4 Men spent at a tavern, 2, 16, 4; what must each pay?

Ans. 14s. 1d.

If 5 bushels of corn cost 1,

bushel?

what is that per Ans. 4s. 6d. 2gr.

CASE 2.

When the divisor is the product of two, or more numbers multiplied together, as they are found in the table.

RULE.

Divide, first, by one of those numbers, and the quotient by the other. The last quotient will be the answer.

Questions resulting from the preceding Rules.

1. What is the sum of 47+29+76+34+98?·

2. What is the sum of 24789-19867?

3. There is an orchard, in which grow 40 trees, and each tree hath ten limbs, and each limb has 20 branches, and on each branch there are 30 apples; how many apples are there in all? Ans. 240,000 apples.

4. 436 men take a prize worth $1569 what must each receive? 5. What is the sum of 247. 138. 6d. 2qr.+981. 188. 7d.+361. 14s. 6d. 1 qr.+100l. 17s.?

6. What is the product of 4s. 7d. 3gr. X6?

7. What is the quotient of 9. 6s. 8d. 3qr÷8?

8. A feast for 36 men cost 197. 17s. 9d. 3qr. what must each man pay?

9. 18 men took a prize worth 4631. 18s. 6d. what is each man's share!

10. What are the contents of a floor 18 feet, 10 inches and 3 quarters long, and 12 feet 8 inches and 2 quarters broad ? 11. What is the product of 4s. 6d. X2s. 8d.?

£.

3. d. gr.

12.467 +426, 7, 6, 2

198, 19, 11, 3

15. 163 men took a prize worth 7231. 16s. 9d. of which the captain had four shares; the first lieutenant, three; the second lieutenant, two; what was the share of each officer, and each private?

16. A tract of land, containing 14378a. 3r. 37rd. 9ft. 137in. is to be equally divided among 236 men, what is each man's share?

17. A West India cargo of 69T. 2hhds. 57gal. Sqt. 1pt. of molasses, is to be equally divided among 27 men, what is each man's share!

846, 2, 3

T. cwt. qr. lb. oz. dr. ÷ 76, 18, 3, 25, 14, 13 by 37

REDUCTION.

By Reduction we change money, measures, weights, &c. our of one denomination into another, and yet retaining the same value. Of this there are two kinds, viz. Reduction Descending, and Reduction Ascending.

1. Reduction Descending is performed by multiplication. 2. Reduction Ascending is performed by division.

REDUCTION DESCENDING.

RULE.

Multiply the highest denomination, by the number of the next less which makes one of that highest; be careful to add to your product the figures of your next less denomination, and proceed in this manner till you have finished the work.

OF MONEY.

1. In 861. 14s. 6d. 2qr. How many farthings?

& d. gr.

X 4 farthings in a penny.

83258farthings; the Answer.

In multiplying by 20, I added the 148. In X12, I added the 64. Inx4, I added 2gr. Which must always be done in similar

cases.

To prove questions in this rule, change the order of them. The foregoing question will become-In 83258 farthings, How many pounds?

4)83258

12)20814d, 2qr.

2)0)173(48, 6d.

Ang 861. 14s. 6d. 2qr. proof.

2. In 3977. 16s. 7d. Sqr. How many farthings? Ans. 381919. 3. In 156 dollars at 6s. How many farthings? Ans. 44928. 4. In 46l. 12s. 8d. How many half penoe? Ans. 22384.

5. In 48 guineas at 28s. How many farthings? Ans. 64512. 6. In 68/. How many groats, or fourpences? Ans.. 4080. 7. In 1796lb. Troy Weight, how many grains?

8. In 4678 oz. Troy Weight, how many grains?

9. In 2347T. 15cwt. 1qr. 18lb. 9oz. 14drs. How many drams? 10. Anaximander, the Grecian philosopher, lived about 600 years prior to the birth of Christ, How many seconds since, to the year 1806?

11. Gen. Washington died, December 14, 1799, How many seconds since, to December 14, 1806?

12. American Independence was declared, July 4, 1776, How many minutes since, to July 4, 1806, and hours, and days, and weeks, and months, and years?

13. In 7296 miles, How many inches?

14. In 3476 acres, How many inches, feet, rods, and roods? 15. In a pile of wood 37 feet long and 14 feet high, How many cords?

16. In 86hhds. brandy, each containing 146 gals. How many gills?

REDUCTION ASCENDING.

By Reduction Ascending, less denominations are brought into higher.

RULE.

First, divide the sum by that number, which it takes to make one in the next higher denomination; secondly, divide the greatest, which it takes in that denomination, to make one in the next higher; and proceed in the same manner, through all the denominations, till the work be done.

EXAMPLES.

1. In 86435 farthings, How many pence, shillings, and pounds?

Farthings in a penny 4)86435

Pence in a shilling

12)21608d. 3qr.

Shillings in a pound 2)0) 180(0s. 8d.

£90, Os. 8d. 3qr. Ans.