that higher; to this product add the number, if any, belonging to this lower denomination; we shall thus obtain an equivalent value in the next lower denomination.

II. Proceed in a similar way for all the successive denominations; the last result will be the number sought.

What is Reduction? When is it called Descending? And when Ascending? Repeat the rule for Reduction Descending.

REDUCTION ASCENDING.

81. Let it be required to reverse the last example, that is, to find the number of pounds, shillings, pence, and farthings, in 7003 farthings.

We must obviously perform a reverse operation to that performed under Reduction Descending.

Collecting results, we have 7003 farthings, equivalent

to £7 5s. 10d. 3 far.

EXPLANATION.

First, we divide the number of farthings, 7003, by 4, because 4 farthings make one penny; the quotient is 1750 pence, and 3 farthings remaining.

Secondly, we divide the number of pence, 1750, by 12, because 12 pence make one shilling; the work being performed by Long Division, we get for the quotient 145 shillings, and 10 pence remaining.

Thirdly, we divide the number of shillings, 145, by 20, because 20 shillings make one pound; cutting off the cipher from the right of 20, and the right-hand figure from the dividend, (ART. 30,) we perform the work by Short Division, and obtain the quotient, 7 pounds, and 5 shillings remaining.

We may, therefore, deduce this general

RULE.

I. Divide the given number by as many of its denomination as make one of the next higher; write down the quotient and remainder, if any.

II. Divide the quotient by as many of its denomination as make one of the next higher; write this new quotient and the remainder as before.

III. Proceed in this way through all the denominations to the highest, and the quotient last found, together with the several remainders, if any, will give the value sought.

Repeat the Rule for Reduction Ascending,

EXAMPLES.

1. In £47 5s. 2d. 1 far., how many farthings?

2. In 118567 farthings, how many pounds, shillings,

Hence, 118567 farthings are equal to £123 10s. 1d. 3 far.

3. Reduce £75 to shillings.

4. Reduce 19s. 6d. to pence.

5. Reduce 25s. 3d. 2 far. to farthings.

Ans. 1500s.

Ans. 234d.

Ans. 734 far.

6. In 48926 grains, Troy Weight, how many pounds, ounces, pennyweights, and grains?

Ans. 8lb. 5oz. 18pwt. 14gr.

7. In 3605 pennyweights, how many pounds, ounces, and pennyweights? Ans. 15lb. Ooz. 5pwt. 8. In 1000 ounces, Troy Weight, how many pounds and ounces?

Ans. 83lb. 4oz.

9. In 4lb. 6oz. 13pwt. 5gr. how many grains?

10. In 100lb. 1gr. how many grains?

Ans. 26237gr.

Ans. 576001gr.

11 In 4 tb 53 13 how many drams? Ans. 425 z. 12. In 1000 grains, Apothecaries' Weight, how many ounces, drams, scruples, and grains? Ans. 23 03 29. 13. In 11521 grains, Apothecaries' Weight, how many pounds? Ans. 2 03 03 09 1gr. 14. In 873450 drams, Avoirdupois Weight, how many tons? Ans. 1T. 10cwt. 1qr. 23lb. 14oz. 10dr. 15. Reduce 5cwt. 21lb. 4oz. to ounces.

16. Reduce IT. 1cwt. 1dr. to drams.

17. Reduce 856702 drams to tons.

Ans. 9300 ounces.

Ans. 602113 drams.

Ans. 1T. 9cwt. 3qr. 14lb. 7oz. 14dr.

18. In 4355 inches, how many yards?

Ans. 120yds. 2ft. 11in.

19. In 248 miles, how many inches?

Ans. 15713280 inches.

20. How many inches in 360 degrees of 69 miles to each degree, which is the circumference of the earth, nearly. Ans. 1577664000 inches. 21. In 12121212 barleycorns, how many miles? Ans. 63mi. 6fur. 6rd. Oyd. Ift. 4in. 22. Reduce 12 Ells French to nails. Ans. 288 nails. 23. Reduce 11 Ells English, 3 quarters, to quarters. Ans. 58 quarters.

ber.

24. Reduce 10 Ells Flemish, 3 quarters, 1 nail, to nails.

25. Reduce 4 yards to quarters.

26. In 1000 nails, how many yards?

Ans. 133 nails. Ans. 16 quarters.

Ans. 62yds. 2qr.

27. How many inches in 6 yards, 3 quarters?

Ans. 243 inches.

28. How many square inches in 10 square feet?

Ans. 1440 square inches.

29. In 3 square miles, how many square rods or poles?

Ans. 307200P.

30. In 3 acres, 27 rods, how many square feet?

Ans. 1380304 square feet.

31. In 26025 square feet, how many square roods?

Ans. 2R. 15P. 1614 sq. ft.

32. In 70000 square links, how many square chains?

Ans. 7 square chains.

33. How many square links in 5 acres?

Ans. 500000 square links.

34. In 17 cords of wood, how many cubic feet?

Ans. 2176 cubic feet.

35. In 17 tons of round timber, how many cubic inches? Ans. 1175040 cubic inches.

36. Reduce 17900345 cubic inches to tons of hewn tim

Ans. 207 Tons, 8 cubic feet, 1721 cubic inches.