the second product, and repeat the process till all the denominations are multiplied; and thus the required product will be determined.

Ex. Multiply 35gals. 3qts. 1 pt. by 7.

gals. 251.0.1 the prod: qts. 3.1 pt: gals. 6.0 qt:

and this may be proved by reducing 35gals. 3qts. 1 pt. to pints, multiplying the result by 7, and then reducing the product to gallons, &c.

63. When the multiplier exceeds 12, this process would be laborious, and it is usual to extend what was said in (35) to such cases.

Ex. To find the product of 3 days. 18hrs. 45min. by 47, we may use either of the following operations:

da. 177. 17. 15 the prod. da. 177. 17. 15 the prod.

If however this method require many factors to make up the multiplier, it is best to reduce the multiplicand to the lowest denomination contained in it, to multiply this result by the multiplier, and then to reduce the product back again.

Examples for Practice.

(1) Multiply £358. 4s. 7d. by 5 and 9.
Answers: £1791. 3s. 2ąd., and £3224. 1s. 9åd.

(2) Required the products of 49cwt. 3qrs. 15lbs. by 7 and 11.

Answers: 349cwt. 21 lbs., and 548 cwt. 2qrs. 25lbs.

(3) Find the products of 154yds. 2ft. 10in. by 6 and 10.

Answers: 929 yds. 2ft., and 1549 yds. 1 ft. 4 in. (4) Multiply 58 gals. 3 qts. 1 pt. by 8 and 12. Answers: 471 gals., and 706 gals. 2qts. (5) Multiply 42 wks. 5 days. 23 hrs. 42 min. by 3 and 4.

Answers: 128 wks. 3 days. 23 hrs. 6 min., and 171 wks. 2 days. 22 hrs. 48 min.

(6) Multiply £125. 15s. 9d. by 28 and 45. Answers: £3522. 1s. 7d., and £5660. 9s. 8d. (7) Multiply £53. 18s. 7d. by 51 and 83. Answers: £2750. 10s. 11 d., and £4476. 7s. 7d. (8) Multiply 17 cwt. 2qrs. 19lbs. 5oz. by 36 and 73. Answers: 636cwt. 23lbs. 4oz., and 1290cwt. 9lbs.

13oz.

(9) Multiply 13 lea. 2mi. 6fur. 25 po. by 42 and 97. Answers: 585 lea. 1 mi. 6 fur. 10 po., and 1352 lea. 1 mi. 2fur. 25po.

111.

(10) Multiply 15 qrs. 6bush. 3pks. 1 gal. by 54 and

1 gal.

Answers: 856qrs. 3 bush. 1pk., and 1760 qrs. 3 bush.

(11) Multiply 43 days. 18 hrs. 45 min. by 77 and 147. Answers: 3371 days. 3hrs. 45 min., and 6435 days. 20hrs. 15min.

(12) Multiply 57°. 7'. 45′′ by 4 and 6.

Answers: 228°. 31', and 342°. 46'. 30".

(13) What is the price of 72 reams of paper, at 13s. 8d. a ream?

Answer: £49. 4s.

(14) Find the price of 120 ounces of silver, at 5s. 3 d. an ounce.

Answer: £31. 17s. 6d.

(15) Find the number of yards in 40 pieces of cloth, each containing 42 yds. 2qrs. 2nls.

Answer: 1705 yards.

(16) Required the price of 279cwt. at £3. 7s. 10d.

a cwt.

Answer: £946. 17s. 1d.

(17) If I spend £2. 7s. 1d. a day, how much is that in a year of 365 days?

Answer: £860. Os. 7d.

(18) What sum will purchase an estate of 2120 acres, when the price of each acre is £32. 5s. 6d.? Answer: £68423.

(19) If each of 114 persons receive £1. 18s. 6d., what is received by them all?

Answer: £219. 13s. 9d.

(20) How many pounds of silver are there in a half-dozen of dishes, each weighing 51 oz. 10dwts., and a dozen of plates each weighing 15oz. 15dwts. 22 grs.?

Answer: 41lbs. 6oz. 11dwts.

(21) If a wheel of 5 yds. 1 ft. 6in. in circumference make 64640 revolutions, what space will it pass over? Answer: 202 miles.

IV. COMPOUND DIVISION.

RULE. Having placed the divisor and dividend as in integers, find how often the divisor is contained in the highest denomination of the dividend, put down the quotient and reduce the remainder, if any, to the next inferior denomination, adding to it the number of that denomination in the dividend, and repeat the division: proceed thus through all the denominations, and the entire quotient will be obtained.

Ex. Divide 41 wks. 6days. 19hrs. by 11.

and the operation may be proved by that of multiplication.

64. When the divisor is greater than 12, the process may be conducted as in (42), if it be a composite number, and by long division, if it be incomposite.

Ex. To divide £1478. 13s. 8d. into 77 equal portions, we may use either of the subjoined methods:

The division may also be effected by reductions analogous to those alluded to in Multiplication.

Examples for Practice.

(1) Divide £189. 88. 4d. by 5 and 8.

Answers: £37. 17s. 8d., and £23. 13s. 6d.

(2) Required the quotients of 182 cwt. 8qrs. 7lbs. by 7 and 9.

Answers: 26cwt. 13lbs., and 20cwt. 1qr. 7lbs.

(3) Divide 1658 yds. 1ft. by 6 and 10.

Answers: 276 yds. 1 ft. 2in., and 165 yds. 2ft. 6in.

(4) Find the quotients of 238 ac. 2ro. 32 po. by 8

and 11.

Answers: 29ac. 3ro. 14 po., and 21 ac. 2 ro. 32 po. (5) Divide 13 wks. 5 days. 19 hrs. 30 min. by 3 and 4. Answers: 4wks. 4days. 6hrs. 30 min., and 3 wks. 3 days. 4hrs. 52 min. 30 sec..

(6) Divide £1738. 12s. 7d. by 18, and £1279. 13s. 8&d. by 23.

Answers: £96. 11s. 9 d., and £55. 12s. 9d.

(7) Divide 425 tons. 15 cwt. 2qrs. 12lbs. by 27, and 2374cwt. 1qr. 12lbs. 12 oz. by 38.

Answers: 15tons. 15cwt. 1qr. 16lbs., and 62 cwt. 1qr. 26lbs. 2oz.

(8) Find the quotient of 1361 mi. 4fur. 28 po. by 28, and of 3179lea. 1 mi. 5fur. 16po. by 46.

Answers: 48 mi. 5 fur. 1po., and 69lea. 2fur. 36 po. (9) Divide 739qrs. 4 bush. 2 pks. 1 gal. into 11 equal portions.

Answer: 67 qrs. 1 bush. 3pks. 1 gal.

(10) What is the twelfth part of 22 wks. 4 days. 20hrs. 43 min. 24sec.?

Answer: 1wk. 6days. 5hrs. 43 min. 37 sec.

(11) If 41 cwt. cost £52. 10s. 7d., what is the price of a cwt.?

Answer: £1. 5s. 7d.

(12) What will be the price of 1lb., when 1cwt. costs £137. 18s.?

Answer: £1. 4s. 7d.

(13) If a soldier's pay for a year of 365 days be £9. 2s. 6d., how much is that for a day?

Answer: 6d.

(14) If a person's yearly income be £65. 12s. 6d., and he lay by £20. a year, how much does he spend each day?

Answer: 2s. 6d.

(15) If 145 sheep cost £169. 5s. 9d., what is the price of a score at the same rate?

Answer: £23. 7s.