and not a composite number, divide after the manner of long division.

The method of proof is by Compound Multiplication,

Note. If the divisor be a whole number with parts annexed, mul tiply it by the denominator of the fractional part, adding the namerator of the fractional part to the product; then multiply the dividend by the denominator of the fractional part in the divisor, and divide as above.

Examples.

(1.) A gentleman's income is 1260/. 15s, 5d. a year, what is that per day, 365 days being contained in one year? £. 8. d. £. s. d.

(16.) If 60 sheep be sold for 112. 108, what is the value of 1?

(17.) If 112lb. of cheese cost 27. 18s. 8d., what is that per lb.?

(18.) If 17cwt. of lead cost 157. 58. 7 d., what costs:1

(19.) Bought 7 yards of cloth for 168. 4d. what is that per yard?

(20.) If 63 oxen cost 25531. 1s. 6d. what cost 1? (21.) If 66lb. of butter cost 57. 15s. 6d. what costs 1lb.? (22.) If528lb. of tobacco cost 237.13s. what costs llb.? (23.) If a tun, or 252 gallons, of wine cost 60%. what costs 1 gallon?

(24.) A prize of 1000 guineas is to be divided among 150 sailors, what is each man's share, after deducting part for the officers ?

(25.) If 125 ingots of silver, each of an equal weight, weigh 13470z. 11dwt. 14gr. what is the weight of 1 ingot? (26.) If 475cwt. 1qr. 14lb. be the weight of 27hhds. of tobacco, what is the weight of 1?

(27.) Bought 62 pieces of tapestry, containing 237 ells Flem. 2qr. 20, what is the length of 1 piece?

CLASS II.

(28.) A common pasture, containing 54a. 1r. 35p. ; another, containing 54 acres; and a third, containing 39a. 13p.; are to be enclosed and divided among 60 parishioners: what is each man's share, after deducting 21a. 2r. for tithes, admitting the land to be equally good?

(29.) Twenty-six wedges of gold, weighing, with a due proportion of alloy, 34lb. 3oz. 11dwt. 14gr. were brought to the mint to be coined into guineas; what is the weight of each wedge, admitting them equal, and how many gui neas may be made out of the whole, supposing no loss in the metal, and that an oz. will make 33 guineas?

(30.) A person sold a hogshead of sugar, weighing 7cwt. 3qr. 14lb. how much pure sugar was contained in it; thirteen times the weight of the dross and hhd. being equal to the weight of pure sugar?

(31.) If a talent of silver be worth 3577. 11s. 10d. what is the value of a shekel, of which 300 make a talent, and what is the weight of a talent, a shekel weighing 9dwt. 3gr.?

(32.) Camillus the Roman general, after conquering the city of Veii, and other services done to his country, was, through the enmity and avarice of the tribunes, fined 1500 as's, value 4l. 138. 9d. Pray what was the value of an as in English money?

REDUCTION.

Definition. Reduction is the method of reducing numbers from one name, or denomination, to another of the same value.

RULE.

All great names are brought into small by multiplying by as many of the next less as make one of the greater, adding to the product the parts of the less name, if the number to be reduced be a compound one; and all small names are brought into great by dividing by as many of the less as make one of the next greater.

The method of proof is by reversing the question.

Note 1. To multiply a whole number by a whole number with a fraction joined to it. When you have multiplied by the whole number, as in simple multiplication, if the part be,,,, or, &c., divide the multiplicand by 2, 3, 4, 5, or 6, &c.; but, if the numerator of the fractional part be greater than 1, let the multiplicand be multiplied by it, and divide the product by the denominator: add this quotient to the product obtained by multiplying with the whole number.

2. To divide a whole number by a whole number with a fraction joined to it. Multiply the divisor by the denominator of the fractional part, and add the numerator to the product; let this be a new divisor: then multiply the dividend by the denominator of the fractional part for a new dividend, which divide by the new divisor to obtain the true quotient. When the dividend has a fraction joined to it, the rule for obtaining the quotient will be exactly the reverse of this.

(3.) In 19 pounds how many shillings, pence, and farthings?

(4.) In 55 guineas how many shillings, pence, and farthings?

(5.) Reduce 547. 11s. 91d. into farthings.
(6.) Reduce 777. 11s. 10 d. into halfpence,
(7.) Reduce 947. 14s. 8d. into pence.

(8.) Reduce 477. 14s. 4d, into two-pences.

(9.) In 347. 11s. 9d. how many three-pences and pence? (10.) In 477. 19s. 8d. how many groats, pence, and farthings?

(11.) In 1087. 11s. 6d. how many sixpences.

(12.) How many crowns, half-crowns, shillings, sixpences, and pence, are in 541.?

(13.) Reduce 747. 13s. 9d. into shillings, three-pences, and farthings.

(14.) In 11520 farthings how many pence, shillings, and pounds?

(15.) In 17880 pence how many pounds?

(16.) Reduce 100800 farthings into guineas.

(17.) In 50400 halfpence how many pounds?

(18.) In 12050 shillings how many crowns and pounds? (19.) Reduce 311040 pence into groats, shillings, crowns, and pounds.

(20.) In 102/. 16s. 3d. how many pieces of coin, each 78. 34d. in value?

(21.) In 7494 dollars, at 4s. 6d. each, how many groats, shillings, half-crowns, crowns, and pounds?

(22.) In a Jacobus, a Carolus, 5 angels, 3 marks, 5% nobles, 6 testers, and 90 groats, how many farthings?

2. TROY WEIGHT.- -See Table II.

(23.) In 17lb. 5oz. how many grains? Ans. 100320. (24.) In 6720 grains how many ounces? Ans. 14. (25.) In 14 ingots of silver, each 27oz. 10dwt., how many grains?

(26.) In 474 spoons, each weighing 3oz. 10dwt., how many pounds of silver?

(27.) How many pints, each 9oz., may be made out of 17lb. 6oz. 14dwt. of silver?

(28.) A gentleman sent a tankard to his goldsmith, weighing 50oz. 8dwt., and ordered him to make it into tea-spoons, each weighing 1oz. how many had he?

3. APOTHECARIES WEIGHT.

See Table III.

(29.) In 25lb. how many scruples and grains?

72003 144000grs.

Ans.

(30.) In 97920 grains how many ounces and pounds? Ans. 2043 17b.

(31.) In 15 13 13 19 2gr. how many grains? (32.) In 174947 grains how many pounds?

(33.) An apothecary made a compound of 123 13 29 14gr. into troches of 19, of 13, and of 14gr.; and into pills of 11gr. and 13gr. each; he made an equal number of troches and pills: how many of each had he?

4.

AVOIRDUPOIS WEIGHT.-See Table IV.

(34.) In 12 tons of iron how many lb.? Ans. 26880lb. (35.) In 31360lb. of iron how many tons? Ans. 14 tons. (36.) In 375cwt. 2qr. 15lb. of copper how many lb. ? (37.) Reduce 740900oz. into cwts. and tons.

(38.) In 39 bags of hops, each 3cwt. 1qr. 14lb., how many cwts.?

(39.) In 750 fother of lead, each 19cwt., how many cwts.?

(40.) In 135cwt. of raisins, how many parcels, each 90lb.?

(41.) In 570 great pounds of silk how many common? (42.) In 525 common pounds of silk how many great? (43.) How many pounds in 54hhds. of tobacco, each weighing 17 cwt.?

(44.) A grocer weighed out an hhd. of sugar, containing 16cwt. 3qr. 10lb., into parcels of 6lb., of 8lb., of 12lb., of 14lb., and of 28lb., and had an equal number of each; how many of each had he?

5. CLOTH MEASURE. See Table V.

(45.) In 314 yards how many nails? Ans. 5024 nails. (46.) In 576 French ells how many yards? Ans. 864 yards.