189. Suppose 100 Ct. 2 qrs. 14 lb. of Beef for Ships Ufe was to be cut up in Pieces of 4lb. 3lb. 2lb. 1lb. and lb. and of each an equal Number, how many Pieces of each would it make? Axsw. 1073 and 3lb. over.

XXX.

Queflions to exercife the Rule of Three, promiscuously fet down.

190. If 1lb. of Pepper coft 1 3d. and 1lb. of Sugar 14d. how much of each can I have for 4l. 1s.? ANSW. 36lb.

191. A. fets out of a certain Town, and goes 9 Miles a Day; 7 Days after B. fets out, and goes 12 Miles a Day, I demand in how many Days B. will overtake A.? ANSW. in 21 Days.

192. If a Ton of Tallow coft 351. and is fold at the Rate of 10 per Ct. Profit, I demand for how much it was fold? ANSW. 381. 10s.

193. At what Rate muft I fell the above Tallow, if I have a mind to gain by 10 Tons as much as one Ton coft? ANSW. as above.

194. Suppofe a Grey-Hound makes 27 Springs whilt a Hare makes 25, and the Springs are alike. Now if the Hare is 50 Springs before the Hound, I would know in how many Springs the Hound will overtake her? ANSW. in 675.

195. If a Ton of Butter coft 371. 10s. I demand at what Rate must I fell it, to gain by 15 Tons as much as one Ton coft? ANSW. 40l.

196. Bought 45 Barrels of Beef, at 21s. per Barrel, among which are 16 Barrels, whereof 4 are

worth

worth but 3 of the reft: I demand how much muft I pay? ANSW.431. Is..

197. In a befieged Fortrefs are 5000 Men provided with fo much Bread, that each Man may have 12 Ounces per Day. Now if 1000 are fent among them, I would know how many Ounces each Man then may have per Day? ANSW. 10 Ounces.

198. If 5 and 3 make 10, how much make 6 and 8? ANSW. 174d.

199. Two Travellers fet out at the fame Time, and from the fame Place, the one goes Eaft 24 Miles a Day, and the other goes Weft 30 Miles a Day, in how many Days, (counting each Day 24 Hours) will they be 2150 Miles afunder? ANsw. 39Ds. 19Hs. 33 Min.

200. How many Guineas of 23s. and Pistoles of 18s. 6d. of each an equal Quantity, can I have for 1861. 15s.? ANSW. 90.

201. If 1 lb. of Sugar which coft 13 d. I demand the Gain per Ct.? Ct.

rod. is fold. for ANSW. 35 per

202. How many Guineas of 23s. each would pay for 10 Pieces of Tapestry, each Piece 25 Yards long, and 4 Yards broad, at 15s. 8d. the fquare Yard? ANSW. 694 Guineas and 18s.

203. If 112 lb. of Tea coft 841. 13s. 4d. at what Rate muft it be fold a lb. to lose by the whole Parcel rol. ANSW. 13. 4d.

204. If I fell Goods at 13 d. the lb. I find to have gained 35 per Cent. I demand what the Goods were bought for? ANSW. rod. a lb.

205. A Gentleman has 510l. 8s. 4d. per Annum, I demand how much he may fpend per Day, if he

H 2

has

has a mind to lay up yearly 100 Guineas at 235. each? ANSW. 21s. 8d.

206. For 20s. I bought 3 Sorts of Wine, the first for 8d. the fecond for 12d. and the third for 16d. the Quart, and I had of each Sort an equal Quantity, I demand how much it was? ANSW.6} Quarts.

207. A. travels 12 Miles a Day, and when he has been gone 15 Days, B. fets out after him; I demand how many Miles in a Day B. muft go to overtake A. in 60 Days? ANSW. 15 Milés.

208. If in 4 Months I spend as much as I gain in 3 Months, how much can I lay up at the Year's end, if I gain every 6 Months 150l.? ANSW. 751.

209. If 840 Eggs are bought at the Rate of 10 a Penny, and 240 more at the Rate of 8 a Penny, and fold all at 18 for 2d. I demand whether Profit or Lofs? ANSw. 6d. Profit.

210. If a Piece of Cloth 30 Yards long, coft 151. how much will a Dutch Ell come to, if 3 Yards are equal to 4 Ells? ANSW. 7s.

211. If 2 lb. of Pepper coft 25d. what will 60 lb. of Cloves come to, if 3 lb. of Cloves are worth 16 lb. of Pepper? ANSW. 161. 1 3s. 4d.

212. How many Dozen of Gloves at 8d. the Pair, will pay for 36 Dozen and 8 Pair of Stockings, at 3s. 6d. the Pair? ANSW. 1923 Dozen.'

213. How much would a Piece of Plank come to of 5 Feet long, 2 Feet broad at one End, and 1 Feet broad at the other End, at 8d. the fquare Foot? ANSW. 15s. gd.

214. I bought a Parcel of Cloth at the Rate of 6s. for every two Yards, of which I fold a certain Quantity at the Rate of 18s. for every 5 Yards, and then I found to have gained as much as 18 Yards did coft. Now I demand how many Yards I fold? ANSW. 90 Yards.

CHAP. IX.

NOTATION and NUMERATION of FRACTIONS.

A

SE C T. I.

FRACTION or broken Number, is a Part or Parts of an Integer, it confifts of two Parts or Numbers fet one over the other, with a Line drawn between them, as 4, 4, 7, 14, &c.

That below the Line is called the Denominator, because it denominates or fhews the Parts any whole Number is divided into, and the Number above the Line is called the Numerator, because it numbers or tells how many of those Parts the Fraction does confift of.

When the Numerator is lefs than the Denominator, the Fraction is lefs than Unity, and this is called a proper Fraction, as 4,,,, &c.

When the Numerator is either equal to, or greater than the Denominator, it is called an improper Fraction, as is equal to 1, or 4 is equal to 1, Compound

H 3

Compound Fractions, or Fractions of Fractions. are fuch as confist of more than one Numerator and one Denominator, as of of, and are always connected by the Word of.

A mixed Number is always written thus, 24, or 51, 77, &c.

С НА Р. X.

Of ABBREVIATION of FRACTIONS.

T

O abbreviate or reduce a Fraction to its least Term, you must find the greatest common Divifor that will divide both the Numerator and Denominator without any Remainder, and the Quotient is a new Fraction of the fame Value, and in its lowest Name or Term.

Rule. Divide the Denominator by the Numerator, and then divide the laft Divifor by the Remainder, and fo continue till nothing remains, then the laft Divifor will be the greatest common Divifor fought, as fuppofe if i was to be reduced, you'll find it to be equal to

ΟΙ

Abbreviate or reduce the following Fractions to

their loweft Name or leaft Term.