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EXAMPLES 1. Reduce 11% to its lowest terms.
(3) (2) 8)1=1= the Answer. 2. Recluse it to its lou est terms. Ans. 3. Recluce is to its lowest terms. Ans. 4. Reduce , to its lowest terms.
plus. 5. Abbreviate as much as possibie. jus. I 6. Reduced to its lowest terms. 7. Reiluce to its lowest terins. 8. Recluce * to its lowest terms. 9.' Reduce 1? Å to its lowest terms.
Hrs. X 10. Reduce to its lowest terms.
PROBLEM II. 'To find the value of a fraction in the koown parts of the intover, as to coin, weight, ineasure, &c.
RÚLE. Multiply the numerator by the common parts of the integer, and divide by the denominator, &c.
201 shillings in a pound. Denom. 3)40(15s. Ad. Ans
'12 2. What is the value of # of a pound sterlingo
Ans. 18s, 5d. 2 grs. 3. Reduce of a shilling to its proper quantity.
. Ans. 4fd. 4. What is the value of of a shilling! Ans. 4jc. 5. What is value of 1 of a pound troy? Ans. 90%.
6. How much is it of an hundred weight?
Ans. Syrs. Ib. 10, 02. 7. What is the value of of a mile :
. Ins. 6fur. 26po. list. & Ilow much is f of an cwt..
Ans. Syrs. 3lb. Inz. 12: dr. 9. Reduce of an El English to its proper quantity
His. 2qrs. öfnu. 10. Ilow much is of a hhd. of wine: fls. 54 gol. 11. What is the value of of a day:
tus. loh. Soinin. 35, see.
PROBLEM III. To reduce any given quisorite to the fraction of any greater denomi:iation if the same kind.
RILLE Reduce the given quantity to the lowest terin inention. ed for a numerator; then reduce the integral part to the sanie term, for a denominator; which will be the frac. tion required.
' .XAMPI.ES. 1. Reduce 158. Gl. 24rs. to the fraction of a poun...
20 Integral part - 13 6 2 given suin.
960 Denominator. 050) Num. Ans.
. 2. What part of an hundred, weight is juris. 1416..
Syrs. 1.11b.=98ib. us. = S. What part of a varil is öyrs. Sna.? ..,s. is 4. What part of a pagini sterling is 135, 411.: tosis 5. Flat part of a civii year is 3 weeks, tavsi
fusteris 6. What part of a mile is Clur. 26po. :syols. 2.: jer. pr. m. ji. Art. 626 2 4400 Num.
a mile =52:0 Denn. Ans. * 7. Reduce 70%. 4pwt. to the fraction of a pound truy.
Ans. 3. What part of an acre is 2 roods, 20 poles ? Ans.
9. Reduce 54 gallons to the fraction of a hogshead of wine.
Ans. of 10. What part of a hogshead is 9 gallons ? Aus. 11. What part of a pound troy is 10uz. 10pwt. 10yrs. ?
DECIMAL FRACTIONS. A Decimal Fraction is that whose denominator is an unit, with a cypher, or cypliers annexed to it, Thus, fu, 187. 1867, &c. &c.
The integer is always divided either into 10, 100, 1000, &c. equal parts; consequently the denominator of the fraction will always, be cit!er 10, 100, 1000, or 10000,&c. which being understoul, need not be expressed; for the true value of the fraction may be expressed by writing the numerator only with a point before it on the left hand thus, is, is written ,5; 146 945; 17025, &c.
But if the numerator has not so many places as the denominator has copliers, put so many cyphers before it, viz. at the left hand, as will make up the defect; so write Tóm thus, ,1.5 ; ani 100 thus, ,006, &c. .
NOTE. The point prefisel is called the separatrix.
Decimals are counted from the left towards the right hand, and each figure takes its value by its distince fiorn the unit's place; if it be in the first place after units, (or separating point) it signifies terths; is in the second, hundredths, &c. decreasing in each place in a tenfold proportion, as in the following
Cypliers placed at the rig!ıt hand of a decimal fraction do not alter its value, since every significant figure con timies to possess the sa:ne place : $0 ,5 ,50 and 950.) are all the saine value, and equal to sor 1.
But eplers placed at the left hand of decimals, de. crease their value in a tentold proportion, by removing olem fuit vifion time fecimal point. Thus, 55 .05 .005, &c. are five terith parts, five hundredth parts, live thousandth parts, &c. respectively. It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure : for in. stance, a fraction beginning with any figure less than ,9 such as .899299, &c. is extended to an infi'rite number af fynres, will not equal ,9.
ADDITION OF DECIMALS.
RUI.P.. 1. Place the numbers, whether mixed or pure decimals, uncler each other, according to the value of their places.
2. Find their suin as in whole numbers, and point off $0) many places for the decimals, its are equal to the great. cat number suf decimal parts in any of the given numbers.
Sum, 109,512 which is 193 intrgers, and the parts of an unit. Or, it is 10.3 muits, and 3 tenth parts, I hun. drreth part, ani 2 thmusandth parts of an unit, er 1.
llence we may observe, that decimals, and FEDERAL Moxky, are subject to one, and the same law of uotation, and consyusitly of operation.
For since. dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousandth part of a collar, or unit, it is rijstorld that ano i nber of Gullars, dimes, cents and millo, is simply the osporession of dillars, and closimai part- of a ...lar: Tinus, 11 dollars, u dimes, 5 cents, <11,1ij er 1116 dol. &c. . Adil the following miseg numbers together (9)