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EXAMPLES.

1. Reduce to its lowest terms. (3) (2)

the Answer.

16

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3. Reduce

·8) 148
2. Reduce to its lowest terms.
16 to its lowest terms.
to its lowest terms.
as much as possible.
to its lowest terms.

278
45

4. Reduce
5. Abbreviate
6. Reduce

216

7. Reduce 144 to its lowest terms. 8. Reduce 32, to its lowest terms. 9. Reduce 1 to its lowest terms. 10. Reduce 1 to its lowest terms.

276

180 6912

PROBLEM 11.

To find the value of a fraction in the known parts of the integer, as to coin, weight. measure, &c. RULE.

EXAMPLES.

What is the value of of a pound sterling?
Numer. 2

20 shillings in a pound.

Denom. 3)40(15s. 4d. Ans.

3

Multiply the numerator by the common parts of the integer, and divide by the denominator, &c.

10

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Ans. Aus. i

Ans.

Aus.

Aus.

Ans.

Aus.

Ans.

Aus.

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4. What is the value of of a shilling? 5. What is value of 1 of a pound troy?

5)12(4

2. What is the value of of a pound sterling Ans. 18s. 5d. 27grs. 5. Reduce of a shilling to its proper quantity. Ans. 44d. Ans. 4id. Ans. 9oz.

6. How much is of an hundred weight?

7. What is the value of

& Ilow much is of an cwt.

980

Ans. Syrs. 3lb. 1oz. 124dr. 9. Reduce of an Ell English to its proper quantity. Aus. 2qrs. Sua. 10. How much is of a hhd, of wine: Ans, 54gal. 11. What is the value of of a day?

Ans. 16h. 36min. 55 sec. PROBLEM III.

Ans. Syrs. 7lb. 10 oz. of a mile?

Ans. 6fur. 26po. 11ft.

To reduce any given quantity to the fraction of any greater denomination of the same kind.

RULE.

Reduce the given quantity to the lowest term mentioned for a numerator; then reduce the integral part to the same term, for a denominator; which will be the fraç tion required.

240

EXAMPLES.

1. Reduce 15s. Gl. 2yrs. to the fraction of a pound. 20 Integral part 13 6 2 given sum,

12

12

162

4

960 Denominator.

650 Num.

Ans. 18. 2. What part of an hundred, weight is 3yrs. Syrs. 14lb.=981b. Jus.

14lb.

58

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Aus. 1

Aus. Z

5. What part of a yard is Sqrs. Sua. ? 4. What part of a pound sterling is 13s. 40. 5. What part of a civil year is 3 weeks, 4 days ? Aus. 245 = 13

6. What part of a mile is Cfur. 26po. Syds. 2ft. fur. po. yd. ft. feet.

6 26 3 24400 Num.

a mile =52-0 Denom.

Ans. 328 7. Reduce 7oz. 4pwt. to the fraction of a pound troy.

Ans.

What part of an acre is 2 roods, 20 poles? Ans.

9. Reduce 54 gallons to the fraction of a hogshead of Ans.

wine.

10. What part of a hogshead is 9 gallons? Aus. 11. What part of a pound troy is 10oz. 10pwt. 10grs. P Ans. $95

DECIMAL FRACTIONS.

A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, fʊ, Top 10809 &c. &c. ,

45

The integer is always divided either into 10, 100, 1000, &c. equal parts; consequently the denominator of the fraction will always, be either 10, 100, 1000, or 10000, &c. which being understood, 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 written,5; 5,45; 7725,725, &c.

But if the numerator has not so many places as the denominator has cyphers, put so many cyphers before it, viz. at the left hand, as will make up the defect; so write Tổ thus,,05; and 756 thus, ,006, &c.

NOTE. The point prefixed is called the separatrix. Decimals are counted from the left towards the right hand, and each figure takes its value by its distance from the unit's place; if it be in the first place after units, (or separating point) it signifies tenths; if in the second, hundredths, &c. decreasing in each place in a tenfold proportion, as in the following

NUMERATION TABLE.

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Cyphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure conties to possess the same place: so,5,50 and,509 are all the same value, and equal to ¿1⁄2 or 3.

But cyphers placed at the left hand of decimals, de. crease their value in a tenfold proportion, by removing dem furt ser from the decimal point. Thus, 5,05,005, &c. are five tenth parts, five hundredth parts, five thou sandth 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 instance, a fraction beginning with any figure less than ,9 such as .899229, &c. if extended to an infinite number of figures, will not equal,9.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers, wnether mixed or pure decimals, under each other, according to the value of their places. 2. Find their sum as in whole numbers, and point off so many places for the decimals, as are equal to the greatest number of decimal parts in any of the given numbers.

EXAMPLES.

1. Find the sum of 41,653+56,05 +24,009+1,6

41,653

$6,05
24.009

Thus,

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Sum, 103,512 which is 103 integers, and 313 parts of an unit. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of an unit, or 1.

Hence we may observe, that decimals, and FEDERAL MONEY, are subject to one, and the same law of notation, and consequently of operation.

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For since dollar is the money umt ; and a dime being the tenth, a cent the hundredth, and a mill the thousandth part of a dollar, or unit, it is evident that any number of dollars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar: "Thus, 11'doliars, & dimes, 5 cents,≈14,65 or 11,5% dol. &c.

2. Add the following mixed numbers together (4) Dollars.

48,9108

1.8191

5,1030

7012

(2)

Yards.

46,23456

24.90400

17.00411

5,01111

(3)

Ounces.

12,5456

7,891

2,54

5,6

5. Add the following sums of Dollars together, viz. $12.84565 47,891 +2,54➡1$, +,601]

150

Aus. R$6,57775, or 856, ádí. Tets. 7736 miils. 6. Add the following parts of an acre together, viz. „:569+,25+,654+,199

Ans. 1,8559 acres.

7. Add 72,5+52,071+2,1574+371,442,75

Ans. 480,8784

8. Add 30,07+200,71+59,4+3207,1

Ans. 5497,28

9. Add 71,46+27,94+16,084+98,009+86.5

Ans. 300

10. Add ,7509+,0074+,69+,8408+,6109

Ans. 2,9
Ans. 2

11. Add ,6+099+,57+,905+.026

12. To 9,999999 add one millionth part of an unit, and the sum wilt be 10.

15. Find the sum of

Twenty-five hundredths,

Three hundred and sixty-five thousandths,
Six tenths, and nine millionths,

Answer, 1,215000

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