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5. Abbreviate as much as possible.

6. Reduce

2

to its lowest terms.

7. Reduce 144 to its lowest terms.

16

8. Reduce 32, to its lowest terms.

9. Reduce

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171

1 to its lowest terms.

10. Reduce to its lowest terms.

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PROBLEM II.

Aus.

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

RULE.

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

EXAMPLES.

What is the value of 4 of a pound sterling?
Numer. 2

20 shillings in a pound.

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

10

9

.12

5)12(4

12

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

Ans. 18s. 5d. 2agrs.

5. Reduce of a shilling to its proper quantity.

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

Ans. 4jd. Ans. 4id. Ans. 9oz.

6. How much is of an hundred weight?

Ans. Syrs. 7lb. 10 oz.

7. What is the value of g of a mile?

& How much is 9. Reduce of an 9289

10. How much is

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of an cwt.?

Ans. Syrs. 3lb. 1oz. 124dr. Ell English to its proper quantity. Aus. 2qrs. sua.

of a hhd, of wine: Aus. 54gal.

11. What is the value of of a day?

1

Ans. 16h. 36min. 55 sec.

PROBLEM III.

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.

EXAMPLES.

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

12

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Ans. $18.

96

2. What part of an hundred weight is 3yrs. 14th.

58

Syrs. 14lb. 98ib. Aus. }=}

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5. What part of a yard is Sqrs. Sua. ?
4. What part of a pound sterling is 15s. 40.
5. What part of a civii year is 3 weeks, 4 days 7

Aus. 72, 73 6. What part of a mile is Cfur. 26po. Syds. 2ft.: fur. po. yd. ft. feet.

6 26 3 24400 Num.
#52:0 Denem.

a mile

Ans.

4400

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

Ans.

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

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

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

DECIMAL FRACTIONS.

A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, fʊ, T852 1857, &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; 725 ,45; 100 1000 ,725, &c.

45

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 thus, ,006, &c.

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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

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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 or 3.

But cyphers placed at the left hand of decimals, decrease their value in a tenfold proportion, by removing them further 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 .899299, &c. if extended to an infinite number of figures, will not equal ,9.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers, whether 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

Thus,

41,653
$6,05

24.009

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Sum, 103,512 which is 103 integers, and 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.

For since dollar is the money unt; 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 decima¦ parts of a dollar: Thus, 11'doliars, & dimes, 5 cents,≈11,65 or 10% $5 dul. &c.

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5. Add the following sums of Dollars together, viz. $12,84565 +7,891 +2,34–14, +6011

150

Aus. R$6,57775, or 856, ádi, Tets. 778 miils. 6. Add the following parts of an acre together, viz. ,569+,25+,654,199

Ans. 1,8599 aeris.

7. Add 72,5+82,071+2,1574+371,442,75

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

Ans. 480,8784

Aus. 5497,28

9. Add 71,467+27,94+16,084+98,009+86,5

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

11. Add ,6+.099+,57+,905+.026 ·

Ans. 300

Ans. 2,9

Ans. 2

12. To 9,999999 add one millionth part of an unit,

and the sum will be 10.

15. Find the sum of

Twenty-five hundredths,

Three hundred and sixty-five thousandths,

Six tenths, and nine millionths,

Answer, 1,15009

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