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10. Add # of a ton to % of an hundred weight, 2510. a qr.

Ans. 12cwt. gr. 7t. 1302. U drs. 11. Suppose I have f of a ship worth $6000, and that I buy another person's share of her, which is bei what part of her belongs to me then, and what is it worth?

Ans. I have it, and it is worth $4125.

SUBTRACTION OF VULGAR FRACTIONS.

Rule.-Prepare the fractions as in addition, and the difference of the numerators written above the common denominator, will give the differepce of the fractions required.

Note 1.-In subtracting 'mixed numbers, when the fraction in the subtrahend is greater than that in the minuend, subtract the numerator of the subtrahend from the denominator, and to the difference add the numerator of the minuend, and carry one to the integer in the subtrahend. If the minuend contain no fraction, proceed in the same way, there being then nothing to add to the difference.

NOTE 2. In fractions of money, weights, &c. you may find the value of each of the given fractions, by Case 7, in Reduction, and then subtract them in their proper terms.

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9. Suppose I own of a farm, which is worth $3600, and that I sell of my share ; what part of it have I left, and what is it worth?

Ans. 2; and.worth $750.

MULTIPLICATION OF VULGAR FRACTIONS.

Rule.-Reduce compound fractions to single ones, mixed numbers to improper fractions, and those of different integers to the same; then multiply all the numerators together for the numerator, and multiply all the denominators together for the denominator, of the product required. But always, before multiplying, cancel equal numerators and denominators, and divide those that are divisible by the same numbers, both here and in division, agreeably to what is seen in Note 8 of Case 1, in Reduction, page 150, and in Case 5, page 154.

Nore.- A fraction is best multiplied by an integer, by dividing the denominator by it, if possible, but if that cannot be done, multiply the numerator by it.

. EXAMPLES. 1. Required the continued product of 2}, }, { of it and 2.

1x5
21={, of =- =ig, and 2=4.

3x6

5x1x5x2
Then {x}X*X= ---=* Ans. -

2x8x18x1 2. Multiply by ir

Ans. 3. Multiply 41 by $.

Ans. 4. Multiply of 8, hy } of 5.

Ans. 21. 5. Multiply 73 by 91.

Ans. 698, 6. Multiply 4], of 4, and 184 continually together.

Ans. 978. 7. What is the product of 5, 7, off, and 44?"

Ans. 2:

DIVISION OF VULGAR FRACTIONS.

Rule.- Prepare the fractions as in Multiplication; then invert the divisor, and proceed as in Multiplication, The products will be the quotient required.

Note-A fraction is divided by an integer, by dividing the numerator by it, if possible, but if it will not exactly divide, then multiply the denominator by it.

'EXAMPLES. 1. Divide L of. 19 by f of .

1x19 19
.of 19=- =-, and soff= ;

5x 1 5

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x =- =&=7 the quotient' required:

5x1 2. Divide 17 by

Ans. 123. 3. Divide 99 by 108.

Ans. 193=1. 4. Divide of thy of a

Ans. 11. - 5. Divide 31 by 92.

Aus. 6. Divide } by 4.

Ans. 3] RULE OF THREE IN VULGAR FRACTIONS..

Rule.-Prepare the fractions as in Multiplication ; and state the question as directed in the Rule of Three in whole numbers; then invert the first term in the stating, and multiply all the three terms continually together, numerators by numerators and denominators by denominators, and the product will be the answer in the same name as the second or middle term.

EXAMPLES. 1. If of a yard cost in of a pound, what will. of an ell English cost ?

3x4x1 First of a yard= of 4 of 1=- - of an.ell.

5x1x5
EN. £. El.

Then ; P :: 15 :
And 45X7* =*£=9s. 8şd. Answer.

Nore.--Here, 25 and 15 are divisible by 5, giving 5 and 3 for quotients; and 6 and one of the 12s. are divisible by 6, giving 1 and 2 for quotients; then the numerators are 5, 7, and 1, whose product is 35; and the denominafors 12, 2, and 3, whose product is 72. And thus always

proceed, in multiplying vulgar fractions, by cancelling equal numerators and denominators, or dividing those that are divisible by the same number.

2. If of a yard cost of a dollar, what will 400 yds. come to?

Ans. $59,42cts. 7m., 3. If 50% bushels of wheat cost $59.4, what is it per bushel ?

. Ans. $1,16cts. Om. 4. If I buy 1001. of butter for $104, how many hundred can I bare for $10511? Ans. 104 hundred.

5. If 4 of 4 of a yard of lace cost 30cts., how much is it per yard ?

Ans $2,40cts. 6. 'lf of a gallon of wine costs of a dollar, what will 8 of a tun cost ?

Ans. $140. 7. A younger brother received 82200, which was just

of his elder brother's fortune ; and 38 times the elder's money was as much again as the father was worth; what was the father worth? Ans. $11000.

8. If, when the day's are 13 hours long, a traveller perforins his journey in 351 days ; in how many days will he perform the same journey, when the days are 1116 hours long?

Ans. 408 15 days. 9. A schoolmaster being asked how many scholars he had, answered, If I had as many, and } as many, and 4 as many, I should have 99 ; how many had he ? Ans. 36.

· RULE OF THREE IN DECIMALS.

RULE.—Reduce vulgar fractions to decimals, and com. pound numbers either to decimals of the higher names, or to integers of the lower, as also the first and third terms to the same name; then state the question and proceed as in whole numbers; the fourth term will be the answer.

EXAMPLES

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EXAMPLES. 1. Required the interest of $425,65cts. for 6 years, at 6 per cent. per annum.

* cts.
425,65 Principal.

,06 Ratio.

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CASE 2.-The amount, time, and ratio given, to find

the principal. RULE.—Multiply the ratio by the time; add unity to the product for a divisor, by which sum divide the amount, . and the quotient will be the principal.

EXAMPLES

1. What principal will amount to $1235,97cts. 5m. in 5 years, at 6 per cent. per annum?

,06x5+1=1,30)1235,975(950,75 Ans. 2. What principal will amount to £950 10s. 4,125d. in 8 years, at 55 per cent. ?

Ans. £645 159. 3. What principal will amount to $1394,50cts. in 7 years, at 6 per cent. per annum?

Ans. 8975. CASE 3.-The amount, principal, and time given, te

find the ratio.

RULE.-Subtract the principal from the amount; divide the remainder by the product of the time and principal, and the quotient will be the ratio.

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