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RULE.* $. 44 PREPARE the fractions as in Addition, and the dif.

ference of the numerators written above the common denot ( nominator, will give the difference of the fraction required.. the

EXAMPLES. soli 1. From 1 take of of = Then and ist

* Therefore 9- = = the Ans.
2. From { take

3. From i take
4. From it take
5. What is the difference of and 17 ?
6. What differs from 1?

7. From 144 take of 19 Ric! 8. From 7 take

O remains. 9. From t of a pound, take , of a shilling. for ļof id=tách. Then from tit. take loke. Ans. ff. on Note.--In fractions of money, weight, &c. you may, if

you plexse, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms.

10. From £. take a shilling. Ans. 5s. 6d. 2grs.
11. From of an oz. take of a pwt.

Ans. 11 pwt. 3gr.
12. From } of a cwt. take is of a lb.

* Ans. "Igr. 6oz. 10% ár. 13. From Sf weeks, take of a day, and j of of of an hour.

Ins. Sw. 4da. 12ho. 19min. 174sec

*In subtracting fixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denonsinator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number.

Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominee tor, and placing the remainder over the denominator, then taking one from the whole number.


RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to siinple ones, and those of different integrers to the same; then multiply all the nunerators together for a new numerator, and all tbe de. nominators together for a new denominator.


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1. Multiply by

Answers. 4 2. Multiply & by * 3. Multiply 5 by Š 4. Multiply & of 7 by 5. Multiply 1 by the 6. Multiply of 8 by 1 of 5 7. Multiply s by 91 8. Multiply of by k of 3

9. What is the continued product of of 1, 7, 51 and f of £?

Ans. 446

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RULE. 3 PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication :- The products will be the quotient required.


4 X 5 1. Divide by i . Thus, i Ans.

3 X 7 2. Divide by

Answers. 137 3. Divider of by } 4. What is the quotient of 17 by ? 5. Diviele 5 by to 6. Divide of of by of . 7. Divide 45 by 1 of 4 8. Divide 71 by 127

Divide 52051 by of 91



RULE. PREPARE the fractions as before, then state your question agreeable to the Rules alread y laid down in the Rule of Tliree in whole numbers, and invert the first terin in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same naine with the second or middle term.

EXAMPLES. 1. If of a yard cost of a pound, what will it of an Ell English cost ?

iyd.= 0; of =48 or { Ell English. ELİ. £. Ell.

s. d. grs. As ::: And xx=ts.=10 3 1 Ans.

2. It of a yard cost of a pound, what will 400 ydsa come to?

Ans. £ 59 Ss. 64ů. 3. If 50 bushels of wheat cost 17*l. what is it per bushel?

Ans. is. Oct. i yrs. 4. If a pistareen be worth 14 pence, what are 100 pigitareen's worth i

Ans. £6 5. A merchant seid 54 pieces of cloth, each containing *244 yuš. at 9s. fd. per yard; what diil the whole amount to?

. Ans. £60 10s. Od. 3 yrs. 6. A person having of a vessel, sells of his share for 3121. ; what is the whole vessel worth it. Ans. 6780

7. ir 1 ut a ship be worth of her cargo, valued at 8 100l. what is the whole ship and cargo worth?

Ans. £10031 148. 11 d.



PREPARE the fractions and state the question as before, then invert the third terin, and multiply all the three ternys together, the product will be the answer.


1. How much shalloon that is yard wide, will line 51 yards of cloth which is 14 yard wide ? Yds. yds. yds.

Yds. As 14:51:: And Xxx = =16, Ans. 2. If a man perform a journey in 3 days, when the day is 124 hours long; in how many days will he do it when the day is but 9 hours. Ans. 4 days.

3. If 13 men in 11 days, mow 213 acres, in how many days will 8 men do the same. Ans. 1821 days.

4. How much in length that is 7 inches broad, will make a square foot ?

Ans. 20 inches. 5. If 25ès. will pay for the carriage of an cwt. 1451 miles; how far may 6 cwt. be carried for the same money?

Ans. 22 miles. 6. How many yards of baizé which is 1+ yards wide, will line 187 yards of camblet { yd. wide ?

Fins. 1lyds. Iqr. 11 na.



REDUCE your fractions to decimals, and state your question as in whole numbers ; multiply the second and third together; divide by the first, and the quotient will be the answer, &c.

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A TABLE OF RATIOS. Rate per cent. I Ratio. T Rate per cent. Ratio.

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Ratio is the simple interest of 1l. for one year; or in federal money, of $1 for one year, at the rate per cent. agreed on.

RULE. Multiply the Principal, Ratio and time continually together, and the last product will be the interest required.

EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 years, at 5 per cent. per annum ?

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