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4. Reduce 5 of a scruple to the fraction of a pound.

5. Reduce of an ounce to the fraction of a hundred weight.

6. Reduce § of a pound to the fraction of a ton. 7. Reduce of an inch to the fraction of an ell English. 8. Reduce 4 of an inch to the fraction of a mile. 9. Reduce 1 of a barleycorn to the fraction of a league. 10. Reduce of an inch to the fraction of an acre.

11. Reduce ] of a quart to the fraction of a tun, wine measure.

12. Reduce of a pint to the fraction of a bushel.

13. Reduce of a minute to the fraction of a year (3651 days).

- CASE X. To reduce fractions of a higher denomination to a lower. 1. What part of a penny is oło of a pound? OPERATION.

We explain this question in 610 X 2= 20 = s. the following manner. As 32 X = 1 = $d. Ans. shillings are twentieths of a

pound, there will be 20 times as many parts of a shilling in oto of a pound, as there are parts of a pound ; therefore, do of a pound is equal to bio of 2 = = zz of a shilling. And as pence are twelfths of a shilling, there will be twelve times as many parts of a penny in of a shilling, as there are parts of a shilling ; therefore,

of a shilling is equal to 35 of * = }= f of a penny, Ans.

The operation of this question may be facilitated in the following manner.

OPERATION. oto X 4 X 4 = 44% = fd. Ans. Rule. — Let the given numerator be multiplied by all the denominations between it and the one to which it is to be reduced; then place the product over the given denominator and reduce the fraction to its lowest terms.

2. Reduce Tzbo of a pound to the fraction of a farthing. 3. Reduce gooo of a pound troy to the fraction of a grain.

4. Reduce zroz of a pound, apothecaries' weight, to the fraction of a scruple.

5. Reduce got of a cwt. to the fraction of an ounce. 6. Reduce pocou of a ton to ihe fraction of a pound.

7. Reduce iz of an ell English to the fraction of an inch. 8. Reduce to go of a mile to the fraction of an inch.

9. Reduce TIMERU of a league to the fraction of a barleycorn.

10. Reduce 25000560 of an acre to the fraction of an inch.

11. Reduce ho of a tun of wine measure to the fraction of a quart.

12. Reduce o of a bushel to the fraction of a pint. 13. Reduce 1201080 of a year to the fraction of a minute.

CASE XI. To find the value of a fraction in numbers of a lower denomination.

1. What is the value of 4 of a £. ? By Case IX. £. = X = ffs. = 54s.; and is.= [ X = fld. = 56d.; and ád. = X= fqr. = 1qr.

Ans. 5s. 5d. 1819r. This question may be analyzed thus:- If i£. is 20s., Å of a £. is 1 of 20s. = 56s. ; and if ls. is 12d., í of a shilling is Ít of 12d. =55d. ; and if ld. is 4qr., Í of a penny is

of 4qr.= 1819r., Answer, as before.
Or, it may be performed in the following manner.
OPERATION.

In this operation, it will be per20

ceived that we multiply the numer11)60(58. ator of the fraction by the successive

lower denominations, beginning with 5

the highest, and divide each product

by the denominator. 11)60(5d,

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RULE. — Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator ; if any thing remain, multiply it by the next less denomination, and divide as before, and so continue as far as may be required; and the several quotients will be the answer.

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6. What part of a £. is 5s. 5d. 1qr. ?

8. d. qr.

5 5 13 In this question, the shillings, 12 12

pence, farthings, &c. are reduced 240 65

to elevenths of farthings for the nu

merator of a fraction. A pound is 960 261

also reduced to the same denomi11

nation, for a denominator. The

fraction is then reduced to its lowest 10560 2880

terms. 26058 = it Ans.

RULE. — Reduce the given number to the lowest denomination it contains for a numerator ; and then reduce the integer to the same denomination, for the denominator of the fraction required.

7. Reduce 3 d. to the fraction of a shilling. Ans. 7. 8. Reduce 21s. 9d. 1fqr. to the fraction of a guinea.

Ans. j. 9. Reduce 2qr. 15lb. 4oz. 5% dr. to the fraction of a cwt.

Ans. 17 10. What part of a pound are Yoz. 17dr. ? Ans.. 11. What part of a pound troy are 10oz. 13dwt. 8gr. ?

Ans.. · 12. What part of a pound apothecaries' weight are 33 53 10 12 gr. ?

Ans. As. 13. What part of a yard are 2qr. Ona. lizin. ? Ans. 75. 14. What part of an ell English are 2qr. 3na. Olin. ?

Ans. ģ. 15. What part of a mile are 6fur. 30rd. 12ft. 8in. 01 br. ?

Ans. it. 16. Reduce 35rd. 9ft. 2in. to the fraction of a furlong."

Ans. s. 17. What part of an acre are 2R. 6rd. 4yd. 5ft. 127-in. ?

Ans. 75: 18. What part of a square rod are 144ft. 19 4in. ?

Ans. 17. 19. What part of a cord are 9ft. 1462 *zin. ? Ans. is.

20. What part of a hogshead of wine are 6gal. 2qt. lpt. 04 gi.

Ans. Ig 21. What part of a hhd. of beer are 42 gal. ? Ans. š.

22. What part of a year (3654 da.) are 174d. 16h. 26m. 5'5 sec. ?

Ans. 11

Section XVII.

ADDITION OF VULGAR FRACTIONS.

CASE I. To add fractions that have a common denominator. 1. What part of an apple is 1 and ? and f? and ? 2. What part of a dollar is ļ and ? Po and 1% ? and ? 3. What part of a shilling is and ? , and ? 4. What part of an orange is į and f? į and f? and ? 5. Add i's, ise Ya, and it together.

OPERATION. 3+5+7 +11= =1= 27 Ans. In this question, we add the numerators, and divide their sum by the denominator.

RULE. — Write the sum of the numerators over the common denominator, and reduce the fraction if necessary. 6. Add

, 4, and te together. Ans. 319. 7. Add , 25, 31, it, and if together. Ans. 217. 8. Add 87, 17, 4, 4, and 77 together. Ans. 24. 9. Add 144, 14, 90, and ill together. Ans. 14. 10. Add 11, R1, 657, and together. Ans. 2438 11. Add 491,741, 698, and 780 together. Ans. 3367. 12. Add jiit, 3717, and 7146 together. Ans. 14311 13. Add 360, 393, and 1996 together. Ans. 21475 14. Add 1920, 1986, and vo together. Ans. 2835.

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126 OTTO 3000 3370

CASE II. To add fractions that have not a common denominator. 1. What is the sum of } , it, and ji ?

First Method.

OPERATION. 4)8 12 16 20 4X2X3X2x5=240 common denominator. 2)2 3 4 5

8 30 X 7=210 1 3 2 5

12 20 x 5= 100
16 15X11= 165

201 12x 13 = 156 Having found a common de

631 nominator by Case VIII., we proceed as in the last Case.

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