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3. Reduce j f f and is to their least common denom, inator.

Ans. t ti ti to 4. Reduce ff and i'r to their least common denominator.

Ans. His 11 11


To reduce the fraction of one denomination to the fraction,

of another, retaining the same value.


Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing it with all the denominations between it and that denumi nation you would reduce it to; lastly, reduce this com pound fraction to a single one, by Case V.


1. Reduce of a penny to the fraction of a pound. By comparing it, it becoines of tz of x' of a pound. 5 X 1 X 1


Ans. 6 x 12 x 20 1440 2. Reduce to of a pound to the fraction of a penny.

Compared thus, two of 4 of Y d. Then 5 X 20 X 12

ī=H*** 440 1 3. Reduces of a farthing to the fraction of a shilling

Ans. s. 4. Reduce of a shilling to the fraction of a pound.

Ans. Top 5. Reduce { of a pwt. to the fraction of a pound troy.

Ans. rosto 6. Reduce of a pound avoirdupois to the fraction of cwt.

Ans. hocwt. 7. What part of a pound avwirdupois is Tizof a cut

Compounded thus, Tig of of == Ans. 8. What part of an hour is itt of a week.

Ans. IH

9. Reduce i of a pint to the fraction of a hhd.

Ans. 10. Reduce ş of a pound to the fraction of a guinea.

Compounded thus, f of of 'ss.= Ans. 11. Express 5] furlongs in the fraction of a mile.

Thus, 54= of =ti Ans. 12. Reduce , of an English crown, at os. 8u. to the fraction of a guinea at 28s.

Ans. of a guinea. CASE VIII.

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To find the value of the fraction in the known parts of the,

integer, as of coin, weight, measure, &c.


Multiply the numerator by the parts in the next infe. rior denomination, and divide the product by the denomia Dator; and if any thing remains, multiply it by the next mferior denomination, and divide by the denominator as defore, and so on as far as necessary, and the quotient will be the answer.

Note.-This and the following Case are the same with Problems II. and III. pages 75 and 76; but for the scholar's exercise, I shall give a few more examples in each.


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1. What is the value of Ht of a pound ?

Ans. 8s. Oldha 2. Find the value of of a cwt.

Ans. Sqrs. 3lb. 1oz. 12fdr. S. Find the value of f of 3s. 6d - Ans. 3s. Utd. 4. How much is not of a pound avoirdupois ?

Ans. 7oz. 10dr. 5. How much is of a hhd. of wine ? Ans. 45 gals. 6. What is the value of 18 of a dollar ?

Ans. 5s. 780. 7. What is the value of £ of a guinea ? Ans. 188.

8. Required the value of 187 of a pound apothecaries.

Ans. 2oz. Igrs. 9. How much is of 5l. 9s. ? Ans. £4 13s. 54d. 10. How much is of of of a hogshead of wine ?

Ans. 15gals. 3qts.


o reduce any given quantity to the fraction of any great

er denomination of the same kind.
[See the Rule in Problem III. page 75.]


1 Reduce 12lb. Soz. to the fraction of a cwt.

Ans, 295 2. Reduce 13cwt. Sqrs. 20lb. to the fraction of a ton.

Ans. S. Reduce 16s. to the fraction of a guinea. Ans.

4. Reduce 1 hhd. 49 gals. of wine to the fraction of a bun.

Ans. 5. What part of 4cwt. 1qr. 24lb. is Scwt. Sqrs. 17lb. 302.

Ans. ]



REDUCE compound fractions to single ones; mixed numbers to improper fractions; and all of them to their least common denominator (by Case VI. Rule II.) then the sum of the numerators written over the common denominator, will be the sum of the fractions required.


1. Add 51 i and of 7 together.

55 and of 2=** l'hen Y } reduced to their least common denominator

by Case VI. Rule II. will become W H H Thon 132+18+14--V=674 or Answer.

2. Add and together.
S. Add andtovether.
4. Add 124 3 and 4; together.
5. Add of 95 and of 14 bugether.

Ans. 1}

Ans. 11 Ans. 2011 Ans. 4411

Nore 1.- In adding rnised numbers that are not com: pounded with other fractions, you may first find the sun of the fractions, to which add the whole numbers of the given mixed numbers.

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6. Find the sum of 537 and 15.
I find the sum of and to be i=113

Then 11t+5+7+15=2817 Ans. 7. Add and 17 together.

Ans. 1718 8. Add 25, 81 and 1 of į of to

Ans: 34 Note 2.—To add fractions of money, weight, &c. re duce fractions of different integers to those of the same.

Or, if you please you may find the value of each frac. tion by Case vill. in reluction, and then add their in their

proper ternis.

9. Acid 4 of a shilling to s of a pound. Ist Method.

2d Method. ; of id=id;

if.=78. 6d. Ogrs. +=

s. =0 6 31

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is 8s. Od. Sigrs. Ans.

Ans. 8 0 3
By Case VIII. Reduction

10. Add } lb. Troy, to fof a pot.

Ans. 7oz. 4put. 1ster 11. Add 9 of a tc:1, to of a cwt.

Ans. 12cict. 1gr. 8lb. 12,7oz. 12. Add of a mile to io of a furlong.

Ans. 6fur. £8po. 13. Ad of a yard, of a foot, and of a mile together.

Jns. 1540yds. 2f1. Sing 14. Add { of a week, f of a day, 1 vf an hour, and Ful minute together Ans. 2da, 2ho, 30min. 45x<



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RULE.* PREPARE the fractions as in Addition, and the difference of the numerators written above the common denot o nominator, will give the difference of the fraction required thes 1. From t take of of Z=14=Then f and hard ta

Therefore 9-=the Ans. 2. From & take

Answers. i 3. From si take 1

4. From 14 take ti lif 5. What is the difference of it and 17 ? कुर्नर 531 6. What differs, 1 from?

ü 7. From 14+ take of 19

11 8. From 7 take i

O remains. 9. From t of a pound, take of a shilling. fri ļof zóstách. Then from ti£. take loke. Ans. ill.

Nore.-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 pro

10. From 1£. take shilling. Ans. 5s. 6d. 2grs. 11. From of an oz. take } of a pwt.

Ans. 11prot. Sgr. 12. From } of a cwt. take it of a lb.

Ans. Igr. 27lb. 6oz. 10, ar. 13. From sweeks, take of a day, and sof of of an hour.

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

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per terms.

*In subtracting thixed 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 denomingo tor, and placing the remainder over the denominator, then taking one from the whole number.

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