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4. Reduces and to a common denominator. 800 300 400

- - and - =is and 1=11Ans. 1000 1000 1000 5. Reduce and 12 to a common denominatur.

Ans. 43 6. Reduce and fof H to a common denoininator.

Ans. 3000 The foregoing is a general Rule for reducing fractions to a common denominator ; but as it will save much labour to keep the fractions in the lowest terms possible, the following Rule is much preferable. .

RULE II. For reducing fractions to the least common denominator.

(Ry Rule, page 155) find the least common multiple of all the denominators of the given fractions, and it will be the common denominator required, in which divide each particular denominator, and multiply the quotient by its own numerator for a new numerator, and the new numerators being placed over the common denominator, will express the fractions required in their lowest terms.

EXAMPLES. 1. Reduce 1 and to their least common denominator.

4)2 4 8

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1. 4.x2=8 the least com. denominator.

8:2x1=4 the 1st. numerator.
8-4X3=6 the 2d. numerator.

8---8x5=5 the 3d. nunierator. These numbers placed over the denominator, give the answer equal in value, and in much lower terms than the general Rule, which would produce 4 * 2. Reduce ff and í to their least common denomiar

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3. Reduce and to their least common denom, inator.

Ans. i ti ti to 4. Reduce it and is to their least cominon uenommator.

Ans. His dit CASE VII.

To reduce the fraction of one denomination to the fraction, of another, retaining the same value.

RULE

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 denomi nation you would reduce it to; lastly, reduce this com pound fraction to a single one, by Case V.

EXAMPLES 1. Reduce of a penny to the fraction of a pound. By coinparing it, it becomes of t' of ty of a pound. 5 X1 X1 5

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

Compared thus, tio of of 4 d. Then 5 x 20 x 12

440 1 1 3. Reduce $ of a farthing to the fraction of a shilling

. Ans. ss. 4. Reduce of a shilling to the fraction of a pourid.

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

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

Ans. Türcwt. 7. What part of a pound avvirdupois is hizof a cut

Compounded thus, tio of 1 of 4*=* = Ans. 8. What part of an hour is it of a week.

Ans. He

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

I Ans. it 10, Reduce of a pound to the fraction of a guinea.

Compounded thus, of 20 of ass= Ans. 11. Express 5] furlongs in the fraction of a mile.

Thus, 5s= of =t& Ans. 12. Reduce of an English crown, at 6s. 8u. to the fraction of a guinea at 28s. Ans. of a guinea.

CASE VIII.

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

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

RULE.

Multiply the numerator by the parts in the next infe. rior denomination, and divide the product by the denomi, Dator; and if any thing remains, multiply it by the next mferior denomination, and divide by the denominator as before, 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 cach.

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8. Required the value of 147 of a pound apothecaries.

Ans. 2oz. 3grs. 9. How much is of 5l. 9s. ? Ans. 64 13s. 5 d. 10. How much is of of of a hogshead of wine ?

Ans. 15gals. 3qts.

CASE IX. 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.]

EXAMPLES FOR EXERCISE.

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

Ans. 1969
2. Reduce 13cwt. 3qrs. 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 jun.

Ans. 5. What part of 4cwt. Iqr. 241b. is Scwt. Sqrs. 17lb.

Ans. f

302.

ADDITION OF VULGAR FRACTIONS.

RULE.

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

she sum of the numerators written over the common des nominator, will be the sum of the fractions required.

EXAMPLES.
1. Add 51 f and off together.

5}=y and of =
Then y reduced to their least common denominatur

by Case VI. Rule II. will become HH
Thon 132 +18+14. 14674 or 4 Answer.

Adil and together...

Ans. 17 S. Add i and together.

Ans. 11 4. Add 12 3 and 4 foyether.

Ans. 2017 5. Add 1 of 95 and of its buyether. Ans. 4441

Nore 1.- In adding mixed 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.

6. Find the sum of 537 and 15.
I find the sum of and to bc =147 .

Then ins +3+7+15=2813 Ans. 7. Add ; and 17 together.

Ans. 17 8. Add 25, 84 and of of to

Ans: 33 11 Note 2.–To add fractions of money, wcight, &c. ro 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 Vlll. in rcduction, and then add their in their proper ternis. 9. Acid 4 of a shilling to of a pound. Ist Method.

2d Method. ; of astok

if.=7s. 64. Oqrs. Then girt=uo £.

s. =( 6 32 Whole value by Case vill. is 8s. Od. Sigrs. Ans. Ans. 8 0 34

By Case VIII. Reduction. 10. Add } Ib. Troy, to $ of a pwt.

Ans. 7oz. 4put. 15 gr 11. Add of a tc:1, to 'of a cwt.

Äits. 12cut. Igr. 8lb. 12, poz. 12. Add of a mile to go of a furlony.

Ans. 6fur. £8po. 13. Add of a yard, of a foot, and all of a mile togetlier.

ins. 15411yds. 2f1. Sing 14. Add for a week, 4 of a day, 1 of an livur, and Rul minute together. "Ans. 2darho, 30min. 45667

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