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der thereof, they may both be expunged, and the ot members continually multiplied (as by the rule) will duce the fraction required in lower terms. 6. Reduceof of to a simple fraction. Thus 2x 5

5. Ans.

4x7 7. Reduce of g off of il to a simple fraction.

Ans. =)

CASE VI. To reduce fractions of different depominations to equiv lent fractions having a common denominator.

RULE I. 1. Reduce all fractions to simple terms.

2. Multiply each numerator into all the denominato except its own, for a new numerator: and all the denom Bators into each other continually for a common denom nator; this written under the several new namerato will give the fractions required.

EXAMPLES.

1. Reduce to equivalent fracțions, having a com mon denominator.

+ f + =24 common denominator.

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24 24 24 denominators. %. Reduce fly and it to a common denominator.

Ans. Stando 3. Reduce and to a common denominator.

Ans. and

mat

4.

inat

72

Tore

34 36 3456 3456

4. Reduce 26

e and to to a common denominator. 800 300 4004

and -=fo is and t=1. Ans. 1000 1000 1000 5. Reduce 15 and 124 to a common denominator.

Ans. 54 66 888 6. Reduce 1 and 1 of 11 to a common denominator.

Ans. 768 259 2 1980 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.

(By 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 inultiply 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.

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EXAMPLES.

1. Reduce j and to their least common denomina: tor:

4)2 4 8

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1 4X2=8 the least com. denominator,

5.

6.

the

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

8:8X5=5 the 3d. numerator.
These numbers placed over the denominator, give
answer equal in value, and in much lower terms
than the general Rule, which would produce the 13

2. Reduces and is to their least common denominator.

Ans. 21 72 73

32 48 40

3. Reduce s and to their least common deno inator.

Ans. ** 1872 4. Reduce it and is to their least common deno inator.

Ans. 12 9

1911

27 27 27 24

CASE VII,

To reduce the fraction of one denomination to the fractic

of another, retaining the same value.

RULE.

Reduce the giren fraction to such a compound one, a will express the value of the given fraction, by comparin. it with all the denominations between it and that denomi nation you would reduce it to; lastly, reduce this con jound fraction to a single one, by Case V.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of is of no of a pound. 5 x 1 x 1

5

dis.

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

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

200

1

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Anssos:

440 3. Reduce of a farthing to the fraction of a shilling 4. Reduce of a shilling to the fraction of a pourid.

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

Ans. 1876 6. Reduce of a pound avoirdupois to the fraction of a cwt.

Ans. hocwt. 7. What part of a pound avoirdupois is the of a cwt

Compounded thus, Tir of of i=114 = Ans. 8. What part of an hour is dit of a week.

Ans. 168

Ans. the

9. Reduce of a pint to the fraction of a hhd.
10. Reduce of a pound to the fraction of a guinea.

Coinpounded thus, of 20 of 25.= Ans. 11. Express 5furlongs in the fraction of a mile.

Thus, 5=of 1=1 Ans. 12. Reduce of an English crown, at os. 8d. to the fraction of a guinea at 285.

Ans. at of a guinea.
CASE VIII.

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

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

RULE.

Multiply the numerator by the parts in the next infe. rior denomination, and divide the product by the denominator; and if any thing remains, multiply it by the next inferior 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 each.

EXAMPLES.

the

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

Ans. 8s. Oid. 2. Find the value of % of a civt.

Ans. Sqrs. Slb. 1oz. 12dr. 3. Find the value of of Ss. Cil. Ins. Ss. Ojd. 4. How much is one of a pound arorlupois ?

..is, 7oz. 10dr. 5. How much is of a hid. of wine? Ins. 45 gals. 6. What is the value of 15 of a dollar ?

Ans. 5s. 71d. 7. What is the value of is of a guinea ? Ans. 185.

8. Required the value of of a pound apothecaries.

Ans. 20%. Sgrs. 9. How much is of 51. 9s. ? Ans. 64 15s. 54. 10. How much is t of of * of a bhd. of wine ?

Ans. 15gals. Sqts.

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CASE IX.
To reduce any given quantity to the fraction of any

greater denomination of the same kind.
(See the Rule in Problem III. Page 75.]

EXAMPLES FOR EXERCISE.
1. Reduce 12 lb. 3 oz., to the fraction of a cwt.

Ans. 123,
2. Reduce 15 cwt. 5 qrs. 20 lb. to the fraction of a ton.
3. Reduce 16s. to the fraction of a guinea.

Ans. 4

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

Ans. . 5. What part of 4 cwt. 1 qr. 24 lb. is Scwt. 3 qrs. 17 lb.

Ans.

39

8 oz.

Ans. }

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 the sum of the numerators written over the common denominator, will be the sum of the fractions required.

EXAMPLES

1. Add 5and sof, together.

5}=1 and of 3
Then 24 reduced to their least common denominater

by Case VI. Rule II. will become
Then 132+18-+-14=*=60 or 6 Answer.

18 1.

9

$

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