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cept its own, for a new numerator; and all the denomina: tors continually for the common denominator.

EXAMPLES.

1. Reduce 1, 3, and to equivalent fractions, having a common denominator.

1x5x7=35 the new numerator for

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2x5x7=70 the common denominator.

Therefore the new equivalent fractions are #8, #8, and 48, the answer.

2. Reduce,,, and to fractions, having a common denominator. Ans. 144, 192 240 258

288 288 285 388

3. Reduce, of 4, 5, and to a common de nomi

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To reduce any given fractions to others, which shall have the least common denominator.

1. Find the least common multiple of all the denomina

other, it will be seen, that the numerator and denominator of every fraction are multiplied by the very same number and consequently their values are not altered. Thus in the first ex ample:

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In the 2d rule, the common denominator is a multiple of all the denominators, and consequently will divide by any of them; it is therefore manifest that proper parts may be taken for all the numerators required.

tors of the given fractions, and it will be the common denominator required.

2. Divide the common denominator by the denominator of each fraction, and multiply the quotient by the numerator, and the product will be the numerator of the fraction required.

EXAMPLES.

1. Reduce, and to fractions, having the least common denominator.

2
3

6 the least common denominator.

62×1-3 the first numerator; 6-3×2=4 the second numerator: 66×5=5 the third numerator.

2. Reduce

4 5 6་ 8

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Whence the required fractions are 3,, and to fractions, having the least com

mon denominator.

2

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3. Reduce, , and to the least common denomina

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4. Reduce, 4, 5, and to the least common denomi

nator.

6 3

Ans ៖៖៖៖៖៖ ៖៖

5. Reduce,,, 71, and 11 to equivalent fractions, having the least common denominator.

Ans. 18, 38, 48, 48 38: 38°

36 40 42 33 34 48 48 48

CASE 7.

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

teger. RULE.*

Multiply the numerator by the parts in the next inferior

* The numerator of a fraction may be considered as a remainder, and the denominator as a divisor; therefore this rule has its reason in the nature of Compound Division.

denomination, and divide the product by the denominator; and if any thing remain, multiply it by the next inferior denomination, and divide by the denominator as before; and so on as far as necessary; and the quotients placed after one another, in their order, will be the answer required.

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2. What is the value of of a pound sterling?

3. What is the value of of a pound Troy?

Ans. 7s. 6d.

Ans. 7oz. 4dwt.

Ans. 9oz. 2 dr.

4. What is the value of of a pound Avoirdupois?

5. What is the value of of a cwt.?

6. What is the value of

Ans. 3qrs. 3lb. 1oz. 124dr. of a mile?

Ans. 1fur. 16pls. 2yds. 1ft. 9-in.

7. What is the value of of an ell English?

Ans. 2qrs. 3 nls.

8. What is the value of of a tun of wine?

Ans. 3hhd. 3.1gal. 2qts.

9. What is the value of of a day?

CASE 8.

Ans. 12h. 55′ 231".

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

RULE.*

Make a compound fraction of it, and reduce it to a single

one.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound.

And

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the answer.

of of
of 20 of 28-d. the proof.

2. Reduce of a farthing to the fraction of a pound.

3. Reduce

to the fraction of a penny.

Ans. 1440
Ans. 40.

4. Reduce of a dwt. to the fraction of a pound Troy.

Ans. Jo

5. Reduce of a pound Avoirdupois to the fraction of a

cwt.

Ans. 1.

6. Reduce of a hhd. of wine to the fraction of a

pint.

Ans. 13.

7. Reduce of a month to the fraction of a day.

Ans..

* The reason of this practice is explained in the rule for reducing compound fractions to single ones.

The rule might have been distributed into two or three different cases, but the directions here given may very easily be applied to any question, that can be proposed in those cases, and will be more easily understood by an example or two, than by a multiplicity of words.

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8. *Reduce 7s. 3d. to the fraction of a pound. Ans. . 9. Express 6fur. 16pls. to the fraction of a mile.

ADDITION OF VULGAR FRACTIONS.

RULE.t

Ans..

Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same; and all of them to a common denominator; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required.

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*Thus 7s. 3d. = 87d. and 11. = 240d... the answer.

87
40

† Fractions, before they are reduced to a common denomina tor, are entirely dissimilar, and therefore cannot be incorporat ed with one another; but when they are reduced to a common denominator, and made parts of the same thing, their sum or difference may then be as properly expressed by the sum or difference of the numerators, as the sum or difference of any

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