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S. Reduce i j j and to their least common denominator.

Ans. is it it's 4. Reduces and it to their least comninon denom. inator.

Ans. 12

9

16 16

CASE VII.

fo 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 coin pound fraction to a single one, by Case V.

EXAMPLES

1. Reduce of a penny to tie fruction of a pound. By comparing it, it becomes of 's of of a pounu. 5 x 1 x

ģ

Aiis 6 x 12 x 20 1440 2. Keduce oso of a pound to the fraction of a penny:

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

-110 440 1 1 3. Reduce 1 of a farthing to the fraction of a shilling 4. Reduces of a shilling to the fraction of a pound.

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

Ans. tapo 6. Reduces of a pound avoirdupois to the fraction of a cwt.

Ans. threwt. 7. What part of a pound avoirdupois is Tágot a cwt

Compounded thus, titofof==, Ans. 8. What part of an hour is zi:

of a weck.

Ans. =

Ans. ' s.

9. Reduce 1 of a pint to the fraction of a hhd.

Ans.

. อร 10. Reduce of a pound to the fraction of a guinea.

Compounded thus, of 20 of 3. Ans. 11. Express 5$ furlongs in the fraction of a mile.

Thus, 5j=1 of 1=it Ans. 12. Recluce of an English crown, at 6s. 8d. to the fraction of a guinea at 288. 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, measure, &c.

RULE.

Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator; 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 each.

EXAMPLES.

1. What is the value of 27 of a pound?

Ans. 8s. 9fd. 2. Find the value of of a cwt.

11 공

Ans. Sqrs. 3lb. 1oz. 12 dr. 3. Find the value of ; of 3s. 6d Ans. 3s. Úsd. 4. How much is one 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 16 of a dollar ?

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

8. Required the value of them of a pound apothccaries,

ins. 20%. Sgre. 9. How much is of 5l. 98. ? Ans. £4 13s. 5 d. 10. How much is s off of # of a lihd. of wine ?

Ans. 15gals. Sats

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 73.

EXAMPLES FOR EXERCISE. 1. Reduce 12 V. S 02. to the fraction of a cut.

Ans. The

2. Reduce 13 cwt. Sqrs. 20 lb. to the fraction of a tun.

Ans.

39

4

aus. A

3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a

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

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ADDITION OF VULGAR FRACTIONS.

RULE.

REDUCE compound fractions to single ones; nised numbers to improper fractions; and ail 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 5) and of together.

5}=and of ?=* Then reduced to their least common denominator

by Case VI. Rule II. will become yo 14 Then 192+18.4-14=160 or 6. Answer.

2. Add and together.
3. Add and together.
4. Add 12: 3 and 4 together.
5. Add ļ of 93 and 3 of 14 together.

Ans, if Ans. 11 ARs. 2011 Ans. 4447

Note 1.--In adding nixed numbers that are not compounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed nuinbers.

Ans. 17 16

6. Find the sum of 57 and 15.
I find the sum of and to be i=117

Then 14+5+7+15=281Ans. 7. Add 1 and 17 together. 3. Add 25, 81 and off of

Ans, St Note 2.-To add fractions of money, weight, &c. reduce fractions of different integers to those of the same.

Or, if you please you may find the value of each fraction by Case VIII. in reduction, and then add them in their proper terms. 9. Add of a shilling to of a pound. Ist Method.

2d Method, of=ts

if.-7s. 6d. Oqrs. Then tot=flife:

is.
fill
.

0 6 3
Whole value by Case VII
is 8s. Od. 34qrs. Ans. Ans. ? 0 st

By Case VIII. Reduction. 10. Add { lb. Troy, to f of a put.

Ans. 7oz. 4pwt. 15 gr. 11. Add of a ton, to j of a cwt.

Ans. 12cwt. Iqr. 8lb. 12x60mi 12. Add of a mile to 7 of a furlong.

SUBTRACTION OF VULGAR FRACTIONS.

RULE. PREPARE the fractions as in Addition, and the dif. ference of the numerators written above the common denominator, will give the difference of the fraction required

EXAMPLES.

708

1. From it take of f # is of j = 1 Then and the Ans.

=1= 2. From take 4

Answers. 3. From it takes 4. From 14 take

13% 5. What is the difference of it and 37? sht 6. What differs from? 7. From 141 take of 19 8. From 7 take 111

O remains. 9. From 1 of a poard, take of a shilling. of stick. Then from tb. take risk. Ans. £.

NOTE.-In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their pro

10. From 1. take 3 shilling. Ans. 58. 6d. 24qrs. 11. From of an oz. take of a pwt.

Ans. liput. 3gr. :2. From } of a cwt. take it of a lb.

Ans. Sigr. 27lb. 6oz. 10 dr. 13. From 3 weeks, take of a day, and off of of

Ans. Sw, 4da. 12ho. 19min. 171sec

per terms.

an hour.

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

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