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Ans. 14 21

16 16

3. Reduce } if and is to their least common denominator.

4. Reduce 1 and to their least common denomizator.

Ans. sif it
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 denomination you would reduce it to; lastly, reduce this compound fraction to a single one, by Case V.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound.
By comparing it, it oecomes of 12 of zy of a pound
5 X1 XI

5

Ans. 6x 12 x 20

1440
2. Reduce theo of a pound to the fraction of a penny,

Compared thus, taho of of Yd.
Then 5 X 20 X 12

144f=
1440 1 1
3. Reduce of a farthing to the fraction of a shilling

1

Ans. Hos

Ans. The

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

Ans. To= 5. Reduce 4 of a pwt. to the fraction of a pound troy.

ត) 6. Reduce of a pound avoirdupois to the fraction of a cwt.

Ans. ilo cwt. 7. What part of a pound avoirdupois is to of a cwt.

Compounded thus to off of >=1) Ans. 8. What part of an hour is zia of a week.

Ans. =

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

Ansatz

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

Compounded thus, i of of os.= Ans. 11. Express 5} furlongs in the fraction of a mile.

Thus 5.=\ of }=li Ans. 1-2. Reduce of an English crown, at 6s. 8d. to the fraction of a guinea at 28s. Ans. Á of a guinea.

CASE VIII.

To find the value of a 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 anything 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.

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EXAMPLES.

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

Ans. 88. 94d 2. Find the value of 7 of a cwt.

Ans. 3qrs. 316. 1oz. 12 dr. 3. Find the value of 1 of 3s. 6d. Ans. 38. 0d. 4. How much is 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 15 of a dollar ?

Ans. 58.71d. 7. What is the value of of a guinea ? Ans. 188.

8. Required the value of 7 of a pound apothecaries.

Ans. 2oz. 3grs. 9. How much is of 5l. 98. ? Ans. £4 13s. 5 d. 10. How much is } of of of a hhd. of wine ?

Ans. 15gals. 3qts.

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.

95

1. Reduce 12 lb. 3 oz. to the fraction of a cwt.

Ans. 10 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a tyn.

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

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

Ans. 8 oz.

Ans. 4

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 5) and of 1 together.

5}=\ and of =* Then yd 14 reduced to their least common denominator

by Case Vl. Rule II. will become il Then 132 +18+14=1464 or 6 Answer.

2. Add 3 and together.
3. Add į and together.
4. Add 12 3 and 4: together.
5. Add } of 95 and 3 of 141 together.

Ans. 15

Ans. 13 Ans. 2011 Ans. 4417

Note 1.-In adding mixed 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 numbers.

6. Find the sum of 574 and 15.
I find the sum of and to be i=117

Then 16 +5+7+15=2810 Ans 7. Add and 17} together.

Ans. 171 8. Add 25, 81 and 1 of 3 of u

Ans. 3312

6 37

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 frac tion by Case VIII. in Reduction, and then add them in their proper terms. 9. Add 4 of a shilling to of a pound. 1st method.

2d Method. of=1£.

£=78; 6d. Oqrs. Then ihoti=imo.

45.50 TVhole value by Case VIII. is 8s. Od. 31 qrs. Ans.

Ans. 8

0 31

By Case VIII. Reductiov. 10. Add 3 lb. Troy, to of a pwt.

Ans. 7oz. 4pwt. 13 gr. 11. Add of atun, tó io of a cwt.

Ans. 12cwt. Iqr. 816. 123.02. 12. Add i of a mile to io of a furlong.

Ans. 6fur. 28po. 13. Add of a yard, of a foot, and / of a mile together.

Ans. 1540yds. 2ft. 9in. 14. Add of a week, of a day, } of an hour, and ! of a minute together. Ans. 2da. Pho. 30min. 45 sec

SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

PREPARE the Fraction as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required.

EXAMPLES.

Answers.

31 Z08

1315

5

10 171

7

12

1. From take of 1
of 1=1=1 Then and 1=1 12

Therefore 9–7=i=ă the Ans. 2. From take 4 3. From id take 4. From 14 take 13 5. What is the difference of fi and 17 ? 6. What differs is from } ? 7. From 14. take of 19 8. From 7 take to

O remains. 9. From 11 of a pound, take of a shilling. ļof britn£. Then from 1 £. take 15£. Ans. 1£.

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 proper terms.

10. From 5 £. take 3 shillings. Ans. 58. 6d. 2gre. 11. From of an oz. take of a pwt.

Ans.11 put. 3gr. 12. From į of a cwt. take 1 of a lb.

Ans. 1qr. 271b. 6oz. 101. dr. 13. From 3 weeks, take of a day, and of of of

Ans. 3w. 4da. 12ho. 19min 17 sec.

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 denominator, and placing the mainder over the denominator, then taking one from the whole number

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