8

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

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

Compounded thus, of 4 of 25.= Ans. 11. Express 5] furlongs in ti.e fraction of a mile.

Thus, 5)= of = Ans. 12. Recluce of an English crown, at 6s. 8d. tu the fraction of a guinea at 28s. 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 denoininator 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 of a pound ?

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

1 3

Ans. Sqrs. 3lb. 1oz. 12 dr. 3. Find the value of 1 of 3s. 60 Ans. 3s. vid. 4. How much is of a pound avoirdupois ? 1998

Ans. 7oz. 10dr. 5. How much is of a hhd. of wine ? Ans. 45 gals.

34 6. What is the value of 15 of a dollar ?

Ans, 5s. 71d. 7. What is the value of its of a guinea ? Ans. 188.

a

8. Required the value of 10% of a pound apothecaries.

Ans. 2oz. Sgrs. 9. How much is of 5l. 9s. ? Ans. £4 15s. 54d. 10. ilow much is of of of a hhd. of wine ?

Ans. 15gals. Sats.

a

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 Ib. 3 oz. to the fraction of a cwt.

Ans.

195

39

Ans.

2. Heduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton.

Ans. It 3. Reduce 16s. to the fraction of a guinea.

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

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

8 02.

*Ans. I

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 numrrators written over the common de. nominator, will be the sum of the fractions required.

EXAMPLES.

1. Add 5) and of together.

辛
5}= and of 1=*

} Then 41 314 reduced to their least common denominator

by Case VI. Rule II. will become Then 132+18-+-14=*=635 or 6 Answer.

18

2. Add and together
3. Add i and together.
4. Add 12 3 and 4 together.
5. Add of 95 and 7 of 141 together.

Ans. 15

Ans. If
Ans. 2011
Ans. 447

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

6. Find the sum of 51 7 and 15.
I find the sum of and to be t=1}}

Then ijo +5+7+15=2811 Ans. 7. Add 1 and 17 together.

Ans. 17 is 8. Add 25, 84 and off of 1

Ans. SSS

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 fracfion by Case VIII. in reduction, and then add them in their proper

terms. 9. Add of a shilling to of a pound. 1st Method.

2d Method. of b=

if.=78. 6d. Oqrs. Then rotfritt

s. 30 6 3 is 8s. Od. 3 qrs. Ans. Ans. 8 0 3

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

Ans. 7oz. 4pwt. 13 gr. 11. Add of a ton, to % of a cwt.

Ans. 12cwt. Iqr. 8lb. 12,70z. 12. Add of a mile to jo of a furlong.

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

콩 gether.

Ans. 1540yds. 2ft. 9in. 14. Add 1 of a week, } of a day, of an hour, and of a migrate together. Ans. ada. Zho. 30min. 45sec.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.* PREPARE the fractions as in Addition, and the difference of the numerator's written above the cominon de. nominator, will give the difference of the fraction required

EXAMPLES.

7

2 1

11 42 31 278

5 378

10 17T

13

1. From take of
f of j=it=ii Thien i and 7

=7 급

Therefore 97=1= the Ans. 2. From take

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

1315 5. What is the difference of 14 and 17 ? 6. What differs is from } ? 7. Froin 144 take of 19 8. From take 116

O remains. 9. From 1 of a pound, take of a shilling. of ibstie: Then from ti£take. Ans. jik.

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

10. From is f. take 37 shilling. Ans. 5s. 6d. 2 qrs. 11. From of an oz. take of a pwt.

Ans. liput. Sgr. 12. From } of a cwt. take te of a lb.

Jins. Igr. 27lb. 6oz. 10 dr. 13. From Sį weeks, take of a day, and fofof of an hour.

Ans. 3w.'4da. 12hv. 19min. 17&sec

20

5
10

per terms.

2

*In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to iinproper fractions, subtract the numerator of the lower fraction from the common denoniinator, 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 ng the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

MULTIPLICATION OF VULGAR FRACTION.

RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

EXAMPLES.

28

1. Multiply by

Answers. H= 2. Multiply by 3. Multiply 5. by 4. Multiply of 7 by

31 5. Multiply its by 2 6. Multiply of 8 by 1 of 5 7. Multiply 7. by 91 8. Multiply of by of s

13 9. What is the continued product of of 5, 7, 54 and of?

Ans. 436

5 12

13 694

DIVISION OF VULGAR FRACTIONS.

RULE. PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication :- The products will be the quotient required.

EXAMPLES.

-= Ans.

4 X 5 1. Divide 4 by #

Thus,

3 X 7 2. Divide 17 by

Answers. 10 3. Divide of by

各 4. What is the quotient of 17 by $?

599 5. Divide 5 by 1o

74 6. Divide of off by of it

35 7. Divide 45 by of 4

235 8. Divide 71 by 127 9. Divide 5205} by of 91