4. Reduce 5. Reduce weight.

6. Reduce

7. Reduce

8. Reduce

9. Reduce

10. Reduce 11. Reduce

ure.

12. Reduce

of a scruple to the fraction of a pound.

of an ounce to the fraction of a hundred

of a pound to the fraction of a ton.

of an inch to the fraction of an ell English.
of an inch to the fraction of a mile.

of a barleycorn to the fraction of a league.
of an inch to the fraction of an acre.

of a quart to the fraction of a tun, wine meas

of a pint to the fraction of a bushel. 13. Reduce of a minute to the fraction of a year (365) days).

CASE X.

To reduce fractions of a higher denomination to a lower.

= 640 3s.

× 22 = 1} =

d. Ans. as many parts of a shilling in parts of a pound; therefore, of a shilling.

20 =

=

of a pound?

We explain this question in As the following manner. shillings are twentieths of a pound, there will be 20 times to of a pound, as there are of a pound is equal to And as pence are twelfths of

of

a shilling, there will be twelve times as many parts of a penny in of a shilling, as there are parts of a shilling; therefore, of a shilling is equal to of 42 = 13 = 3 of a penny, Ans.

12

The operation of this question may be facilitated in the fol lowing manner.

RULE.

60 × 2 × 12 = 48=3d. Ans.

- Let the given numerator be multiplied by all the denominations between it and the one to which it is to be reduced; then place the product over the given denominator and reduce the fraction

lowest terms.

to its

bo of a pound to the fraction of a farthing,
of a pound troy to the fraction of a grain.
of a pound, apothecaries' weight, to the

2. Reduce 3. Reduce 4. Reduce fraction of a scruple.

5. Reduce 6. Reduce

of a cwt. to the fraction of an ounce.
of a ton to the fraction of a pound.

7. Reduce

8. Reduce TT0's

of an ell English to the fraction of an inch. of a mile to the fraction of an inch.

9. Reduce 1140480 of a league to the fraction of a barley

corn.

10.

Reduce 5090560 of an acre to the fraction of an inch. 11. Reduce of a tun of wine measure to the fraction of a quart.

12. Reduce

of a bushel to the fraction of a pint.

13. Reduce 4207680 of a year to the fraction of a minute.

CASE XI.

To find the value of a fraction in numbers of a lower denomination.

1. What is the value of of a £. ?

By Case IX.

1qr.

=

=

£. = 3 × 40 = £is. 55s.; and s. = ffd. = 5, 5d.; and d. X = 29qr.= Ans. 5s. 5d. 1qr.

=

This question may be analyzed thus:- If 1£. is 20s., of a £. is of 20s. 55s.; and if ls. is 12d., of a shilof 12d. = 55d.; and if 1d. is 4qr., of a penny is 1qr., Answer, as before.

ling is

of 4qr.

Or, it may be performed in the following manner.

OPERATION.

3

20
11)60(5s.

55

5

12

11)60(5d.

RULE.

In this operation, it will be perceived that we multiply the numerator of the fraction by the successive lower denominations, beginning with the highest, and divide each product by the denominator.

From these illustrations, we derive the following

Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator; if any thing remain, multiply it by the next less denomination, and divide as before, and so continue as far as may be required; and the several quotients will be the answer.

2. What is the value of
3. What is the value of

24

Ans. 3 d.

of a shilling? of a guinea, at 28 shillings? Ans. 21s. 9d. 14qr.

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

Ans. 2qr. 15lb. 4oz. 5dr.

5. What is the value of of a lb. avoirdupois ?
香

6. What is the value of of a lb. troy?

7. What is the value of

8. What is the value of

9. What is the value of

Ans. 7oz. 13dr.

Ans. 10oz. 13dwt. 8gr. of a b. apothecaries' weight. Ans. 33 53 19 12 gr.

of a yard ?

Ans. 2qr. Ona. lin.

of an ell English?

Ans. 2qr. 3na. 0țin.

15. What is the value of of a hhd. of wine?

Ans. 6gal. 2qt. 1pt. Ogi.

16. What is the value of 3 of a hhd. of beer?

Ans. 42gal. 17. What is the value of of a year (365 days)? Ans. 174d. 16h. 26m. 5 sec.

18. What is the value of 731

of a dollar?

42

Ans. $7.7412

CASE XII.

To reduce any mixed quantity of weights, measures, &c., to the fraction of the integer.

1. What part of a shilling is 1d.? is 2d.? is 3d.? is 4d. ? 2. What part of a pound is 2s.? 3s.? 4s.? 5s.? 6s.? 9s.? 3. What part of a furlong is 3rd.? 4rd.? 5rd.? 8rd.? 9rd.? 4. What part of a hogshead is 5gal.? 8gal.? 10gal.? 5. What part of a foot is 2 inches? 3in.? 4in.? 5in.? 8in. ?

RULE.

2880

5 1/1

Ans.

In this question, the shillings, pence, farthings, &c. are reduced to elevenths of farthings for the numerator of a fraction. A pound is also reduced to the same denomination, for a denominator. The fraction is then reduced to its lowest terms.

- Reduce the given number to the lowest denomination it contains for a numerator; and then reduce the integer to the same denomination, for the denominator of the fraction required.

7. Reduce 34d. to the fraction of a shilling.
8. Reduce 21s. 9d. 14qr. to the fraction of a guinea.

Ans. 4

Ans. 7.

9. Reduce 2qr. 15lb. 4oz. 5dr. to the fraction of a cwt.

Ans. T

Ans. $.

10. What part of a pound are 7oz. 1zdr.?
11. What part of a pound troy are 10oz. 13dwt. 8gr.?

Ans. .

12. What part of a pound apothecaries' weight are 33 53

19 12 gr.?

Ans. 13. Ans. 13.

13. What part of a yard are 2qr. Ona. 1in.?
14. What part of an ell English are 2qr. 3na. Oдin. ?

Ans. §.

15. What part of a mile are 6fur. 30rd. 12ft. 8in. 01br.?

Ans.

16. Reduce 35rd. 9ft. 2in. to the fraction of a furlong.

17. What part of an acre are 2R. 6rd. 4yd. 5ft.

18. What part of a square rod are 144ft. 19

19. What part of a cord are 9ft. 1462in. ? 20. What part of a hogshead of wine are 0gi.?

21. What part of a hhd. of beer are 42gal. ? 22. What part of a year (365 da.) are 174d.

sec.?

Ans. §. 1271⁄2in. ? Ans.

SECTION XVII.

ADDITION OF VULGAR FRACTIONS.

CASE I.

To add fractions that have a common denominator.

1. What part of an apple is
2. What part of a dollar is
3. What part of a shilling is

and ? and ? and ?

and?

and? and and? 12, 12, and? 4. What part of an orange is and ? and ? § and ? 5. Add 2, 12, 1, and together.

OPERATION.

3+5+7+11=3§ = 18 = 2 Ans.

In this question, we add the numerators, and divide their sum by the denominator.

RULE.

Write the sum of the numerators over the common denom

inator, and reduce the fraction if necessary.

?

8. Add, 17, 3, 4, and 77 together.

29 49
87

9. Add T44, 144? 19 29 and 117 together. 10. Add 619, 491, 867, and 1 together. 11. Add $81, 71, 998, and 780 together.

Ans. 24.

6. Add 17, 17, 17, 14, 14, and 1 together.
7. Add,, 11, 1, and 18 together.

Ans. 319.

Ans. 219.

Ans. 27.

Ans. 18.

26 631

Ans. 37.

Ans. 12

Ans. 21.
Ans. 212

83

7126 9110 3000 3370

13. Add 331, 3398, and 3998 together.

14. Add 999 888, and

1000

CASE II.

To add fractions that have not a common denominator.

1. What is the sum of 7, 12, 11, and 18?

First Method.

OPERATION.

4)8 12 16 20 4×2×3×2×5=240 common denominator. 2)2 3 4 5