6. Reduce go of a ton to the fraction of a pound.

8000

7. What part of an inch is

8. What part of an inch is

25 of an ell English?
1080 of a mile?

9. Reduce 380160 of a league to the fraction of an inch. 10. Reduce 25090560 of an acre to the fraction of an inch. 11. Reduce Tz of a tun of wine measure to the fraction of a quart.

12. What part of a pint is ʊ of a bushel?

13. What part of a minute is 4204650 of a year?

14. Reduce 3200 of a hundred-weight to a fraction of an

ounce.

254. To reduce a denominate fraction from a lower denomination to a higher.

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

Since 12 pence make a shilling, there will be as many shillings as pence, or s. ; and

since 20s. make a pound, there will be as many pounds as shillings, or £. Ans.

RULE.

Divide the fraction by the same numbers that would be employed in the reduction of whole numbers to a higher denomination.

EXAMPLES.

2. What part of a pound is

of a farthing?

of a grain troy?

3. What part of a pound is

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

5. Reduce

weight.

of an ounce to the fraction of a hundred

6. Reduce of a pound to the fraction of a ton.

7. Reduce of an inch to the fraction of an ell English.

8. Reduce of an inch to the fraction of a mile.

9. Reduce of an inch to the fraction of a league. 10. Reduce of an inch to the fraction of an acre.

11. Reduce of a quart to the fraction of a tun, wine measure. of a pint to the fraction of a bushel.

12. Reduce

13. Reduce days).

of a minute to the fraction of a year (3651

14. What part of a hundred-weight is of an ounce ?

3 Ans. 200. 255. To find the value of a fraction in whole numbers of lower denominations.

Ex. 1. What is the value of of a £. Ans. 5s. 5d. 1far.

1s.
12d.

=

11

--

of

20s, of a £. is s. 55s.; and since 12d., of a shilling is fd.=55d.; and, since 1d. 4far., of a penny of 4far. far.1far. Therefore, £. 5s. 5d. 1 far. This is equivalent to multiplying the numerator of the fraction by the numbers required to reduce it to successive lower denominations, beginning with the highest, and dividing each product_by the denominator, as in the operation.

=

RULE. - Multiply the numerator of the given fraction by the number required to reduce it to the next lower denomination, and divide the product by the denominator.

Then, if there is a remainder, proceed as before, until it is reduced to the denomination required.

EXAMPLES.

2. What is the value of

3. What is the value of

Ans. 3 d.

of a shilling? of a guinea, at 28 shillings? Ans. 21s. 9d. 1¿far.

4. What is the value of 71 of a cwt.?

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

Ans. 7oz. 17dr.

Ans. 10oz. 13pwt. 8gr.

7. What is the value of of a lb. apothecaries' weight? Ans. 33 53 19 12 gr.

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

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

Ans. 6gal. 2qt. 1pt. 0gi.

15. What is the value of 3 of a hhd. of beer? Ans. 42gal.

子

16. What is the value of of a year (365 days)?

Ans. 174d. 16h. 26m. 5sec.

17. What is the value of 7

3,3

of a dollar?

42

256. To find the value of whole numbers in a fraction of a higher denomination.

Ex. 1. What part of a £. are 5s. 5d. 19far.?

RULE. Reduce the given numbers to the lowest denomination mentioned in either of them. Then write the number which is the fractional part for the numerator, and the other number for the denominator, of the required fraction.

EXAMPLES.

2. Reduce 34d. to the fraction of a shilling.
3. Reduce 21s. 9d. 14far. to the fraction of a guinea.

Ans. Z

Ans. .

4. Reduce 2qr. 13lb. 10oz. 219dr. to the fraction of a cwt.
Ans. 71.

5. What part of a pound avoirdupois are 7oz. 17dr.?
6. What part of a pound troy are 10oz. 13pwt. 8gr.?

Ans. 8.

7. Express 1 gallon liquid measure as a fraction of a gallon dry measure.

Ans. 11.

Ans. 73

8. What part of a yard are 2qr. Ona. 1-in. ?
9. What part of an ell English are 2qr. 3na. 0țin.?

Ans. .

10. What part of a mile are 6fur. 30rd. 12ft. 8in. ? 11. Reduce 35rd. 9ft. 2in. to the fraction of a furlong.

Ans. 8.

12. What part of an acre are 2R. 6rd. 4yd. 5ft. 1275in.

13. What part of a square rod are 144ft. 19in. ?

Ans.

Ans. 17.

14. What part of a cord are 9ft. 14622in.? 15. What part of a hogshead of wine are 6gal. 2qt. 1pt. 04gi..?

Ans.

16. What part of a pound avoirdupois is 1 pound troy?

Ans. 14.

17. What part of a year (365 days) are 174d. 16h. 26m. 5 sec.?

Ans. 3

By the second operation, we first add the two fractions together, and then find the value of their sum. (Art. 255.)

EXAMPLES.

2. Add together of a ton and of a cwt.

Ans. 13cwt. 2qr.

3. Add together of a yard, of an ell English, and § of a qr.

4. Add together of a mile, of a furlong, and 2o of a yard. Ans. 5fur. 16rd. Oft. 323in.

5. A has three house-lots; the first contains of an acre, the second of an acre, and the third of an acre. How many acres do they all contain ?

Ans. 2A. 1R. 9p. 142ft. 87 in. 6. A man travelled 183 miles the first day, 2311 miles the second day, and 19 miles the third day. How far did he travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 4 in.

SUBTRACTION OF DENOMINATE FRACTIONS.

258. To subtract one denominate fraction from another. From of a £. take of a £.

Ex. 1.

fraction from the greater, and then find the value of their difference (Art. 255.)

EXAMPLES.

2. From of an ell English take of a yard.

Ans. 3qr. Ona. 2in.

Ans. 1fur. 5rd. 10ft. 10in.

3. Take of a furlong from of a mile.