3. What part of an ounce is of a scruple?

4. What part of a ton is of an ounce?

Ans.

5. What part of a mile is § of a rod?

Ans. boo
Ans.

10. What part of of a solid foot is a cube whose sides are

each

of a yard square

?

Ans. 2.

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

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.

171. What is the rule for finding the value of a fraction in whole numbers of a lower denomination?

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

Ans. 1qr. 1na.

Ans. 18gal.

7. What is the value of

of a hogshead of wine?

8. What is the value of

of a year?

Ans. 232da. 10h. 21m. 49 sec.

172. To reduce one denominate number to the frac

tional part of another.

Ex. 1. What part of 1£ is 3s. 6d. 23far.

Ans. £.

Since numbers compared must be of the same unit, we reduce the 3s. 6d. 23far. to thirds of far., the low

est denomination in the question, for the numerator of the required fraction, and 1£ to the same denomination for the denominator. We then reduce this fraction to its lowest terms, and obtain for the

answer.

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

NOTE. The part that one abstract number is of another may be found in like manner.

EXAMPLES FOR PRACTICE.

2. Reduce 4s. 8d. to the fraction of 1£.

Ans. Jo

3. What part of a ton is 4cwt. 3qr. 12lb.?
4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ?

5. What part of 2A. 2R. 32p. is 3R. 24p. ?

Ans..

6. What part of a hogshead of wine is 18gal. 2qt.?

Ans.

172. What is the rule for reducing a denominate number to the fractional

part of any other denominate number of the same kind?

7. What part of 30 days are 8 days 17h. 20m.? Ans. 17.

8. From a piece of cloth containing 13yd. Oqr. 2na. there What part of the whole piece was

were taken 5yd. 2qr. 2na. taken ?

9. What part of 3 yards square are 3 square yards?

Ans. .

Ans..

ADDITION OF FRACTIONS OF DENOMINATE NUMBERS. 173. To add fractions of denominate numbers.

Ex. 1. Add & of a pound to of a shilling.

Ans. 17s. 11d. Ofar.

We find the value of each fraction separately, and add the two values, according to the rule for adding compound numbers. (Art. 101.)

$£++fo £= 1138£ 17s. 11d. Ofar.

=

We first reduce the fraction of a shilling to the fraction of a pound, then add the two

fractions and find the value of their sum. (Art. 171.)

EXAMPLES FOR PRACTICE.

2. Add of a pound to of a shilling.

Ans. 7s. 11d. 349far.

3. Add together 1 of a ton, of a ton, and 4 of a cwt. Ans. 1T. 14cwt. 1qr. 581. 4. Add together of a yard, § of a yard, of a quarter. Ans. 1yd. 2qr. 2na. 01in.

5. Add together of a mile, of a mile, of a furlong. and Ans. 6fur. 29rd. 3yd. 1ft. Offin.

of a yard.

6. Add together of an acre, of a rood, and of a square Ans. 1A. OR. 3p. 169ft. 102§in.

rod.

7. Sold 4 house-lots; the first of an acre, the second ✈ of an acre, the third of an acre, and the fourth of an acre; what was the quantity of land in the four lots?

Ans. 3R. 38p. 45ft.

173. What is the first method of adding fractions of denominate numbers ? What is the second 7

SUBTRACTION OF FRACTIONS OF DENOMINATE NUMBERS.

174. To subtract fractional parts of denominate numbers.

Ex. 1. From of a pound take

of a pound.

Ans. 9s. 10d. 149far.

We find the value of each fraction separately, and subtract one from the other, according to the rule for subtracting compound numbers. (Art. 102.)

We first subtract the less fraction from the greater, and then find the value of their difference. (Art. 171.)

EXAMPLES FOR PRACTICE.

2. From of a ton take of a cwt.

Ans. 11cwt. Oqr. 7,67 lb.

3. From of a mile take of a furlong.

Ans. 5fur. 33rd. 5ft. 6in.

4. From f of an acre take of a rood.

Ans. 3R. 16p. 154ft. containing 100 gallons,

5. From a hogshead of molasses of it leaked out; of the remainder I kept for my family; what quantity remained for sale? Ans. 24gal. Oqt. 13pt.

6. The distance from Boston to Worcester is about 41 miles. A sets out from Worcester, and travels of this distance towards Boston; B then starts from Boston to meet A, and, having travelled of the remaining distance, it is required to find the distance between A and B. Ans. 12m. 6fur. 9rd. 5ft. 9 in.

7. A agrees to labor for B 365 days; but he was absent on account of sickness part of the time; he was also obliged to be employed in his own business of the remaining time; required the time lost. Ans. 137da. 11h. 13m. 149 sec.

8. From 11 acres, 33 poles, 101 feet of land, I sold to A, of the remainder to B, and four house-lots, each 144 feet square, to C; what is the value of the remainder, at 84 cents per square foot? Ans. $3937.8972.

174. What is the first method of subtracting fractions of denominate numbers?

The second?

QUESTIONS TO BE PERFORMED BY ANALYSIS.

1. If one yard of cloth cost $ 4.40, what will of a yard cost?

ILLUSTRATION.

$ 4.40, or $ 0.88; and

If 1 yard cost $4.40, of a yard will cost of will cost 4 times $ 0.88, or $ 3.52, Ans.

2. If a barrel of flour cost $7.80, what will cost?

of a barrel

Ans. $2.34.

3. If a load of hay cost $17.84, what will .of a load cost? Ans. $15.61.

4. If $786.63 are paid for a cargo of wheat, what is the cost of the cargo?

Ans. $665.61.

Ans. $80.208.

Ans. 13£ 9s. 0ąd.

of

Ans. 2T. 3cwt. 3qr. 234lb.

of 27A. 3R. 33p.?

Ans. 12A. 1R- 28p.

8. What is 9. If $3.52 are paid for of a yard of cloth, what is the price of 1 yard? Ans. $4.40.

ILLUSTRATION. If of a yard cost $3.52, will cost of $3.52, or $ 0.88; and §, or a whole yard, will cost 5 times $0.88, or $4.40, Ans.

10. If of a barrel of flour cost $2.34, what will be the cost of a whole barrel? Ans. $7.80.

11. When $15.57 are paid for 3 of a ton of hay, what will 1 ton cost?

12. When

Ans. $17.80.

of a cargo of flour cost $ 665.50, what sum will pay for the whole cargo? Ans. $786.50. 13. If $73.60% are paid for 12 of a ton of potash, what sum must be paid for a ton?

Ans. $80.30.

14. Bought of a bale of broadcloth for 13£ 9s. Oğd.; what would have been the cost of the whole bale?

Ans. 17£ 18s. 9d. 15. If of an acre produce 18cwt. Oqr. 12lb. of hay, what quantity will a whole acre produce? Ans. 77cwt. Oqr. 1lb. 16. Bought of a lot of land containing 12A. 1R. 307p.; what were the contents of the whole lot?

Ans. 27A. 3R. 394p.

17. If of a ton of potash cost $80.20%, what is the value

of a ton?

Ans. $87.50,