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3. What part of an ounce is of a scruple?
4. What part of a ton is of an ounce?
5. What part of a mile is § of a rod?
6. What part of an acre is

of a square foot?

7. What part of a day is 8. What part of 3 acres is



Ans. 294030.
Ans. 1323

of a quart?

9. What part of 3hhd. is 10. What part of of a solid foot is a cube whose sides are each of a yard square? Ans. 2.

18) 140 (7s.




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

Ex. 1. What is the value of 7 of 1 £?

18) 168 (9d.




18) 24 (1 far.





Ans. boo
Ans. to

of a second?

of a square foot?




Since 1£ =
of a shilling is
and since 1d. :



Ans. 140

Ans. oooo

11far. Therefore

Ans. 7s. 9d. 14far.

20s., of a £ is
and since 1s.
of 12d.

of 12d.,


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.



188d.=9&d.; of 4far. far. 7s. 9d. 11far.



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?

2. What is the value of 3 of a cwt.?

3. What is the value of 4. What is the value of


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5. What is the value of of a mile?

Ans. 1fur. 31rd. 1ft. 10in. 6. What is the value of of an ell English?

Ans. 1qr. 15na. 7. What is the value of of a hogshead of wine?

Ans. 18gal.

8. What is the value of of a year? Ans. 232da. 10h. 21m. 49sec. 172. To reduce one denominate number to the fractional part of another.

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


Ans. 3qr. 2lb. 12oz. 7jdr. of a yard? Ans. 3qr. 0žna.

of an acre?

= 512

Ans. £.

3s. 6d. 23far.

Since numbers compared must be of the same unit, we reduce the 3s. 6d. 23far. 1£ to thirds of far., the lowest 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

= 2880


Ans. 1R. 28p. 155ft. 82 in.

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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.


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

3. What part of a ton is 4cwt. 3qr. 12lb.?

4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ?

Ans. Jo Ans.



5. What part of 2A. 2R. 32p. is 3R. 24p.?
6. What part of a hogshead of wine is 18gal. 2qt.?



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. 127. 8. From a piece of cloth containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken ? Ans. .

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


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. 0far.


Value of £
Value of s.



d. far.

17 1 29
9 11
17 1. 0

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


= TO £.

9 × 20

kê tro£ = 138£178. 11d. Ofar. fractions and find the value of their sum. (Art. 171.)

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


2. Add of a pound to of a shilling.

Ans. 7s. 11d. 349far. 3. Add together 1 of a ton, of a ton, and of a cwt. Ans. 1T. 14cwt. 1qr. 5§§. 4. Add together of a yard, § of a yard, of a quarter. Ans. 1yd. 2qr. 2na. 0 in.

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


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

Ans. 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 1 What is the second ?


174. To subtract fractional parts of denominate numbers. Ex. 1. From & of a pound take

of a pound.

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2. From of a ton take of a cwt.

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.)


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

3. From of a mile take of a furlong. Ans. 5fur. 33rd. 5ft. 6in.

4. From 1f 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. 13 pt.

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 the time lost.

of the remaining time; required Ans. 137da. 11h. 13m. 149 sec.

8. From 11 acres, 33 poles, 1016 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?


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

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

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

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

of a barrel Ans. $2.34.


4. If $786.63 are paid for a cargo of wheat, what is the cost of the cargo? Ans. $665.61. Ans. $80.20%. Ans. 13£ 9s. 0ğd.

5. What is

6. What is

7. What is

of $ 87.50?

of 17£ 18s. 9d.?

of 3T. 16cwt. 3qr. 23lb.?

Ans. 2T. 3cwt. 3qr. 234lb.
Ans. 12A. 1R- 28p.

8. What is

of 27A. 3R. 33p.?

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

Ans. $4.40.

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ILLUSTRATION. - If of a yard cost $3.52, will cost of $3.52, or $0.88; and ğ, 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? Ans. $17.80.

12. When of a cargo of flour cost $ 665.50, what sum will for the whole cargo? pay Ans. $786.50.

13. If $73.60% are paid for 1 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,

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