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8. What is the value of 198 of a solar day?

Ans. 5h. 48m. 48sec.

9. What is the value of 14 of a pound Avoirdupois ?

10. What is the value of 11. What is the value of

Ans. 13oz. 214dr.

of a bushel? Ans. 34 quarts.

of a year of 365 days?

Ans. 30 days.

12. What is the value of of of of an acre?

Ans. 25 rods.

ADDITION OF DENOMINATE FRACTIONS.

92. So long as fractions are of different denominate values, they cannot be added, any more than integers can of different denominate values. Hence, before seeking to add, it is necessary to reduce them to the same denomination, then, to a common denominator, and apply the rule under ART. 43.

What is the Rule for the Addition of Denominate Fractions?

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pound, which added to of a pound of a pound, gives of a pound for the sum.

II. of a pound of 20 of a shilling 5 shillings, which, added to of a shilling, gives 5-26 of a shilling for the sum.

If our work is right, these two results ought to be of the same value, that is, 13 of a pound must equal 5 shillings. We know that 13 of a pound=13 of 2o of a shilling= 26 of a shilling.

2. Add of a yard, § of a foot, and 3 of a mile.

These fractions, before adding, might be reduced to frac tions of a yard, or of a foot, or of a mile, or of any of the denominate values of Long Measure. But a better way would be to reduce each to its integral denominate value, by Rule under ART. 91.

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Thus of a yard=} of of a foot=1 foot.

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Hence, the sum is 3 days, 16 hours, 15 minutes.

4. Add of a year, of a week,

of a day, together

Ans. 75da. 2hr.

5. What is the sum of of a cwt., of a qr., of a lb.?

Ans. 2qr. 9lb. 9oz. 5 dr.

6. What is the sum of of a bushel, a quart?

7. What is the sum of of a yard, and

8. What is the sum of of a week,

Ans.

of an hour?
9. What is the sum of of a bushel,
of a quart?

of a peck, of

Ans. 5ogt.

of a foot?

Ans. 7 inches.

of a day, and

4da. 21hr. 8m.

of a peck, and

Ans. 3pk. Oqt. Opt.

SUBTRACTION OF DENOMINATE FRACTIONS.

93. As in Addition, the fractions must be first reduced to the same denomination; afterwards they must be brought to a common denominator, and then the work may be completed, by Rule under ART. 44.

What is the Rule for the Subtraction of Denominate Fractions.

EXAMPLES.

1. From of a pound subtract of a shilling.

=

I. of a £= of 20 of a shilling of a shilling. Therefore, -=15-14=23. So that the difference

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of a minute.

is of a pound of 20 of a shilling

200

ling, as before.

23

=

200

2. From of a day subtract

of a day of 24 of an hour=9 hours.

of a minute = cf oo of a second=12 seconds.

Henee, From 9hr. Om. Osec.

Take 0 0 12

Difference 8 59 48

3. From of of 15 yards of cloth, subtract of of one quarter.

nail.

of of 15 yards=5 yards.

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of of one quarter of off of a nail of a

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4. From of 5 acres of land, subtract of 3 roods.

Ans. 2R. 44P.

5. From of an ounce, take of a pennyweight.

Ans. 7pwt. 15gr.

6. From of a hogshead, take † of a quart.

94.

Ans. 6gal. 3qt ŝpt.

EXERCISES IN DENOMINATE FRACTIONS.

1. A person gave

for some thread, and

did he pay for all?

of a pound for a hat, of a shilling of a penny for a needle. What Ans. 3s. 2d. 3+far.

2. What is the value of of a week, of a day, and + of a minute?

Ans. 3da. 20hr. 15sec. of a pound, of an ounce, Ans. 2oz. 13pwt. 34gr. cents, how much is

3. What is the value of and of a pennyweight, Troy? 4. If 4 pounds of sugar cost 43 it per pound?

Ans. 10 cents.

5. If I pay $4.04 for 84 bushels of apples, how much lo I give per bushel? Ans. 46 cents.

6. Four persons, A, B, C, and D, own a ship, of which A owns of of the whole; B owns of as much as A; C owns as much as B; and D owns the remainder. What are the respective parts owned by each?

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7. From of of a day of 24 hours, take of of 11 hour. Ans. 8h. 30m.

8. To of 4 days of 24 hours each, add of of 31 hours Ans. 3d. 9d. 11m. 40sec.

9. A certain sum of money is to be divided between 4 persons, in such a manner that the first shall have of it, the second, the third, and the fourth the remainder, which is $28. What is the sum?

++, which wants just of being the whole; hence, the fourth one had of the whole. Consequently, $28 is of the whole, and the whole is $28x4=$112.

10. A received of a legacy, B, and C the remainder. Now it is found that A had $80 more than B. How much did each receive?

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Hence, $80 was of the whole legacy; the legacy was therefore $80 × 15=$1200.

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11. Eight detachments of artillery divided 4608 cannon balls in the following manner: The first took 72 and of the remainder; the second took 144 and of the remainder; the third took 216 and of the remainder; the fourth took 288 and of the remainder. The balance was equally divided among the remaining four detachments. How many balls did each detachment receive?

Ans. Each received 576 balls.

.2. Five persons divide 100 pounds of sugar as follows The first takes of of the whole; the second takes of of the remainder; the third takes of of the remainder; the fourth takes of of the remainder;

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