8. What part of 100 acres is 63 acres, 2 roods, 7 rods of land? Ans. 18187.

9. In the Eagle there are 2324 grains of pure gold, and 12 grains of silver, and the same quantity of copper. The silver and copper is each what part, by weight, of the gold? And the silver and copper together is what part of the gold? Silver and copper are each

10. In the United States standard silver coin of one dollar, there are 3714 grains of pure silver, and 414 grains of copper. What fractional part is the copper of the silver? Ans..

11. The silver in standard gold coin is what part of the silver in the same value of standard silver coin?

Ans. T

12. The pound Troy contains 5760 grains, the pound Avoirdupois contains 7000 grains. A pound Troy is what part of a pound Avoirdupois ?

Ans. 14. cubic inches, What part of Ans. 124. minutes, 48 exceed 365 Ans. 188.

13. The imperial gallon contains 277 nearly; the old wine gallon contains 231. the imperial gallon is the old wine gallon? 14. The solar year is 365 days, 5 hours, 48 seconds. By what part of a day does this days?

450

91. To reduce a fraction of any given denomination to whole denominate numbers.

of a

Suppose we wish to know the value of 3 of a yard; we know that of a yard equals of 4 of a quarter quarter 1 quarter of a quarter. The of a quarter. may be considered as a remainder.

Again, of a quarter equals of of a nail 2 nails. Therefore, of a yard equals 1 quarter and 2 nails. Hence, we deduce this

RULE.

Multiply the numerator by the number expressing how many of the next lower denomination make one of the denomination of the fraction, and divide the product by the denominator; multiply the remainder, if any, by the number expressing how many of the next lower denomination make one of that remainder, and again divide the product by the denominator; continue this process until there is no remainder, or until we reach the lowest denominate value. The successive quotients will form the whole denominate numbers required.

EXAMPLES.

1. What is the value of of an hour?

In this example, of an hour equal of oo of a minute, equals 12 minutes.

Ans. 1 quarter, 29 nails.

3. What is the value of of of 1 mile?

Ans. 1 furlong, 20 rods.

4. What is the value of of 5 of 1 cwt.?

5. What is the value of Ans. 2 miles, 6. What is the value of each?

Ans. 1 quarter, 12 pounds. of 14 miles, 6 furlongs? 3 furlongs, 26 rods, 11 feet. of of 2 days of 24 hours Ans. 9 hours, 36 minutes,

7. What is the value of of of of an hour?

Ans. 5 minutes, 37 seconds,

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

Ans. 5h. 48m. 48sec.

9. What is the value of 1 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 4 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?

EXAMPLES.

1. Add of a shilling to

of a pound.
of

of a pound

of a

I. of a shilling equals 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 of a pound must equal 5 shillings.

same value, that is, We know that

26 of a shilling.

of a pound=3 of 4o of a shilling=

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

These fractions, before adding, might be reduced to fractions 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.

Thus

of a yard

of a foot

of a mile

of of a foot=1 foot.

of 12 of an inch=10 inches.

of † of a furlong=3 furlongs.

Therefore, the sum is 3 furlongs, 1 foot, 10 inches.

3. Add of a week, of a day, of a week of 7 of a day

of an hour=3 days, 12 hours.

of an hour.

3

days=3 days+of

of a day of 24 hour 4 hours.

=

of an hour of of a minute

15 minutes.

Hence, the sum is 3 days, 16 hours, 15 minutes. 4. Add of a year, of a week,

5. What is the sum of of a cwt.,

of a day, together.

Ans. 75da. 2hr.

of a qr., ‡ of a lb.? Ans. 2qr. 91b. 9oz. 51⁄2dr.

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,

of an hour?

Ans.

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

of a peck, of Ans. 5gt.

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 2o of a shilling=1⁄2 of a shilling. Therefore, -=25-14=23. So that the difference

is of a shilling=2 of a shilling.

II. of a shilling of of a pound

And

23

5

=

1 20

1-2-3-220. So that the difference

of a pound.

of a shil

of a minute.

is of a pound=23 of 20 of a shilling

200

ling, as before.

200

2. From of a day subtract

of a day

of 24 of an hour-9 hours.

of a minute of of a second=12 seconds.

=

Hence, 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.

1

nail.

of of 15 yards=5 yards.

8

of of one quarter of off of a nail of a

T5

8 15