́quarts, 2 pints and 4 gills; therefore, our compound fraction is of 3 of 4 of 2 of 4, which, multiplied by the given fraction, becomes of 2 of 3of 4 of 2 of 4; this becomes, after cancelling like factors, I gill.

4. Reduce 14 of a yard to a fraction of a mile.

Ans. 400.

5. Reduce of a gill to the fraction of a gallon.
Ans. 96

6. Reduce 39 of a pound to the fraction of a ton.
Ans. 3360

7. Reduce of a mile to the fraction of a foot.

Ans. 1760 feet.

8. Reduce of of of a yard to the fraction of a Ans. 36960

mile.

9. Reduce of of of a gallon to the fraction of a Ans. 4.

gill.

10. Reduce of 4 of a hogshead of wine to the fraction of a gill. Ans. 172-597+. 11. Reduce of 4 of 4 yards to the fraction of an inch. Ans. 23-344. 12. Reduce of of a farthing to the fraction of a shilling. Ans. 16. 13. Reduce of an ounce to the fraction of a pound avoirdupois. 14. Reduce of of 1 rod to the fraction of an inch,

of a foot, and of a yard.

Ans. 14.

27212915 inches.

Ans.

231

1053 feet.

339 yards.

15. Reduce of of 1 hour to the fraction of a month

of 30 days, and to the fraction of a year of 365 days.

Ans. {Too of a month.

26280 of a year.

90. To find what fractional part one quantity is of another of the same kind, but of different denominations.

-

Suppose we wish to know what part of 1 yard, 2 feet 3 inches is. We reduce 1 yard to inches, which gives 1 yard 36 inches; we also reduce 2 feet 3 inches to inches, which gives 2 feet 3 inches=27 inches. Now, it is obvious that 2 feet 3 inches is the same part of a yard that 27 is of 36, which is 7-2.

Hence, we deduce this

RULE.

Reduce the given quantities to the lowest denomination mentioned in either. Then take the number which expresses the quantity of which the other is to be the fractional part, for a denominator, and the other number for a numerator, and the fraction thus formed will denote the fractional part sought.

EXAMPLES.

1. What part of £3 4s. 1d. is 2s. 6d.?

In this example, the quantities, when reduced, become £3 4s. 1d. 769d.; and 2s. 6d. 30d.; therefore, is the fractional part which 2s. 6d. is of £3 4s. 1d.

2. What part of 3 miles, 40 rods, is 27 feet 9 inches?

3 What part of a day is 17 minutes 4 seconds?

4. What part of $700 is $5.30?

Ans. 37

Ans. 45.

Ans. 7530.

5. What fractional part of 2 hogsheads is 3 pints?

6. What part of $3 is 2 cents?

Ans. 36.

Ans To

7. What part of 10 shillings, 8 pence, is 3 shillings

penny?

37

Ans. 1.

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

9. In the Eagle there are 232 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 41+ 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.

13. The imperial gallon contains 2771 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 minutes, 48 seconds. By what part of a day does this exceed 365 days? Ans. 188.

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

of of a quarter

of a

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

The of a quarter

Again, of a quarter equals of 4 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 50 of a minute, equals 12 minutes.

Ans. 1 quarter, 24 nails.

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

Ans. 1 furlong, 20 rods.

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

5. What is the value of of 14 miles, 6 furlongs?

6. What is the value of

each?

Ans. 1 quarter, 12 pounds.

Ans. 2 miles,

3 furlongs, 26 rods, 11 feet.

of of 2 days of 24 hours Ans 9 hours, 36 minutes.

Ans. 5 minutes, 37 seconds.

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

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

Ans. 5h. 48m. 48sec.

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

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

Ans. 13oz. 21tdr.

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?

1. Add

EXAMPLES.

of a shilling to 4 of a pound.

25

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

II. of a pound of 2o of a shilling=5 shillings, which, added to of a shilling, gives 5=26 of a shilling for the sum.