2. A dry good merchant in Philadelphia purchased 50 pieces of broad cloth, in London, at 1£. 10s. 6d. per yard, what was the cost of the whole, allowing 30 yards to each piece?

3. Five ladies purchased each a silver tea sett, what was the weight of the whole, allowing each sett to weigh 12lbs. 9ozs. 15dwts. 18grs., what did the whole cost, at of a cent per grain? how much is that per ounce? how much per pound?

4. Five ships of the line brought each a cargo of 83Ts. 16cwts. 3qrs. 26lbs., what was the freight of the whole? what would have been the freight if each ship had brought 96Ts. 12cwts. 14lbs. ?

5. A sea captain ordered an apothecary to mix 8 parcels of medicine, each weighing 3s. 93s. 63s. 29s. 18 grains, what was the weight of the whole? what would have been the weight if each parcel had weighed 7s. 63s. 33s. 19s. 12 grains?

6. A farmer sent 8 loads of apples to market, and each of which guaged 45bus. 3pks. 7qts. 1pt. 2 gills, what quantity of apples was sent altogether?

7. How much wine in 9 casks, each measuring 1hhd. 36gals. 2qts. 3gills? i. e., what denominate number can be formed from the whole quantity?

8. What regular denominate number can you form from 12 times the distance between Philadelphia and Trenton, allowing these places to be 27 miles, 5 furlongs, 30 poles, 3 yards, 2 feet, 8 inches, apart?

9. How much land in 9 lots, each measuring 1 acre, 3 rods, 25 poles, 18 square yards, 6 square feet, 96 square inches? what would the whole cost, at the rate of 1 mill for every square inch?

10. How much wood in 12 loads, each measuring 1 cord, 25 cubic feet, 960 cubic inches.

11. What denominate number can you form from 11 times 8s. 23°, 45', 56"? what denominate number can be formed from 20 times the same quantity?

12. Suppose the Earth revolves once in 365 days, 6 hours, 48 minutes, 57 seconds, what time would be required to make 8 revolutions?

DIVISION OF DENOMINATE NUMBERS.

RULE.

Place the DIVISOR on the left of the DIVIDEND; then, First, if the DIVISOR is 12, or less than 12, proceed as in Case I., page 50. Divide the highest denomination first, and reduce the remainder (if any,) to the next lower denomination, to which add the number in the latter, (if any,) and divide the SUM, as before, and so on, till all the denominations are divided, observing to place the respective quotients immediately under the denomination DIVIDED, the result will be the ANSWER.

Second, if the divisor is greater than 12, set down the numbers as in the General RULE for Division, page 45, and proceed in the same manner as directed above, except in the arrangement of the QUOTIENT which will appear on the right of the dividend, and having marked ITs denominations in order, the result will be the ANSWER.

EXAMPLES.

1. Divide 37£. 7s. 5d. 3fars. equally among 9 men, and give the share of each in a proper denominate number.

Here we say, first, 9 is

into 37, 4 times, and 1£. over; second, 1£ = 20s. and 20s. +7s. 27s. which divided by 9, gives 3s.; third, 9 is into 5d. 0 times; but 5d. =20fars. and 20fars. +3fars.

£.

d. far.

=23fars. which contain 9 Thus: 9)37
9)37 7 5 3

2 times, hence, we have

To prove this, we have only to multiply the quotient by the divisor, as already directed,

2. Suppose the freight of 136 cars is equal to 1634Ts. 19cwt. 3qrs. 27lbs. what is the burden of each?

Ts.

cwts. qrs. lbs. Ts. cwt. qr. Ibs.

Thus: 136)1634 19 3 27(12 0

136

1 21136.

55

Ans.

274

272

2

20 i. e., 2 times 20cwt. +19cwt.=59cwt. 136)59(0 cwt.

4 ì. e. 59 times 4qrs.+3qrs.=239qrs.

136)239(1 qr.

136

103

28 i. e. 103 times 28lbs. +27lbs.=2911lbs.

851 206

136)2911(21,5lbs.

272

191

136

55 remains.

3. A merchant purchased 248 yards of cloth, at auction, for which he paid 984.875 dollars, what did the cloth cost him per yard?

$3

744

Here we divide as in whole numbers, 248)984.875(3.971 and fix the POINT in the QUOTIENT, when we bring down the FIRST figure in the DECIMAL, by which we reduce the remainder (240), to tenths, making 2408 tenths which contains the divisor (248), 9 times, and therefore, gives 9 tenths (.9), in the quotient, and by continuing the process, (as in whole numbers,) we obtain $3.971 to $3.97 cts. 1-mill, for the price of a yard, or the ANSWER.

2408

2232

1767

1736

315

248

67 rem.

Hence, the burden of each car = 12Ts. Ocwt. 1qr. 215lbs. Answer.

In the same way solve the following

QUESTIONS FOR EXERCISE.

1. The salary of the PRESIDENT of the UNITED STATES is $25000 per year, what is that per day, allowing 365 days to the year?

NOTE.-In performing the division necessary in the above question, the pupil should in this and every similar case, set down the dividend, placing ciphers in the decimal for three places; thus, $25000.000, and then divide as in example 3, page 160, giving the answer in dollars, cents, and mills.

2. A ferry master labored one year for 520 dollars, what was that per month? what was it per day, allowing 26 working days to the month?

3. A mercantile house in LONDON, freighted in one year, 87 vessels, at an expense of 327568£. 18s. 6d. 1qr., what was the average expense of this house for 1 day, allowing 312 working days to the year?

4. Suppose the 87 vessels, mentioned above, carried 75386Ts. 17cwts. 1qr. 25lbs. of freight, what was the average amount of freight carried by each?

5. Suppose a ship sails 12 degrees, 2 leagues, 1 mile, 7 furlongs, 25 yards, in 13 days, what distance does she sail per day, and how far per hour, allowing 24 hours to each day?

6. Suppose 26 pieces of muslin contain 795 yards, 3qrs. 2 nails, how much is contained in each piece, allowing the pieces to be all of the same size?

7. In 25 lots there are 87 acres, 3 roods, 27 square rods, 29 square feet, what is the average size of each lot?

8. Divide 36revs. 11s. 28°, 36', 47", into 48 parts, and give the denominate number, showing the size of each part?

9. Suppose the sun travels through 12 signs of the zodiac. in a year, what denominate number will show the distance

he travels each day, in the measure?

proper

denominations of circular

10. According to the above statement, how long would it take the sun to travel through one sign, allowing a year to contain 365 days, 6 hours, 48 minutes 57 seconds.

RATIO OF DENOMINATE NUMBERS.

To find the ratio of one denominate number to another, or to find what part of a fraction of one denomination a certain part of another denomination is, when both are of the same kind, i. e., of the same weight, measure, or currency, we have only to observe the following

General RULE.

Reduce both the quantities to the same denomination, and then proceed as in Article XIV., page 70, or mentally, as on page 100.

EXAMPLES.

1. What is the direct ratio of $3 to 3 cents, i. e., what part of 3 cents is three dollars?

Thus: $3=300 cents. Now, the ratio of 3 cents to 3 cents is 1 (one), hence, the ratio of 1 cent to 3 cents is, i. e., of l = to, and therefore, the ratio of 300 cents to 3 cents, is 300 times = to 300=100, wherefore, the ratio of $3 to 3 cents, is 100. Answer.

By equations thus, 3 cents given = to 1, and $3 = to 300 cents required.

2. What is the direct ratio of of a farthing to of a shilling; i. e., of a farthing is what part of of a shilling? Thus, 1s.=48fars., and s. of 48fars.

=

to 48 of