MULTIPLICATION.

256. 1. Let it be required to find the product of 4 bu. 3 pk.

4 qt. 1 pt. multiplied by 7.

OPERATION.

qt.

bu.

pk.

pt.

4

3

4

1

7

Ans. 34 0.

7

1

For convenience, we begin with the lowest denomination to multiply.

7 times 1 pt. are 7 pt., which equal 3 qt. 1 pt.; we write the 1 pt., and reserve the 3 qt. to add to the product of the quarts.

7 times 4 qt. are 28 qt., which, with the 3 qt. added, are 31 qt., or 8 pk. 7 qt.; we write the 7 qt. and reserve the 3 pk. to add to the product of the pecks.

7 times 3 pk. are 21 pk., which, with the 3 pk. added, are 24 pk., or 6 bu. 0 pk.; we write the 0 pk., and reserve the 6 bu. to add to the product of bushels.

7 times 4 bu. are 28 bu., which, with the 6 bu. added, are 34 bu., which we write.

Therefore, the product required is 34 bu. 0 pk. 7 qt. 1 pt.

RULE. Beginning at the right, multiply the number of each denomination in its order, and reduce each product to the next higher denomination; write the remainder, if any, and add the quotient to the next product.

PROOF. The same as in multiplication of simple numbers.

4. Multiply 3 hhd. 57 gal. 3 qt. 1 pt. by 11.

Ans. 43 hhd. 6 gal. 2 qt. 1 pt.

5. Multiply 36 d. 21 h. 48 m. 56 sec. by 6. 6. Multiply 111 C. 7 c. ft. 7 cu. ft. by 12.

Ans. 1343 C. 1 c. ft. 4 cu. ft.

7. Multiply 4 bu. 1 pk. 5 qt. 1 pt. by 7.

Ans. 30 bu. 3 pk. 6 qt. 1 pt.

Explain the operation. Repeat the Rule. What is the Proof?

8. Multiply 17 A. 71 P. by 72.

Ans. 1255 A. 152 P.

9. Multiply 2 lb. 7 oz. 9 pwt. 22 gr. by 50.

Ans. 131 lb. 2 oz. 15 pwt. 20 gr.

APPLICATIONS.

1. What is the weight of 5 hogsheads of sugar, if each weighs 12 cwt. 1 qr. 23 lb. ? Ans. 3 T. 2 cwt. 1 qr. 15 lb. 2. What is the weight of 12 spoons, if each weighs 1 oz. 12 pwt. 20 gr.?

3. If a car will take on 4 C. 56 cu. ft. of wood, how much will 8 cars take on? Ans. 35 C. 64 cu. ft. 4. If the daily motion of the moon is 13° 10′ 35′′, how much is it in 15 days? Ans. 197° 38′ 45′′. 5. If 3 yd. 14 qr. of cloth are required for one garment, how much is required for 14?

6. How much molasses in 25 casks, if each contains 61 gal. 1 qt. 1 pt.? Ans. 1534 gal. 1 qt. 1 pt. 7. If a man travel at the rate of 22 m. 7 fur. 32 rd. 4 yd. per day, how far can he travel in 56 days?

Ans. 1286 m. 5 fur. 32 rd. 4 yd. 8. How much land in 9 farms, each containing 74 A. 87 P. Ans. 670 A. 144 P. 5 sq. yd. 6 sq. ft. 108 sq. in.

4 sq. yd.?

DIVISION.

257. 1. Let it be required to find the quotient of 34 bu. 0 pk. 7 qt. 1 pt. divided by 7.

OPERATION.

wu. pk. qt. pt.

7)34

0

7

1

4 3

4

1

For convenience, we begin with the highest denomination to divide.

One seventh of 34 bu. is 4 bu., with a remainder of 6 bu., equal to 24 pecks; we write the 4 bu., and add the 24 pecks tc the 0 pecks in the dividend.

24 pk. and 0 pk. are 24 pk.; and one seventh of 24 pk. is 3 pk., with a remainder of 3 pk., equal to 24 quarts; we write the 3 pk., and add the 24 quarts to the 7 quarts in the dividend.

Explain the operation.

24 qt. and 7 qt. are 31 qt.; and one seventh of 31 qt. is 4 qt. with a remainder of 3 qt., equal to 6 pints; we write the 4 qt., and add the 6 pints to the 1 pint of the dividend.

pt. and 1 pt. are 7 pt., and one seventh of 7 pt. is 1 pt., which we write.

RULE. Beginning at the left, divide the number of each denomination of the dividend in its order; write the quotient, and reduce the remainder, if any, to the next lower denomination, adding the same to that denomination in the dividend, before dividing it.

PROOF. The same as in division of simple numbers.

4. Divide 6 cwt. 2 qr. 4 lb. 15 oz. 15 dr. by 6.
5. Divide 131 A. 140 P. by 20.

6. Divide 131 lb. 2 oz. 15 pwt. 20 gr. by 50.
7. Divide 1 w. 3 d. 0 hr. 54 m. by 18.
8. Divide 1343 C 1 c. ft. 4 cu. ft. by 12.

Ans. 6 A. 95 P.

Ans. 13 h. 23 m.

9. Divide 100 y. 20 d. 13 h. 25 m. 10 sec. by 11.

Ans. 9 y. 35 d. 1 h. 13 m. 11 sec.

Repeat the Rule. What is the Proof? When the divisor is large, how

is it often convenient to proceed?

258. When both dividend and divisor are denominate numbers,

Reduce them to equivalent numbers of the same denomina tion, and proceed as in division of simple numbers.

10. How many times 5 pwt. 9 gr. in 9 lb. 9 oz. 3 pwt. 12 gr.? Ans. 436.

11. How many times 17 m. 5 fur. 27 rd. in 513 m. 4 fur. 23 rd.? Ans. 29.

APPLICATIONS.

1. If 169 gal. 3 qt. 1 pt. be contained in equal quantities in 9 casks, how much is there in each cask? Ans. 18 gal. 3 qt. 1 pt.

2. If 5 hogsheads of sugar weigh 3 T. 2 cwt. 1 qr. 15 lb., what is the average weight of each?

3. If 2 dozen spoons weigh 7 lb. 6 oz. 13 pwt., what is the weight of each spoon? Ans. 3 oz. 15 pwt. 13 gr.

4. When a ship passes over 99° 22′ 30′′ in 30 days, what is the average progress per day? Ans. 3° 18′ 45′′. 5. If it take 4 bu. 3 pk. of wheat to make a barrel of flour, how many barrels may be made from 456 bushels ? Ans. 96. 6. When a railroad train moves 148 m. 4 fur. in 8 hours, what is the rate per hour? Ans. 18 m. 4 fur. 20 rd.

7. If a man travel 12 m. 3 fur. 19 rd. per hour, in what time can he travel 174 m. 26 rd. ? Ans. 14 hours.

8. When the weight of 27 loads of hay is 30 T. 8 cwt. 2 qr. 23 lb., what is the average weight of a load?

Ans. 1 T. 2 cwt. 2 qr. 4ğ lb.

LONGITUDE AND TIME.*

259. The earth, by turning upon its axis once in 24 hours, causes of 360°, or 15°, of longitude to pass under the sun

When both the dividend and divisor are denominate, how do you proceed

* Optional.

in 1 hour, and

of 15°, or 15′, to pass under it in 1 minute of 15', or 15", to pass under it in 1 second of Hence, the following

of time, and time.

Table.

15° of longitude equal a difference of 1 hour in time.

RULE. Divide the difference of longitude of two places by 15, and the quotient marked hours, minutes, and seconds, instead of degrees, minutes, and seconds, will express their difference of time.

Multiply the difference of time of two places by 15, and the product marked degrees, minutes, and seconds, instead of hours, minutes, and seconds, will express their difference of longitude.

Since the earth turns from west to east, time is later to places east, and earlier to places west of any given meridian.

Examples.

1. When it is 9 o'clock, A. M., at Washington, 77° 2' 48" west of Greenwich, what time is it at the latter place?

Ans. 2 h. 8 m. 11 sec. P. M.

2. If the time at St. Louis, longitude 90° 15′ 10′′ west, is 40 m. 23 sec. earlier than that of a place east, what is the longitude of the latter place? Ans. 80° 14' 34" west.

3. When it was 10 o'clock, P. M., Dec. 31, 1865, in San Francisco, longitude 48° 26′ 45′′ west of New York, what time was it in New York?

Ans. 1 h. 13 m. 47 sec. A. M., Jan. 1, 1866. 4. A captain, at sea, at noon, observed that his chronometer, set to the time of Greenwich, longitude 0, pointed to 2 h. 45 m. 30 sec.; in what longitude was he? Ans. 41° 22′ 30′′ west.

What does the earth, by turning upon its axis, cause? Repeat the Table. The Rule. At what places is time carlier with reference to any given meridian?