346. To add and subtract denominate fractions. ILL. Ex. Add 1⁄2 rd. with § yd.

Explanation. - These fractional numbers, being of different denominations, must first be changed to numbers of the same denomination. This may be done either by changing both fractional numbers to num

OPERATION.

rd.3 yd. = 33 yd. # yd. Ans. 4 yd.

11. Add

bers of lower denominations (Art. 340), by changing § of a yard to part of a rod (Art. 342), or by changing of a rod to yards. Here the operation is by the last method.

EXAMPLES.

of a day and of an hour. 12. Add of a gallon and 21 pints.

13. Add

Ans. 12 h.

14. If of a journey of of a mile a man has 7 rods yet to travel, how far has he travelled? Ans. 205 rd.

15. John sawed } of a cord of wood before tea and 1⁄2 of a cord foot after tea, how many cord feet did he saw in all ?

16. How much more did he saw before tea than after? 17. Add .25 sq. rd. and 3.36 sq. yd. Ans. 10.924 sq. yd. 18. Add .62 lb. and 5 oz. (Av. weight).

19. How much more is there in a lump of gold which weighs of a pound than in one which weighs 19.5 pwts.?

For Dictation Exercises, see Key.

347. ILL. Ex. taining 2 gallons 3

OPERATION.

gal.

2

qt.

3

5

MULTIPLICATION.

How much milk is there in 5 cans, conquarts each?

Explanation.3 quarts multiplied by 5 equals 15 qt. or 3 gal. with 3 qt. We express the 3 quarts, and reserve the 3 gallons to add to the next product. 2 gal. mul

Ans. 13 gal. 3 qt. tiplied by 5 equals 10 gal.; 10 gal. with 3 gal. are 13 gal. Ans. 13 gal. 3 qt.

Compare multiplication of compound numbers with multiplication of simple numbers, and make a rule for the multiplication of compound

numbers.

EXAMPLES.

1. If 1 cubic foot of water weighs 62 lbs. 8 oz., how much will 35 cubic feet weigh?

Ans. 1 T. 187 lb. 8 oz. 2. If a person in going once to school walks 19 rods 4 yards, how far does he walk in going twice and returning? Ans. 78 rd. 5 yd.

3. How much glass is there in 24 windows of 12 panes each, if each pane contains 2 sq. ft. 8 sq. in. ?

4. How far does a locomotive run in a day, that makes 4 trips of 27 m. 16 rd. 4 yd. each way?

5. How many revolutions are made in 1 hour by a wheel that turns 300° 40′ in every second of time? Ans. 3,006§.

6. In how many days can I stitch 12 dozen garments, allowing 2 h. 15 m. to each, and 8 working hours to a day? 7. How many cubic yards of earth are there in 15 loads each containing 1 cu. yd. 20 cu. ft.?

NOTE.-A cubic yard of earth is generally considered a load

8. Multiply 5 oz. 3 pwt. 6 gr. by 21.

For Dictation Exercises in Multiplication, see Key.

DIVISION.

348. ILL. Ex. If 14 cd. 6 cd. ft. 12 cu. ft. of wood are divided equally among 5 persons, what will each person

receive?

OPERATION.

cd. cd. ft. cu. ft.

5) 14

6

12

Explanation.-Dividing what we can of the dividend, and have cords as the result, we have 2 cords in the quotient and a remainder of 4 cords, which equal 32 cord feet. 32 cd. ft.+6 cd. ft. = 38 cd. ft. Dividing as before, we have 7 cord feet in the quotient and a remainder of cord feet, which equal 48 cubic feet. 48 cu. ft.+ 12 cu. ft. cu. ft. 1 fifth of 60 cu. ft. 12 cu. ft.; therefore each person will receive 2 cd. 7 cd. ft. 12 cu. ft.

2 7

12

= € 60

Compare division of compound numbers with division of simple numbers, and make a rule for the division of compound numbers.

EXAMPLES.

1. Divide 4 lb. 5 oz. 18 pwt. 2 gr. by 6.

Ans. 8 oz. 19 pwt. 163 gr.

2. Divide 5 T. 290 lb. by 8.

Ans. 1,286 lb. 4 oz.

3. What is 1 eleventh of 29° 42′ 32" ?

4. What is 1 twenty-fifth of 1 sq. m. 35 A. 2 sq. rd. 49 sq. ft.? Ans. 27 A. 2337 sq. ft.

5. If a piece of land containing 48 A. 150 sq. rd. 8 sq. yd. is divided into 100 house-lots of equal size, what is the size of each lot? Ans. 78 sq. rd. 9 sq. yd.

6. How far will a boy walk in a minute who walks 4 miles in an hour? Ans. 21 rd. 1 yd. 2 ft. 7. If a person consumes 10 gallons of milk in 4 weeks, how much does he consume in 1 day?

8. How many 3-pint cans will be required to contain 9 gal. 1 qt. 1 pt. of preserved peaches? Ans. 25.

NOTE.

Change 9 gal. 1 qt. 1 pt. to pints before dividing.

9. If a boy walks 3 m. 40 rd. in an hour, how long will it take him to walk 25 m. 19 rd. ? Ans. 8 hours.

10. How many bins, each containing 4 bu. 3 pk., will be required to hold 242 bu. 1 pk.?

11. Among how many persons may 35 bushels of corn be divided, that each one may receive 2 bu. 1 pk., and how many pecks will remain ?

12. What is 1 eighteenth of 20 y. 5 d. 12 h. 24 min. ? For Dictation Exercises in Division, see Key.

LONGITUDE AND TIME.

349. As there are 360° of longitude in the circumference of the earth, and as the earth turns upon its axis once in 24 hours, it follows that 24 of 360°, or 15° of longitude, must pass under the sun in 1 hour, and of 15°, or 15', must pass under it in 1 minute of time, and of 15′, or 15′′, must pass under it in 1 second of time; therefore a difference upon the earth's surface

of 15° of longitude makes a difference of 1 hour in time,

RULE.-To find the difference of longitude between any two places when the difference of time is given: Multiply the numbers expressing the difference of time between the two places given in hours, minutes, and seconds, by 15. The resulting products will indicate the number of degrees, minutes, and seconds of longitude between the two places.

NOTE. As the earth turns from west to east, the sun reaches the meridian of any place east of us before it reaches ours, and it reaches the meridian of any place west of us after it reaches ours. Hence at any given time of day with us, it is later in the day at all places east of us and earlier in the day at all places west of us.

EXAMPLES.

1. When the difference of time between two places is 5 hours 27 minutes, what is the difference of longitude?

Ans. 81° 45'.

2. At a certain time at Cincinnati the time at Buffalo is 22 min. 8 sec. later; what is the difference of longitude between the two places? Ans. 5° 32'.

3. What is the longitude of Buffalo? (Art. 345.)

Ans. 78° 55′ W.

4. When it is noon at New Orleans, the time at Rio Janeiro is 3 h. 7 min. later; what is the longitude of Rio Janeiro? Ans. 43° 15' W.

5. The time at Edinburgh is 2 h. 14 min. earlier than at St. Petersburg; what is the longitude of Edinburgh?

Ans. 3° 11′ W.

350. From Art. 349 we also derive the following

RULE. — To find the difference of time between two places when the difference of longitude is given: Divide the numbers expressing the difference of longitude between the two places given in degrees, minutes, and seconds by 15. The resulting quotients will indicate the number of hours, minutes, and seconds of time between the two places.

EXAMPLES.

What is the difference of time between

6. New York and Chicago? Ans. 54 min. 301 sec. 7. Boston and Mexico?

Ans. 2 h. 10 min. 48 sec.

8. London and San Francisco ?

9. London and Paris?

10. Canton and Boston?

Ans. 9 min. 447 sec.

Ans. 11 h. 42 min. 50 sec.

11. When it is 2 o'clock P. M. in Washington, what

time is it in Boston?

Ans. 2 h. 23 min. 47 sec. P. M.

12. When it is 8 o'clock A. M. in Philadelphia, what time

is it in Quebec?

Ans, 8 h. 15 min. 50% sec. A. M.