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83. To reduce a compound number to a simple concrete number.

EXAMPLES.

1. Reduce 43 £ 2 s. 4 d. to pence; 8 m. 3 fur. 25 r. to rods; 63 gal. 2 qt. 1 pt. to pints.

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MODEL FOR RECITATION.

(1) PROBLEM.-How many pence in 13 £ 2 s. 4 d? (2) REDUCTION.-Since there are 20 s. in 1 £, in 13 £ there are as many shillings as are represented by the product of 13 multiplied by 20 (see 37, example 43. REMARK), or 260 shillings; 260 s. and 2 s. are 262 shillings. Since there are 12 d. in 1 s., in 262 shillings there are as many pence as are represented by the product of 262 multiplied by 12, or 3144 pence; 3144 pence and 4 d. are 3148 d.

(3) RESULT.-Hence, in 13£ 2 s. 4 d. there are 3148 d.

RULE.

Arrange the simple numbers composing the compound numbers in a line, and over each simple number place the number connecting it with the next higher simple number, as given by the Table.

Multiply the units of the highest value by that number which stands over the next lower units, and to the product

add the same lower units; then multiply the sum by the number standing over the next lower units, adding the same lower units, and continue the work till the lowest units given have been added.

2. Reduce 5 lb. 9 oz. 8 dr. to drams.

Ans. 1432 dr. 3. Reduce 131b. 5 oz. Troy to grains. Ans. 77280 gr. 4. Reduce 3 m. 5 fur. to feet. Ans. 19140 ft. 5. Reduce 21. 4 fur. 18 r. to yards. Ans. 11539 yd. 6. Reduce 5 acres 3 roods to sq. yards.

Ans. 27830 sq. yd.

7. Reduce 9 cu. yd. 17 cu. ft. to cu. inches.

Ans. 449280 cu. in.

8 Reduce 6 days 8 hours to seconds.

Ans. 547200 sec.

9. In 4 tons 6 cwt. 2 qr. 17 lb. 9 oz., ounces?

how many

Ans. 138681 oz.

10. Find the number of inches in 5 miles 6 furlongs 22 yards. Ans. 365112 in. 11. How many seconds are there in 1 day 5 h. 48 m. Ans. 107310 sec. 12. How many farthings in 3 sovereigns, 3 halfsovereigns, and 3 crowns?

30 sec.

Ans. 5040 far. 13. In 1 T. 1 cwt. 1 qr. 1 lb. 1 oz. 1 dr., how many drams? Ans. 544273 dr. 14. In 1 m. 1 fur. 1r. 1yd. 1 ft. lin., how many inches? Ans. 71527 in. 15. In 3° 25′ 30′′ how many seconds? Ans. 12330". 16. In 365 d. 5 h. 48 m. 47.57 sec., how many seconds?

Ans. 31556927.57 sec.

17. In 25 dol. 3 cts. 7 m., how many mills.

Ans. 25037 mills.

18. In 376 dol. 8 m. how many mills?

Ans. 376008 m.

84. To reduce a simple concrete number to a com

pound number.

EXAMPLES.

1. Reduce 3148 pence to £. s. d.; 2705 rods to m. fur. r.; 509 pints to gal. qt. pt.

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(1) PROBLEM.-How many £. s. d. in 3148 pence? (2) REDUCTION.-Since there are 12 d. in 1 s., there are as many shillings in 3148 d. as are represented by the quotient of 3148 divided by 12; that is, 262 s. 4 d. Since in 1 £ there are 20 s., in 262 s. there are as many pounds as are represented by the quotient of 262 divided by 20; that is, 13 £. 2 s.

(3) RESULT.-Hence, in 3148 d. there are 13 £. 2 s. 4 d.

RULE.

Divide the given number by that number which connects it with the unit of the next higher value, as learned from the Table, placing the remainder, if there be any, to the right.

Continue the work till the unit of the highest value is reached, or, till the next divisor would be greater than the dividend.

The last quotient and the several remainders, written in the order of their unit values, will be the compound number.

2. Reduce 4903 far. to a c. n. Ans. 5£ 2s. 1 d. 3 far. 3. Reduce 6265 gr. to a c. n.

Ans. 1 lb. 1 oz. 1 dwt. 1 gr.

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Ans. 6 hhd. 7 gal. 3 qt. 0 pt. 1 gi.

13. Reduce 235 pt. to bu. pk. qt. pt.

Ans. 3 bu. 2 pk. 5 qt. 1 pt.

14. Reduce 31556927.57 sec. to a c. n.

Ans. 365 d. 5 h. 48 m. 47.57 sec.
Ans. 4 d. 4 h.
Ans. 3° 25' 15".

15. In 100 hours how many days?
16. In 12315" how many °!"?
17. In 3427 mills, how many dollars, cents, and mills?

Ans. $3.427 18. If 5 £ 2 s. 1 d. 3 far. be equally divided among 9 boys, how many farthings will each boy get?

Ans. 5447.

19. What is the value of 1 lb. 3 oz. of gold at $16 per ounce? (Avoirdupois weight.)

Ans. $304.

20. What is the value of 5 oz. 16 dwt. 4 gr. of jewelry at 5 cents per grain? Ans. $139.40 21. A gold chain weighs 5 oz. 7 dwt. 13 gr. What is the value of the chain at 9 cts. per grain? Ans. $232.29

ADDITION OF COMPOUND NUMBERS.

85. To add compound numbers.

EXAMPLES.

1. Add together 5 A. 2 R. 21 r.; 9 A. 3 R. 25 r., and 12 A. 1 R. 23 r. Ans. 27 A. 3 R. 29 r. 2. Add together 7 bu. 3 pk. 5 qt.; 9 bu. 2 pk. 7 qt., and 23 bu. 1 pk. 3 qt. Ans. 40 bu. 3 pk. 7 qt.

3. Add together 5 m. 2 fur. 21 r.; 9 m. 3 fur. 25 r., and 12 m. 1 fur. 23 r.

Ans. 26 m. 7 fur. 29 r.

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REMARK 1.—The manner of conducting the recitation is apparent.

RULE.

(1.) Write the units of the same name under each other, and place over each column that number which connects its unit with the next higher unit.

(2.) Add the column of units of the least value, and divide the sum by that number which stands over it, placing the remainder under the column.

(3.) Add the column of units of the next higher value, including the quotient of the preceding division, and divide by the number which stands over it, placing the remainder

under the column.

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