SECTION XXX.

REDUCTION OF COMPOUND NUMBERS. 335.--1. How many inches are 6 feet 5 inches?

SOLUTION. Since 1 foot is 12 inches, 6 feet must be 6 times 12 inches, or 72 inches; and 72 inches plus 5 inches are 77 inches. Hence, 6 feet 5 inches are 77 inches.

2. How many cord feet in 5 cords 6 cord feet? 3. Reduce 1 peck 3 quarts 1 pint to pints.

4. Reduce 2 tons 9 hundred-weight to hundred-weights. 5. How many feet in 77 inches?

SOLUTION. Since 12 inches are 1 foot, 77 inches must be as many feet as 12 inches are contained times in 77 inches, which are 6 times, with a remainder of 5 inches.

are 6 feet 5 inches.

6. How many cords in 46 cord feet?

7. Reduce 37 gills to quarts.

8. How many pecks in 33 pints?

Hence, 77 inches

9. How many tons are 49 hundred-weight?

10. What will 2 gallons 3 quarts of vinegar cost, at 5 cents a pint?

11. A wall is 4 yards 6 inches long; what is its length in inches?

DEFINITIONS.

336. A Simple Denominate Number is a number expressed in units of only one denomination.

Thus, 5 yards is a simple denominate number.

337. A Compound Denominate Number is a number expressed in units of more than one denomination.

Thus, 6 yards 7 inches is a compound denominate number.

338. Reduction of Denominate Numbers is the process of changing them from one denomination to another without changing their value.

339. Principle.-Denominate numbers are reduced to lower_denominations by multiplication, and to higher denominations by division.

REDUCTION DESCENDING.

340. Reduction Descending is the process of changing a number to an equivalent number expressed in units of a lower denomination.

WRITTEN EXERCISES..

341.-1. How many pints are 3gal. 2qt. 1pt.?

3 gal. 2 qt. 1 pt.

4

14 qt.

2

SOLUTION. Since 1 gallon is 4 quarts, 3 gallons must be 3 times 4 quarts, or 12 quarts; and 12 quarts plus 2 quarts are 14 quarts.

Since 1 quart is 2 pints, 14 quarts must be 14 times 2 pints, or 28 pints; and 28 pints plus 1 pint are 29 pints. Hence, 3gal. 2qt. 1pt. are 29pt.

29 pt.

2. Reduce 4yd. 2ft. 7in. to inches.

3. Reduce 5 sq. yd. 7 sq. ft. 27 sq. in. to square inches.

342. Rule for Reduction Descending.-Multiply the number of the highest denomination given, by that rumber of the next lower which equals one of the higher, and to the product add the number, if any, of the next lower denomination.

Reduce this result in like manner, and so proceed until the given number is reduced to the required denomination.

PROBLEMS.

343.-1. Reduce 3° 4' 16" to seconds. 2. Reduce 3A. 140P. to square yards. 3. Reduce 1mi. 138rd. 4yd. to feet.

4. Reduce 100 cu. yd. 20 cu. ft. 100 cu. in. to cubic inches.

5. Reduce 7bu. 3pk. 5qt. to quarts.
6. Reduce 9oz. 11pwt. 17gr. to grains.
7. Reduce 4T. 9cwt. 9lb. to ounces.
8. Reduce 1hhd. 20gal. 3qt. to quarts.

9. How much must be paid for 1A. 40 sq. rd. of land, at $1.50 per square rod?

10. What will it cost to make 1mi. 100rd. of fence, at $1.20 a rod ?

11. How much must be paid for 13 63 29 of medicine, at 5 cents a grain?

12. How many hours has a man lived who is 50y. 125d. old, allowing 365 days to the year?

REDUCTION ASCENDING.

344. Reduction Ascending is the process of changing a number to an equivalent number, expressed in units of a higher denomination.

WRITTEN EXERCISES.

345.—1. How many gallons are 29 pints?

Since 4 quarts are 1 gallon, 14 quarts must be as many gallons as 4 quarts are contained times in 14 quarts, which are 3 times, with a remainder of 2 quarts. Hence, 14 quarts are 3 gallons 2 quarts; and 29 pints are 3 gallons 2 quarts 1 pint.

2. Reduce 175 inches to yards.

3. Reduce 7515 square inches to square yards. 4. Reduce 37038 seconds to hours.

346. Rule for Reduction Ascending.-Divide the given number by that number of its denomination, which equals one of the next higher, and write the remainder, if any.

Divide the quotient in like manner, and so continue until the given number is changed to the required denomination.

The last quotient, with the remainders, if any, written in their order from the highest to the lowest, will be the required number.

Reductions Descending and Ascending, being performed by opposite processes, are proofs of each other.

PROBLEMS.

347.-1. Reduce 11056 seconds to degrees. 2. Reduce 18755 square yards to acres.

3. Reduce 7569 feet to miles.

4. Reduce 4700260 cubic inches to cubic yards. 5. Reduce 275 quarts to bushels.

6. Reduce 4601 grains to ounces.

7. Reduce 142494 ounces to tons.
8. Reduce 335 quarts to hogsheads.

9. How many acres of land will $300 purchase, at $1.50 per square rod?

10. How many miles of fence, at $1.20 per rod, can be built for $504?

11. How many ounces of medicine, at 5 cents a grain, can be bought for $44?

12. How many years has a man lived who is 438300 hours old, allowing 365 days to a year?

348. TEST QUESTIONS.-1. What is a denominate number? A simple denominate number? A compound denominate number?

2. What is reduction? The principle of reduction ?

3. What is reduction descending? How is a number reduced from a higher to a lower denomination?

4. What is reduction ascending? How is a number reduced from a lower to a higher denomination?

5. Why are reductions descending and ascending proofs of each other?

SECTION XXXI.

ADDITION OF COMPOUND NUMBERS. 349.-1. What is the sum of 6 yards 1 foot, and 4 yards 1 foot?

2. Add 6 cords 3 cord feet, and 5 cords 6 cord feet.

SOLUTION.-6 cords 3 cord feet, and 6 cord feet, are 6 cords 9 cord feet, or 7 cords 1 cord foot; 7 cords 1 cord foot, and 5 cords, are 12 cords and 1 cord foot.

3. Add 10 bushels 2 pecks, and 4 bushels 3 pecks. 4. If you should buy in one month, 4 gallons 3 quarts of kerosene, and the next month, 3 gallons 3 quarts, how much would you buy in all?