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reduce the decimal as before, and thus continue as far as

necessary.

What is the value

2. Of.9375 of a gal.? 3. Of.1296 of a ton? 4. Of.6783 lb. Ap.?

Ans. 3 qt. 1 pt. 2 gi. Ans. 2 cwt. 59 lb. 3.2 oz. Ans. 83 13 9.6 gr.

Ans. 1 da. 10 h. 13 min. 26.4 sec. Ans. 103 da. 20 h. 13 min. 12 sec. Ans. 58 mi. 182 rd. 5 yd. .82944 in.

5. Of 1.426 of a day? 6. Of .2845 of a year? 7. Of.8469 deg.?

REDUCTION ASCENDING.

CASE I.

454. To reduce a common denominate fraction to a common fraction of a higher denomination. 1. Reduce of a farthing to the fraction of a shilling. SOLUTION.-There are 4 farthings in a penny, therefore of the number of farthings equals the number of pence: there are 12 pence in one shil

OPERATION.

=

ling, therefore of the number of pence equals the number of shillings; hence far. equals ××12 = of a shilling.

Rule.-Express the division by the required divisors, and reduce by cancellation.

Reduce

2. of a gill to the fraction of a gallon.
3. 3 sq. in. to the fraction of a sq. rd.
4. 8 in. to the fraction of a mile.
5. of 3m to the fraction of a Cong.
6. 4×6 cu. in. to the fraction of a cord.
7. What part of a cable length is 1 link?

CASE II.

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455. To reduce a compound number to a common fraction of a higher denomination.

1. Reduce 9 oz. 6 pwt. 16 gr. to the fraction of a pound.

SOLUTION.-By reduction we find 9 oz. 6 pwt. 16 gr. equals 4480 gr. ; and also 1 lb. equals 5760 gr.; 1 gr. equals 60 of a pound, and 4480 gr. equals 4480 times 5760, which equals 488, which reduced to its lowest terms, equals 3. Therefore, etc.

OPERATION.

oz. pwt. gr.

9

6 16-4480 gr. 1 lb. 5760 gr.

4480

1488=3, Ans.

5760

Rule.

Reduce the number to its lowest denomination, and write under it the number of units of this denomination which make a unit of the required denomination; and then reduce the resulting fraction to its lowest terms.

Reduce

Ans..

Ans..

Ans. .

2. 213 rd. 1 yd. 21 ft. to the fraction of a mile. 3. 13 quires 8 sheets to the fraction of a ream. 4. What part of a bu. of wheat is 52 lb. 8 oz.? 5. What part of a quintal is 85 lb. 113 oz.? 6. What part of 9 feet square is 9 sq. ft.? 7. What part of 10 ft. square is 4 ft. square and 4 sq. ft.?

Ans. .

Ans..

Ans.

8. Reduce 114 P. 8 sq. yd. 5 sq. ft. 1134 sq. in. to the fraction of an acre. Ans. 5.

9. What part of a hhd. does a box 7 in. long, 51⁄2 in. wide, and 3 in. deep contain? Ans.

CASE III.

456. To reduce a compound number to a decimal of a higher denomination.

1. Reduce 3 qt. 1 pt. 2 gi. to the decimal of a gallon.

OPERATION.

412.00

21.50

43.75

SOLUTION.-There are 4 gi. in 1 pt., hence of the number of gills equals the number of pints; of 2 equals .5, which with the 1 pt., equals 1.5 pt.: there are 2 pt. in 1 qt., hence of the number of pints equals the number of quarts; of 1.5 equals .75, which with 3 qt. equals 3.75 qt.: there are 4 qt. in 1 gal., hence of the number of quarts equals the number of gallons; of 3.75 equals .9375; hence 3 qt. 1 pt. 2 gi. equals .9375 gal.

.9375, Ans.

Rule.-I. Divide the lowest term by the number of units which equals one of the next higher, and annex the decimal quotient to the integer of the next higher denomination.

II. Proceed in a similar manner until the whole is reduced to the required denomination.

NOTE. It may also be done by reducing to a common fraction, and the common fraction to a decimal.

2. Reduce 13 s. 6 d. to £.

3. Reduce 2 cwt. 59 lb. to tons.

Ans. £.675.

Ans. .1296 ton.

4. Reduce 93 13 29 8 gr. to lb.
5. Reduce 12 cwt. 87 lb. 33 oz. to tons.
6. 58 mi. 182rd. 5 yd. .82944 in. to deg.
7. 1 da. 10 h. 13 min. 26.4 sec. to days.
8. 103 da. 20 h. 13 min. 12 sec. to yr.

Ans. .768 lb.

Ans. .6436 ton.
Ans. .8469 deg.
Ans. 1.426 da.
Ans. .2845 yr.

ADDITION OF DENOMINATE FRACTIONS.

457. Addition of Denominate Fractions is the process of finding the sum of two or more denominate fractions. 1. Find the sum of £3, and of a shilling.

SOLUTION.-£3, we find by Art. 452, equals 13 s. 4d.; and s. equals 9 d. Taking the sum of 13 s. 4 d. and 9 d. we have 14 s. 1 d. Therefore, etc.

OPERATION. £ 13 s. 4 d. ås.= 9 d. 14 s. 1 d.

Rule. Reduce the fraction to integers, and then add as in

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SUBTRACTION OF DENOMINATE FRACTIONS. 458. Subtraction of Denominate Fractions is the process of finding the difference between two denominate fractions.

1. Subtract of a shilling from of a pound.

SOLUTION.-£ equals 13 s. 4 d.; & of a shilling equals 9 d.; 9 d. subtracted from 13s. 4 d. leaves 12s. 7 d. Therefore, etc.

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Rule.

Reduce the fractions to integers and then subtract

as in subtraction of compound numbers.

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MULTIPLICATION OF DENOMINATE
FRACTIONS.

459. Multiplication of Denominate Fractions is the process of finding the product when the multiplicand is a denominate fraction.

1. Multiply £ by 7.

SOLUTION.-7 times £ equals £21, which by reduction we find equals £5 5s. There

fore, etc.

OPERATION.

£×7=£4=£5 5 s.

Rule. Multiply the denominate fraction by the given multiplier and reduce the product to integers.

NOTE. It may also be done by first reducing the fraction to integers and multiplying as in multiplication of denominate numbers.

2. Multiply lb. Troy by 11.
3. Multiply .82 yd. by 13.
4. Multiply 23 lb. by 3.25.
5. .978 mi. by 3.45.
6. .083 A. by .35.
7. .324 A. by 23
31

8. 12.16 C. by 7.01.

Ans. 7 lb. 4 oz.

Ans. 10 yd. 1 ft. 11.76 in.
Ans. 9 lb. 43 13.

Ans. 3 mi. 29 ch. 92 li. 6.336 in.
Ans. 4 P. 20 sq. yd. 1 sq. ft. 72 sq. in.

Ans. 34 P. 17 yd. 8 ft. 1261 in.

Ans. 85 C. 10 S. 3° 20'.

9. If a man dig 63 yd. of ditch in 1 day, how much would

he dig in 7 days?

Ans. 9 rd. 2 yd. 2 ft. 54 in.

DIVISION OF DENOMINATE FRACTIONS.

460. Division of Denominate Fractions is the process of finding the quotient when the dividend is a denominate fraction.

461. There are Two Cases:

1st. To divide a denominate fraction into equal parts.

2d. To divide a denominate fraction by a denominate integer or fraction.

CASE I.

462. To divide a denominate fraction into a number of equal parts.

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Rule.-Divide the denominate fraction by the given

divisor, and reduce to integers.

Ans. 2 ft. 9 in.

Ans. 14 da. 19 h. 52 min. 30 sec.
Ans. 18 da. 8 h.
Ans. 1 mi. 106 rd. 3 yd. 2 ft.

2. Divide rd. by 3.
3. Divide .325 yr. by 8.
4. Divide 3.43 da. by .182.
5. Divide 6.3 mi. by 44.
6. Divide 2.7 bu. by .436.
7. Divide 12.16 wk. by .i.
8. Divide 4.35 P. by 14.

1199

Ans. 6 bu. 1 pk. 400 pt. Ans. 3 mo. 3 wk. 4 da. 12 h.

Ans. 2 P. 12 sq. yd. 5 sq. ft. 63 sq. in.

9. If a bird fly 20.36 mi. in 1.33 hours, how far does it fly in one hour?

Ans. 15 mi. 86 rd. 2 yd. 7.2 in.

CASE II.

463. To divide a denominate fraction by a denomi

nate integer or fraction.

1. Divide 1 cwt. by 16 lb.

SOLUTION.-11 cwt. equals 144 lb.; dividing 144 lb. by 16 lb. we have for a quotient 9. Hence the following

OPERATION.

1 cwt.144 lb.

144 lb. 16 lb. 9, Ans.

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