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fore if 3 be divided by 4, the quotient is the answer required. Reduce to a decimal fraction. Answer .4 Reduce is

48 Reduce its

,1146789 Reduce }

.7777+ Reduce it's

.9130434+ Reduce }, }, }, }, and so on to jo, to their corresponding decimal fractions; and in this

operation the various modes of interminate decimals may be easily observed.

RULE II.

To reduce Quantities of the same, or of different

denominations to Decimal Fractions of higher denominations.

If the given quantity consist of one denomination only, write it as the numerator of a vulgar fraction; then consider how many of this make one of the higher denomination, mentioned in the question, and write this latter number under the former, as the denominator of a vulgar fraction. When this has been done, divide the numerator by the denominator, as directed in the foregoing rule, and the quotient resulting will be the decimal fraction required.

But if the given quantity contain several denominations, reduce them to the lowest term for the numerator; reduce likewise that quantity, whose fraction is sought, to the same denomination for the denominator of a vulgar fraction; then divide as before directed.

EXAMPLES.

Reduce 9 inches to the Decimal of a foot.

The foot being equal to 12 inches, the vulgar fraction will be ; then 12)9.00

.75=decimal frac

[tion required. Reduce 8 inches to the decimal of a yard.

8 inches,

1 yard x 3 x 12 = 36 inches.

36)8.01.22+ = Answer.

72

80
72

8

Reduce 5 furlongs 12 perches to the decimal of a mile. 1 mile

5 furlongs 8

40

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Reduce 21 minutes 54 seconds to the decimal of

a degree. Ans. .365 Reduce 056 of a pole to the decimal of an Acre.

Ans. .00035

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G

What is the value of .6875 of a yard ?

3=number of feet in a

[yard. 2.0625 12 = number of inches

[in a foot. .7500 12 =number of lines in

[an inch. 9.0000 The answer here is 2 feet 9 lines.

What is the value of .084 of a furlong? Ans. 3

per. I yd. 2 ft. 11 in. What is the value of 683 of a degree ? Ans. 40

m, 58 sec. 48 thirds. What is the value of .0053 of a mile? Ans. ]

per. 3 yds. 2 ft 5 in. + What is the value of .036 of a day? Ans. 51' 50" 24".

PROPORTION

IN DECIMAL FRACTIONS.

Having reduced all the fractional parts in the given quantities to their corresponding decimals, and having stated the three known terms, so that the fourth, or required quantity, may be as much greater, or less than the third, as the second term is greater, or less than the first, then multiply the second and third terms together, and divide the product by the first term, and the quotient will be the answer ;-in the same denomination with the third term.

EXAMPLES.

If 3 acres 3 roods of land can be purchased for 93 dollars 60 cts. how much will 15 acres 1 rood cost at that rate ?

3 acs. 3 rds.

3.75 acres. 15 acs. I rd

15.25 acres. 8 93, 60 cts. = 8 93.60 Then 3.75 : 15.25 : : 93.60 :

15.25

468 00 18720 46800 9360

$ ! 3.75)1427.4000(380.64=Answer.

1125

3024
3000

2400
2250

1500
1500

If a clock gain 14 seconds in 5 days 6 hours; líow much will it gain in 17 days d5 hours? Ans. 47 seconds.

If 187 dollars 85 cents gain 12 dollars 33 cents interest in a year, at what rate per cent is this interest? Ans. 6.56+

SECTION II.

INVOLUTION AND EVOLUTION

INVOLUTION is the method of raising any number, considered as the root, to any required power.

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