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RULE. : Divide the upper term by the lower. Note. This case, and case 3, prote each other.

EXAMPL E S. 1 Reduce to its proper terms.

17)219(1274 facit.

17

49 34

1 26
27

to its proper

TT

15 2 Reduce 14,7 to its proper terms.

facit. 84 3 Reduce terms.

21 4 Reduce 901 to its proper terms.

564 Ś Reduce to its proper terms.

1 6 Reduce to its proper terms.

1836 CASE 5. To reduce a compound fraction to a single one ;

RULE Multiply all the numerators together for a new numerator, and all the denominators for a new denominator. Note. Like figures in the numerators and denominators may

be cancelled, and frequently others contracted, by taking their aliquot parts.

EX AMPLE S. i Reduce of of to a single fraction. 2 X3 X4=

it = facit. Or, f of of=2= 3X4X5=

3
Or, cancelled, -of-of

--as before.

3. Å 55 Reduce off of to a single fraction. facit 3 Reduce 3 of of io to a single fraction. 4 Redace i of of to a single fraction, 5 Reduce of of to a single fra&tion. 6 Reduce of of to a single fra&ion.

CASE. CASE 6. To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value;

RULE. Make it a compound fraction, by comparing it with all the denominations between it and that to which it is to be reduced; which fraction reduce to a single one.

EXAMPLES. 1 Reduce of a penny to the fraction of a pound.

of is of '=14=nL. facit. 2 Reduce 1 of a farthing to the fraction of a shilling.

facit s. 3 Reduce of an oz, troy to the fraction of a lb,

facit lb. 4 Reduce of a lb. avoirdupois to the fraction of a C.wt.

facit *.C.ut. 5. Reduce jof a pint of wine to the fraction of a hhd.

facit i hhd. 6 Tieduce of a minute to the fraction of a day.

facit īss day.

CASE 7. To reduce the fraction of one denomination to the fraction of another, but less, retaining the same value;

RULE. Multiply the given numerator by the parts of the denomination between it and that to which it is to be reduced, for a new numerator, and place it over the given denomi. nator; which reduce to its lowest terms.

Note. This case, and case 6, prove each other.

EXAMPLES 1 Reduce this of a L. to the fraction of a penny.

5X20x121208=d. facit. 2 Reduce o of a shilling to the fraction of a farthing.

facit 291. 3 Reduce of a lb. troy to the fraction of an oz.

$! facit oz

. L

4 Reduce o of an C.wt. to the fraction of a lb.

facit lb. 5 Reduce of a hhd. to the fraction of a pint.

facit is pt. 6 Reduce 1507 of a day to the fraction of a minute.

facit 11 min.

CASE 8, To reduce the value or quantity of a fraction to the known parts of an integer;

RULE. Multiply the numerator by the common parts of the integer, and divide by the denominator.

EXAMPLES. i Reduce of a pound to its proper value.

of 2=40=185. 4d. facit. 2 Reduce 1 of a shilling to its value. facit 5d.ch 3 Reduce of 5l. 9s. to its value,

41. 13s. 5d. 4. Reduce iz of a pound troy to its value.

9oz. 5 Reduce 1 of 10C. 1gr. 121b. to its value.

facit 8C. Iqr. 25lb. 1oz. 71 dr. 6 Reduce of a mile to its value,

facit 4fur. 125 yds. 2ft. lin. 24.c. 7 Reduce of an ell English to its value. facit lyd. 8. What is the value of of a yard ? answer 3gr. 1&na. 9 What is the value of of an acre ?

1R. 2 pls. 10 What the value of x of a day? 7hr. 12inin. 11 What is the value of of a dollar ?

11fd. 12 What is the value of li of a French crown?

answer 81d. 13 What is the value sterling off of an English guinea ; and what in Pennsylvania currency?

answer 4s 8d. sterling, 78 9d. Pennsylvania currency,

14 What is the value sterling of of a moidore; and what in Pennsylvania currency? answer il 1s 7do sterling,

il 16s. currency. CASE 9.

To reduce any given value, or quantity, to the fraction of any greater denomination of the same kind;

RULE. Reduce the given quantity to its lowest term mentioned, for a numerator, and the integer into the same name for a denominator ; which reduce to their lowest terms. Note 1. If a fraction be given, multiply both parts by the denominator thereof, and to the numerator add the numerator of the given

fraction. 2. Cases 8 and 9 prove each other.

S.

}

EXAMPLES.
1 Reduce 138 4d. to the fraction of a pound.

d.
13
20

14=L. facit. 2 Reduce 5d.j' to the fraction of a shilling. facit s. 3 Reduce 9oz. troy to the fraction of a lb. alb. 4 What part of 51 9s. is 41 138 50.1? answer 5 Reduce 3C. 8lb. 9oz. 13dr. to the fraction of a ton.

facit ton. 6 Reduce 2ft. 8in. 1b.c. to the fraction of a yard.

facitsyd. 7 Keduce lyd. to the fraction of an ell English.

facit Fell. 8 Reduce 3qr. 2na. to the fraction of a yard. facit žyd. 9 Reduce 1R. 30P, to the fraction of an acre.

facit 1 acre. 10 Reduce 13hr. 30min. to the fraction of a day.

facit ir day. CASE 10.* To reduce fractions from one denomination to another of the same value, having the numerator of the required fraction given;

RULE.

1

As the numerator of the given fraction
Is to the denominator;
So is the numerator of the intended fraction
To its denominator,

Note. As the tenth, eleventh, and twelfth cases are seldom useful, they may be taught, or omitted, at the option of the teacher.

EXAMPLES.

EXAMPLES. * 1 Reduce to a fraction of the same value, whose numerator shall be 15..

As 3: 4 :: 15 : 20 facit 15. 2 Reduce to a fraction of the same value, the numerator of which shall be 42.

facit te 3 Reduce to a fraction of the same value, the numerator of which shall be 34.,

facit 4 Reduce to the fraction of the same value, the numerator of which shall be 73.

CASE. 11.

facit in

To reduce fractions from one denomination to another of the same value, having the denominator of the required

fraction given;

RULE.
As the denominator of the given fraction
Is to its numerator;
So is the denominator of the intended fraction

To its numerator.
Note. Cases 10 and 11 prove each other.

EXAMPLES.

facit 428

facit

1 Reduee to a fraction of the same value, whose denoninator shall be 20.

As 4 : 3 :: 20. : 15 facit .=. 2 Reduce to a fraction of the same value, the denominator of which shall be 49.

3 Reduce to a fraction of the same value, the denominator of which shall be 46. * 4 Reduce to a fraction of the same value, the denominator of which shall be 131

CASE 12.
To reduce a mixt fraction to a simple one;

RULE. Multiply each term of the principal fraction by the denominator of that annexed, for the like term of the simple fraction, adding the annexed numerator to the product of the term to which it belongs.

facit ?s'i

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