RULE.

Divide the upper term by the lower.

Note. This case, and case 3, prove each other.

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.

EXAMPLES.

1 Reduce of of to a single fraction.

2X3X4 == facit. Or, of of #==

3X4X5=

3

Or, cancelled, of-of-- as before.

3

2 Reduce of of Reduce of of Reduce of of 5 Reduce of of 6 Reduce of of

4 5 5
to a single fraction.

to a single fraction.
to a single fraction.
to a single fraction.
to a single fraction.

facit

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.

2 Reduce of a farthing to the fraction of a shilling.

facitis.

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.wt.

392

5. Reduce of a pint of wine to the fraction of a hhd.

facit hhd.

6 Reduce 1 of a minute to the fraction of a day.

CASE 7.

1

facit day.

1584

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 denominator; which reduce to its lowest terms.

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

EXAMPLES.

of a L. to the fraction of a penny. 5X20X12-1200-d. facit.

of a shilling to the fraction of a farthing.

1 Reduce

2 Reduce

facit gr.

3 Reduce

of a lb. troy to the fraction of an oz.

facit fox.

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

facit & lb.

5 Reduce

of a hhd. to the fraction of a pint.

facit pt.

6 Reduce

facit 1 min.

of a day to the fraction of a minute.

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.

1 Reduce

2 Reduce

3 Reduce

EXAMPLES.

of a pound to its proper value.
of 20-40-18s. 4d, facit.
of a shilling to its value.

of 5l. 9s. to its value.

4. Reduce 12 of a pound troy to its value.
of 10C. 1gr. 12lb. to its value.

5 Reduce
6 Reduce of a mile to its value.

facit &C. 1gr. 25lb. 1oz. 7-3dr.

facit lyd.

facit 4fur. 125yds. 2ft. 1in. 24b.c.
English to its value.
of a yard ?
of an acre?
of a day?

7 Reduce of an ell
8 What is the value of
9 What is the value of
10 What is the value of
11 What is the value of

12 What is the value of

of a dollar?

answer 3qr. 1§na. 1R. 23 pls.

7hr. 12min.

114d.

of a French crown?

answer 84d.

13 What is the value sterling of of an English guinea; and what in Pennsylvania currency?

answer 48 8d. sterling, 7s 9d. Pennsylvania currency. 14 What is the value sterling of of a moidore; and what in Pennsylvania currency?

answer il is 7d. sterling, 1 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.

EXAMPLES.

1 Reduce 13s 4d. to the fraction of a pound.

2 Reduce 5d. to the fraction of a shilling. 3 Reduce 9oz. troy to the fraction of a lb.

4 What part of 51 9s. is 41 13s 5d.?

facitis. alb.

answer &

5 Reduce 3C. 8lb. 9oz. 13dr. to the fraction of a ton.

facitton.

6 Reduce 2ft. 8in. 13b.c. to the fraction of a yard.

facityd.

7 Reduce 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 acre.

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

To reduce fractions from one denomination to another of the same value, having the numerator of the required fraction given;

RULE.

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.

2 Reduce

As 3

4 15 20 facit 15-3.

to a fraction of the same value, the nume

rator of which shall be 42.

facit

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

facit 21

facit 73

17318

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

CASE 11.

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.

1 Reduce to a fraction of the same value, whose denominator shall be 20.

As 43 20: 15 facit 15=1.

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.

facit 438

facit 24 facit 1

73

* 4 Reduce & to a fraction of the same value, the denominator of which shall be 181

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.