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 cancel led, and frequently others contracted, by taking their aliquot parts.

EXAMPLES.

Reduce of of to a single fraction.

2X3X4=2 = } facit. Or, 3 of 4 of ¿=¿4=;

3×4×5=

2 3.4 2

Or, cancelled- of- of as before.

3 4 5 5

2 Reduce of of to a single fraction.
3 Reduce of of to a single fraction.
4 Reduce of of to a single fraction.
5 Reduce of of 2 to a single fraction.
6 Reduce of of 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.

EXAMPLES.

I Reduce of a penny to the fraction of a pound.

of of 1740

1. facit.

2 Reduce of a farthing to the fraction of a shilling. 12442

facit s

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

facit, Ib.

4 Reduce of a lb. avoirdupois to the fraction of a C.t.

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

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

CASE 7.

facit C.wi.

facit bhd.

facit 1 day.

728

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 dena, mination 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.

Reduce rizo

I

2 Reduce

3 Reduce

EXAMPLES.

of a . to the fraction of a penny.
5×20 × 12400 = d. facit.
of a shilling to the fraction of a farthing.

facitqr.

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

L

facst & 0.2

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.

EXAMPLE S.

1 Reduce of a pound to its proper value.

facit 4 fur. 125yds. 2ft. xin. 24b.c.

of an ell English to its value.

7 Reduce 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

To

of a yard?

of an acre?

of a day?

answer 3qr. Ina.

facit lyd.

1R. 27 pls.

7hr. 12 min.

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 I. If a fraction be given, multiply both parts by the denominator thereof, and to the numerator add the numerator of the given fraction 2. Cafes 8 and 9 prove each other.

2 Reduce 5d.

to the fraction of a shilling. troy to the fraction of a lb.

4 What part of 519s. is 4/ 13s 5d.?

3 Reduce 90%.

5 Reduce 3G. 8lb. 9oz. 13dr.

facit 1. 216.

answer

to the fraction of a ton.

facitton.

facit fyd.

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

7 Reduce lyd. to the fraction of an ell English.

8 Reduce 3gr. 2n2. to the fraction of a yard.
9 Reduce IR. 30P. to the fraction of an acre.

facit ell. facit Zyd

2

EXAMPLES.

1 Reduce to a fraction of the same value, whose nume merator shall be 15.

As 34 15: 20 facit 11.

2 Reduce to a fraction of the same value, the numerator of which shall be 42.

3 Reduce to a fraction of the same value, the numerator

of which shall be 34.

4 Reduce

facit facit

to a fraction of the same value, the nume

rator of which shall be 73.

CASE

11.

facit r

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

Note.

RULE,

As the denominator of the given fraction

Is to its numerator;

So is the denominator of the intended fraction
To its numerator.

Cases 10 and 11 prove each other.

EXAMPLES.

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

facit 423

3 Reduce to a fraction of the same value, the denomina tor of which shall be 46.

facit

facit Hy

4 Reduce & to a fraction of the same value, the denominator of whch shall be 1313.

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.