(37) Reduce of a Gallon of Wine to the Fraction of a Hogshead.

(38) Reduce of a Hhd. of Ale to the Fraction of a Pint. (39) Reducer of a Chaldron to the Fraction of a Bushel. (40 Reduce of a Gallon to the Fraction of Chaldron. (41) Reduce TZ of a Week to the Fraction of a Second. (42) Reduce of a Minute to the Fraction of a Day.

Case 7. To find the proper Quantity or Value of a Frac tion in Money, Weights, Measures, &c.

RULE.

Multiply the Numerator of the given Fraction by the Parts contained in the Integer to which it belongs; then divide that Product by the Denominator; and if any Thing remains, reduce it to the next Denomination less, and divide again by the Denominator: thus proceed to the least Denomination, and the Quotients placed in their Order will be the Answer.

EXAMPLES.

(43) Reduce of a Moidore to its proper Quantity. (44) Reduce of a Guinea to its proper Quantity. (45) Reduce 4 of a Shilling to its proper Quantity. (46) Reduce of a Three-Pound-Twelve to its proper Quantity.

(47) What is the Value of of a £.?

(48) Reduce of a lb. Troy to its proper Quantity.
(49) What is the Value of of a cwt?

(50) Reduce of a Ton to its proper Quantity.
(51) What is the Value of of a Mile?
18

(52) Reduce of an Ell English to its proper Quantity.
(53) Reduce of an Acre to its proper Quantity.
(54 What is the Value of of a Hhd. of Wine?
(55) Reduce of a Barrel of Beer to its proper Quantity.
(56) Reduce of a Chaldron of Coals to its

fity.

(57) What is the Value of 3 of a Month?

proper Quan

(58) Reduce of a Day to its proper Quantity.

Case 8. To reduce Money, Weights, or Measures, into Tractions.

RULE.

Reduce the given Quantity to the lowest Name mentioned, for a Numerator; under which put the Number of those Parts contained in an Unit of the Integer for a Denominator, then reduce the Fraction to its lowest Terms.

EXAMPLES.

(59) Reduce 6s 84d. to the Fraction of a Pound. (60) Reduce 41d. to the Fraction a Shilling.

(61) Reduce 21 17s 7 d. to the Fraction of a Three-PoundTwelve.

(62) Reduce 8s 2d. to the Fraction of a Guinea.

(63) Reduce 6 oz. 17 dwts. 21 grs. to the Fraction of a lb.

Troy.

(64) Reduce 3 qrs. 3lb. 1 oz. 121⁄2 drs. to the Fraction of a

cwt.

(65) Reduce 10 cwt. 18lb. 1 oz. to the Fraction of a Ton. (66) Reduce 3 qrs. to the Fraction of an Ell English. (67) Reduce 2 ft. 6 in. to the Fraction of a Yard. (68) Reduce 4 fur. 32 p. to the Fraction of a Mile. (69) Reduce 3 r. 2 p. to the Fraction of an Acre. (70) Reduce 42 gal. of Wine to the Fraction of a Hhd. (71) Reduce 28 gal. of Beer to the Fraction of a Barrel. (72) Reduce 14 bu. 2p. to the Fraction of a Chaldron. (73) Reduce 1 w. 3 d. 12 h. to the Fraction of a Month. (74) Reduce 243 d. 8 h. to the Fraction of a Year (allowing 365 Days to the Year.)

XXXIX. ADDITION of VULGAR FRACTIONS.

Case 1. TO add Fractions together having different Denominators.

RULE.

1. Reduce the given Fractions to a common Denominator, by Case V. in Reduction.

2. Add all the Numerators together for a new Numerator, under which subscribe the common Denominator. And, if it is an improper Fraction, reduce it to its proper Terms (by Case IV.) and you have the Sum of all the Fractions.

EXAMPLES.

(1) Add,, and together.
(2) Add 4, 3, 4, 4, and together.
(3) Add of, and, together.

(4) Add of %, to of 4.

(5) Add 1, 3, 4, and of, into one Sum.

Case 2. To add mixed Numbers.

RULE.

Reduce the Fractions to a common Denominator, and add them together, as before directed and annex their Sum to the Sum of the Integers.

EXAMPLES.

(6) Add 4 and 17 together.

7) Add 73, 94, and 6%, together.

(8) Add 8, 93, 104, 114, and 12 into one Sum.

Case 3. When the given Fractions are of several Denomi nations.

RULE..

Reduce them to one Denomination (by Case VIII.), then add them together as before directed; or you may reduce them to their proper Quantities (by Case IX.) and add them together.

EXAMPLES.

(9) Add 2 of a L. to of a Shilling. (10) Add 4 of a lb. Troy to of an oz. (11) Add & of a cwt. to of a lb.

(12) Add of a Yard, to of an Ell English.
13201
(13) To g of a Mile, add of a Yard.

(14, Add of a Chaldron, to of a Peck.
(15) To & of a Week, add g of a Month.
(16) Add 4 of an Hour, to § of a Week.

(17) Add of 127. + 441. + 3 of 1 of a £. + of % of a Shilling into one Sum.

XL. SUBTRACTION of VULGAR FRACTIONS.

RULE.

1. PREPARE the Fractions as before directed in Addition..

2. Subtract one Numerator from the other, and their Difference will be a new Numerator, under which subscribe the common Denominator.

(6) From 104 take 6.

(7) From 17 take 169.

(8) From 12 take of 7 of 4.

(9) From of a Shilling take of a Penny.
(10) From of a cwt. take 4 of an oz.

(11) From of a Yard take of an Inch.
(12) From of a Chaldron take of a Peck.
(13) From of a Day take of an Hour.

XLI. MULTIPLICATION of VULGAR FRAC.

TIONS.

RULE.

I. REDUCE compound Fractions to simple ones, per Case II; bring mixed Numbers into improper Fractions, per

Case III.

2. Multiply the Numerators together for a new Numerator: and the new Denominators for a new Denominator; or, if the Fractions will cancel, do it as in Case II.

I. PREPARE the Fractions as before directed in Multiplication.

2. Multiply the Numerator of the Dividend into the Denominator of the dividing Fraction for a new Numerator, and multiply the other Numerator and Denominator toge. ther for a new Denominator; or invert the Divisor, and then proceed as in the last Rule.

THERE are two Methods to perform this Rule: the se cond of which is the most expeditious, and easiest.

RULE.

1. Prepare the Fractions, if required, as directed in Multiplication; then proceed as in Sec. 12.-Or,