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(37) Reduce

head.

7

of a gallon of wine to the fraction of a hogs

(38) Reduce of a hhd. of ale to the fraction of a pint.
(39) Reduce of a chaldron to the fraction of a bushel.
(40) Reduce of a gallon to the fraction of a chaldron.
(41) Reduce of a week to the fraction of a second.
(42) Reduce of a minute to the fraction of a day.

7 742 I O TI

Case 7. To find the proper quantity or value of a fraction 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 remain, 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 37 of a moidore to its proper quantity.
(44) Reduce of a guinea to its proper quantity.
(45) Reduce 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 41% of a lb. Troy to its proper quantity. (40) What is the value of of a cwt. ?

(50) Reduce of a ton to its proper quantity. (51) What is the value of 7 of a mile?

(52) Reduce of an eli English to its proper quantity. (53) Reduce of an acre to its proper quantity.

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(54) What is the value of of a hhd. of wine?

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(55) Reduce of a barrel of beer to its proper quantity. (56) Reduce of a chaldron of coals to its proper quantity. (57) What is the value of of a month?

(58) Reduce of a day to its proper quantity.

Case 8. To reduce money, weights, or measures, into fractions.

RULE.

Reduce the given quantity to the lowest name mentioned, for a numerator; under which put the number of those parts contained in a unit of the integer for a denominator, then reduce the fraction to its lowest terms.

EXAMPLES.

(59) Reduce 6s. 8d. to the fraction of a pound. (60) Reduce 44d. to the fraction of a shilling.

(61) Reduce 27. 17s. 7 d. to the fraction of a three-pound

twelve.

(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. 3 lb. 1 oz. 123 drs. to the fraction of a

cwt.

(65) Reduce 10 cwt. 18 lb. 1 oz. to the fraction of a ton. (66) Reduce 3 qrs. to the fraction of an ell English. (67) Reduce 2 f. 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 bhd. (71) Reduce 28 gal. of beer to the fraction of a barrel, (72) Reduce 14 bu. 2 p. 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 be an improper fraction, reduce it to its proper terms by Case IV. and you have the sum of all the fractions.

H

EXAMPLES.

(1) Add 4, 4, and together.

(2) Add 1, 4, 4, 4, and together.
(3) Add of, and, together.
(4) Add of, to 5 of 2.

(5) Add, 1, 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 44 and 17 together.

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

(8) Add 8, 93, 103, 114, and 123, 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.

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of a yard, to

of an ell English.

(13) To of a mile, add of a yard.
of a chaldron, to of a peck.
of a week, add 1⁄2 of a month.

(11) Add

(12) Add

(14) Add

(15) To

(16) Add

(17) Add

of an hour, to & of a week.

of 12.+4+3 of 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.

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(11) From

of a yard take

of an inch.

of an hour.

(12) From of a chaldron take of a peck.

(13) From of a day take

XLI. MULTIPLICATION of VULGAR FRACTIONS.

RULE.

1. 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.

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1. 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 together for a new denominator; or invert the divisor, and then proceed as in the last rule.

EXAMPLES.

(1) Divide by 4.
(2) Divide by 3 of 7.
(3) Divide 12 by 17.
(4) Divide 123 by 37.
(5) Divide of by of 12.
(6) Divide 7 by 9.

(7) Divide 96 by 146. (8) Divide 143 by 4 of 12. (9) Divide 1427 by 123. (10) Divide of 6 by of of II.

XLIII. THE RULE of THREE DIRECT,

In VULGAR FRACTIONS.

THERE are two methods to perform this rule: the second of which is the easiest and most expeditious.

RULE.

1. Prepare the fractions, if required, as directed in multiplication; then proceed as in Sect, 12.-Or,

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