$55000m. and 5000m. 625m.=62c. 5m. answer, as before.

4. What is the value of of a lb. Avoirdupois ?

Ans. 12oz. 12 dr.

CASE X.*

To reduce any given quantity to the fraction of any greater denomination of the same kind.

RULE. Reduce the given quantity to the lowest term mentioned, for a numerator; then reduce the integral part to the same term for a denominator; which will be the fraction required.

NOTE-It appears from this rule, and what has been said before, that, in Federal Money, where the given quantity contains no fraction of its lowest denomination, the annexing of as many ciphers to 1 of the required denomination, as will extend to the lowest denomination in the given quantity, will form a denominator, which, placed under the given quantity used as one number for a numerator, will make the answer, which may be reduced to its lowest terms. if there be a fraction of the lowest denomination, multiply the given whole numbers by its denominator, adding its numerator, for a numerator; and let the denominator itself, at the left of as many ciphers as were mentioned above, be a denominator; the fraction so formed will be the answer; which may be reduced to its lowest terms.

Or,

EXAMPLES.

1. Reduce 6d. 2c. 5m. to the fraction of a dollar.

2. Reduce 26c. 5ğm. to the fraction of a dollar.

* This case is the reverse of the former, therefore proves it.

If there be a fraction given with the said quantity, it must be farther reduced to

the denominative parts thereof, adding thereto the numerator.

163. What is your rule for reducing any given quantity to the fraction of a greater denomination of the sume kind?

3. Reduce 14s. 31d. to the fraction of a pound.

Ans. 488 4£.

Ans. 4lb.

4. Reduce 12oz. 124dr. to the fraction of a lb. Avoirdupois.

ADDITION OF VULGAR FRACTIONS.

RULE.

REDUCE Compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same; and all of them to a common denominator; then, the sum of the numerators written over the common denominator will be the sum of the fractions required.

NOTE.-Fractions, before they are reduced to a common denominator, are entirely dissimilar, and therefore cannot be incorporated with one another; but when they are reduced to a common denominator, and made parts of the same thing, their sum, or difference, may then be as properly expressed by the sum or difference of the numerators, as the sum or difference of any two quantities whatever, by the sum or difference of their individuals; whence the reason of the rules, both for Addition and Subtraction, is manifest.

164. What is the rule for addition of vulgar fractions?

Ans. 128.

80

Ans. 20c. 9m.

4. Add 1. s. and d. together.

Ans. 2s. 8,64, d.

105

5. Add of a week, 3 of a day, of an hour, and of a minute together.

Ans. 2 days, 2 hours, 30 minutes, 45 seconds.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.

PREPARE the fractions as in Addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required.*

* In subtracting mixed numbers, when the fractions have a common denominator, and the numerator in the subtrahend is less than that in the minuend, the difference of the whole numbers will be a whole number, and the difference of the numerators a numerator to be placed over the given denominator; this whole number and the fraction thus formed will be the remainder; but, when the numerator in the subtrahend is grea er than that in the minuend, subtract the numerator in the subtrahend from the common deuominator, adding the numerator in the minuend, and carrying one to the integer of the subtrahend.

165. What is your rule for the subtraction of vulgar fractions?

Hence,

REDUCE Compound fractions to simple ones, and mixed numbers to improper fractions; then the product of the numerators will be the numerator, and the product of the denominators, the denominator of the product required.

NOTE. Where several fractions are to be multiplied, if the numerator of one fraction be equal to the denominator of another, their equal numerators and denominators may be omitted.

Hence, a fraction is subtracted from a whole number. by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

166. What is the rule for multiplying vulgar fractions?

1