4)3 4 8

312

4×3×2=24, the least common denominator

24÷3x1=8, the first numerator; 24÷4× 3=18, the 2d numerator; 24÷8×7=21, the 3d numerator. So the required fractions are 4, 1, 1.

2. Reduce,, 3, and 4, to a fraction having the least common denominator. ́Ans. 38, 40, 45, 13.

CASE 8.

To reduce a fraction of one denomination to the fraction of another, but greater, retaining the same value.

RULE.

Multiply the given denominator by the parts of the denominations between it and that denomination you would reduce it to; reduce this compound fraction to a single one, by Case 5, and you will have a fraction of the required denomination, equal in value to the given fraction.

EXAMPLES.

1. Reduce of a cent to the fraction of a dollar.

4x100 == dollar. 2. Reduce of a penny to the fraction of a pound.

Ans. £.

20

3. Reduce of a pennyweight to the fraction of a pound troy. Ans. lb. 4. Reduce of an ounce to the fraction of a pound avoirdupois. Ans. lb.

CASE 9.

To reduce a 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 denominations between it and that denomination you would reduce it to, for a new numerator; then reduce the compound to a single one.

EXAMPLES.

1. Reduce of a dollar to the fraction of a cent. T1oct. Ans. 2. Reduce of a pound to the fraction of a penny.

Ans. 3d.

3. Reduce of a lb. avoirdupois, to the fraction of an

ounce.

4. Reduce of a cwt. to the fraction of a lb. avoirdupois. Ans. 4lb.

CASE 10.

To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, &c.

RULE.

Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator, and if anything remain, multiply it by the next inferior de nomination, and divide by the denominator as before, and so on, as far as necessary; and the quotients placed after each other, in their order, will be the answer required.

In examples of federal money, annex as many ciphers to the numerator as may be necessary. If a remainder occur when at its lowest denomination, place it as a numerator over the denominator, for a fraction of the lowest denomination.

of a pound? Ans. 14s. 3d. 14. of a lb. avoirdupois?

Ans. 12oz. 124dr.

4. What is the value of 1⁄2 of a mile? Ans. 6fur. 26p. 11ft.

5. What is the value of

of a day?

Ans. 16h. 36m. 55,5s.
Ans. 3r. 174p.

6. What is the value of of an acre?

CASE 11.

To reduce any given quantity to the fraction of any larger 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 1.-If there be a fraction given with the said quantity, it must be farther reduced to the denominative parts thereof, adding thereto the numerator.

NOTE 2.-This case is the reverse of the former, therefore proves it.

EXAMPLES.

1. Reduce 62cts. 5m. to the fraction of a dollar.

2. Reduce 14s. 3d. 1qr. to the fraction of a pound.

Ans. £. 3. Reduce 12oz. 124dr. to the fraction of a lb. avoirdu

pois.

Ans. 4lb.

4. Reduce 6fur. 26p. 11ft. to the fraction of a mile.

Ans. m.

5. Reduce 16h. 36m. 55,5s. to the fraction of a day.

Ans. day.

6. Reduce 3r. 174p. to the fraction of an acre.

CASE 12.

Ans. acre.

To reduce a given fraction to another equivalent one, having a given numerator.

RULE.

As the numerator of the given fraction

Is to the numerator of the proposed fraction,

So is the denominator of the given fraction
To the denominator required.

EXAMPLES.

1. Reduce to a fraction of the same value, the numerator of which shall be 15.

As 3'15: 4:20 denominator Ans.

2. Reduce to a fraction of the same value, having its numerator 42.

Ans.

3. Reduce to an equivalent fraction, the numerator of which shall be 27.

Ans. 27

30%

4. If be reduced to an equivalent fraction, having its numerator 36, what will that fraction be?

Ans. 36

115

CASE 13.

To reduce a given fraction to another equivalent one, having a given denominator.

RULE.

As the denominator of the given fraction
Is to the denominator of the intended fraction,
So is the numerator of the given fraction
To the numerator required.

EXAMPLES.

Ans. 1.

1. Reduce to an equivalent fraction, having its denominator 24. As 8:24:7:21, num. 2. Reduce & to a fraction of the same value, the denominator of which shall be 45.

3. Reduce

nator 68.

4. Reduce

to an equivalent fraction, having its denomi

Ans.

Ans.

Ans. 34

46

to a fraction of the same value, the denomi

nator of which shall be 46.

5. Reduce to an equivalent fraction, having its denominator 20.

Ans. 12

20

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. After the fractions are prepared, multiply each numerator into all the denominators but its own, and take their sum for a new numerator-multiply all the denominators for a new denominator. See Case 6, Reduction.

2. What is the sum of 7 of 4%, † of 1⁄2, and 91?

6. Add of a dollar, of a dime, and together.

7. Add & of a dollar to ‡ of a dollar. 8. Add of a lb. troy, to of an oz.

9. Add 4 of a ton to

of an eagle, Ans. $6.03. Ans. $1.12,5.

231

Ans. 6oz. 11dwt. 16gr.

of a cwt. Ans. 12cwt. 1qr. 8lb. 12oz. 124dr. of a furlong.

10. Add & of a mile to

of a yard to

11. Add
12. Add of a yard,

Ans. 6 furlongs, 28 poles.

of a foot, and 3 of a mile, together. Ans. 1540 yards, 2 feet, 9 inches. 13. If a merchant owns of a ship, valued at $4000, and buys another person's share, which is what part belongs to him, and what is it worth?

Ans.

belongs to him, and is worth $2750.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.

*

Prepare the fractions, when necessary, as in Addition,

* In subtracting mixed numbers when the fractions have a common denominator, and the numerator in the subtrahend (or lowest number) is less than that in the minuend, (or upper number) 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. But when the numerator in the subtrahend is greater than that in the minuend, subtract the numerator in the subtrahend from the common denominator, adding the numerator in the minuend, set it down and carry one to the whole number, or integer of the subtrahend.