CASE IV.

To reduce a whole number to an equivalent fraction, hav ing a given denominator.

RULE.-Multiply the whole number by the given denominator place the product over the said denominator, and it will form the fraction required.

12.

EXAMPLES.

1. Reduce 7 to a fraction whose denominator will be 9. Thus, 7×9-63, and 3 the Ans.

2. Reduce 18 to a fraction whose denominator shall be Ans. 21

3. Reduce 100 to its equivalent fraction, having 90 for a denominator.

Ans.

CASE V.

To reduce a compound fraction to a simple one of equal

value.

RULE.-1. Reduce all whole and mixed numbers to their equiva lent fractions.

2. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required.

EXAMPLES.

1. Reduce of 2 of 2 of to a simple fraction.

1×2×3×4

==% Ans.

Ans.

2×3×4×10

2. Reduce of 4 of 2 to a single fraction.

3. Reduce of 1 of 1 to a single fraction. 眚

4. Reduce of 3 of 8 to a simple fraction.

Ans. T

Ans. 3

5. Reduce of 3 of 42 to a simple fraction.

Ans. 188-217

NOTE.-If the denominator of any member of a com. end fraction be equal to the numerator of another mem

Der thereof, they may both be expunged, and the other members continually multiplied (as by the rule) will produce the fraction required in lower terms.

6. Reduce of of to a simple fraction.

7. Reduce of of of 1 to a simple fraction.

CASE VI.

Ans.

To reduce fractions of different denominations to equiva lent fractions having a common denominator.

RULE I.

1. Reduce all fractions to simple terms.

2. Multiply each numerator into all the denominators except its own, for a new numerator; and all the denominators into each other continually for a common denominator; this written under the several new numerators will give the fractions required.

EXAMPLES.

1. Reduce,,, to equivalent fractions, having a comnon denominator.

+ + } + {=24 common denominator.

24 24 24 denominators.

2. Reduce 7,1%, and 11, to a common denominator.

Ans. 1, 4, and .

3. Reduce †,†, f, and 7, to a common denominator.

Ans. 1, II, II, and fit

5. Reduce 2, 5, and 123, to a common denominator.

Ans...

6. Reduce 3, 3, and § of 11, to a common denominator Ans. 768 2592 1980

3456 34569 3456

The foregoing is a general rule for reducing fractions to a common denominator; but as it will save much labour to keep the fractions in the lowest terms possible, the following Rule is much preferable.

RULE II.

For reducing fractions to the least common denominator. (By Rule, page 143) find the least common multiple of all the denominators of the given fractions, and it will be the common denominator required, in which divide each particular denominator, and multiply the quotient by its own numerator, for a new numerator, and the new nume rators being placed over the common denominator, will ex press the fractions required in their lowest terms.

EXAMPLES.

1. Reduce,,and, to their least common denominator 4)2 4 8

22 1 2

1 1 1

4×28 the least com. denominator.

8-2x14 the 1st numerator.

8÷4×3-6 the 2d numerator.

8÷8x5-5 the 3d numerator.

These numbers placed over the denominator, give the answer,,, equal itr value, and in much lower terms than the general Rule would produce

2. Reduce 2, 3, and, to their least common denomina

tor.

Ans. 4, 4, 4t.

3. Reduce and to their least common denomi

nator.

Ans. 1

Ans.

4. Reduce and to their least common denominator. 18 Å

CASE VII.

To Reduce the fraction of one denomination to the fraction of another, retaining the same value.

RULE.

Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly, reduce this cons Found fraction to a single one, by Case V.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of of

5 x 1 x 1

6 × 12 × 20

of a pound.

Ans.

1440

of a pound to the fraction of a penny. of of yd.

2. Reduce Compared thus T

Then 5 × 20 × 12

1440 1

1

3. Reduce of a farthing to the fraction of a snilling.

Ans.

4. Reduce & of a shilling to the fraction of a pouna. Ans. To 5. Reduce of a pwt. to the fraction of a pound troy. 鼻 Ans. T

6. Reduce of a pound avoirdupois to the fraction of B

Ans.

cwt. 7. What part of a pound avoirdupois is T of a cwt. Compounded thus r oft of 4 Ans. 8. What part of an hour is of a week.

9. Reduce of a pint to the fraction of a hhd. Ans. T{1 10. Reduce of a pound to the fraction of a guinea.

Compounded thus, 3 of 2o of ‚'s.=4 Ans.

11. Express 5 furlongs in the fraction of a mile.

Thus 5

of 11

Ans.

12. Reduce of an English crown, at 6s. Sd. to the frac Ans. of a guinea.

tion of a guinea at 28s.

CASE VIII.

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 any thing remains, multiply it by the next inferior de nomination, and divide by the denominator as before, and se on as far as necessary, and the quotient will be the answer.

NOTE. This and the following Case are the same with Problems II. and III. pages 70 and 71; but for the scho lar's exercise, I shall give a few more examples in each.

EXAMPLES.

1 What is the value of 11 of a pound? Ans. 8s. (Id. 2. Find the value of of a cwt. Ans. 3 qrs, 3 b, 1 oz.12f dr 3. Find the value of 1 of 33. M.

Ans. 3s. 0ąd.

4. How much is of a pound avoirdupois?

Ans. 7 oz. 10 dr.

6. Ilow much is § of a hhd. of wine? 6. What is the value of 15 of a dollar?

What is the value of of a guinea?

Ans. 45 gals.

Ans. 5s. 71d

Ans. 18