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 shall be 9. Thus, 7×9-63, and 63 the Ans. 2. Reduce 18 to a fraction whose denominator shall be

12

Ans. 216 3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 30°=90° 10°

CASE V.

To reduce a compound fraction to a simple one of equal

value. RULE.

1. Reduce all whole and mixed numbers to their equivalent fractions.

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

2. Reduce of of to a single fraction. Ans. S. Reduce of of to a single fraction.

4. Reduce of of 8 to a simple fraction.

Ans.

Ans. 133}

5. Reduce of 13 421 to a simple fraction.

Ans. 1880-21

NOTE. If the denominator of any member of a com pound 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) ili produce the fraction required in lower terms.

6. Reduce of 3 of § to a simple fraction.

Thus 2×5

4x7

7. Reduce of of of 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 denomi nators 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 com mon denominator.

1 + } + {-24 common denominator.

6. Reduce and of to a common denominator. Ans. 768 128

1980

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 155) 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 numerators being placed over the common denominator, will express the fractions required in their lowest terms.

tor.

EXAMPLES.

1. Reduce and to their least common denomina.

4)2 4 8

2)2 1 2

1 1 1 4x2-8 the least com. denominator.

82x1 4 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 in value, and in much lower terms than the general Rule, which would produce # ++} 2. Reduce and to their least common denomi

Ans.

S. Reduce and to their least common denominator. Ans. Hi

4. Reduce and to their least common denommator. Ans. HAH

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 denomi nation you would reduce it to; lastly, reduce this com pound 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

of a pound.

5 x 1 x 1

5

2. Reduce

of a pound to the fraction of a penny. Compared thus, T of 20 of 4 d.

Then 5 x 20 x 12

S. Reduce of a farthing to the fraction of a shilling

Ans. S 4. Reduce of a shilling to the fraction of a pound.

Ans.

5. Reduce of a pwt. to the fraction of a pound troy. Ans. 1810-138

a cwt.

6. Reduce of a pound avoirdupois to the fraction of Ans. cwt. 7. What part of a pound avoirdupois is of a cwt Compounded thus, T1 of 1 of 28=1}} =¦ Ans. 8. What part of an hour is of a week.

Ans. 1

9. Reduce of a pint to the fraction of a hhd.

Ans. Th 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 20 of S. Ans.

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

Thus, 5 of {={} Ans. 12. Reduce of an English crown, at 6s. 8d. to the fraction of a guinea at 28s. Ans. of a guinea.

CASE VIII.

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

RULE.

Multiply the numerator by the parts in the next infe rior denomination, and divide the product by the denomi nator; and if any thing remains, multiply it by the next mferior denomination, and divide by the denominator as before, and so 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 75 and 76; but for the scholar's exercise, I shall give a few more examples in each.

EXAMPLES.

1. What is the value of of a pound?

2. Find the value of } of a cwt.

Ans. 8s. 94d.

Ans. Sqrs. 3lb. 1oz. 12tdr.

3. Find the value of 7 of 3s. 6d. Ans. Ss. vid.

4. How much is

5. How much is

of a pound avoirdupois ?

Ans. 7oz. 10dr.

of a hhd. of wine? Ans. 45 gals.

6. What is the value of 45 of a dollar?

Ans. 5s. 7 d.

7. What is the value of of a guinea? Ans. 18s.