Or, It you chuse, you may take that easy metnod in Problem I. (paye 74.)

EXAMPLES.

48/35 (1

48

Ans. 36 sins. 13

1. Reduce to its fowest terms.
:(

Operation.
08 (6

common mea. 8)*8=. Ans.
18 Rein,
2. Reduced to its lowest terms.
3. Reduce to its lowest terms.
4. Reduce 3798 to its lowest terms.

Ans.
CASE II.
To reduce a mixed number to its equivalent improper

fraction.

RULE. Multiply the whole number by the denominator of the given fraction, and to the product add the numerator, this sum written above the denominator will form the fraction required.

EXAMPLES.

18

360

1. Reduce 451 to its equivalent improper fraction.

45x8+7=387 Ans. 2. Reduce 194 to its equivalent improper fraction.

Ans. 354 3. Reduce 16 10 to an improper fraction.

Ans. 1618
4. Reduce 6116 to its equivalent improper fraction.

Ans. 22085
CASE III.
To find the value of an improper fraction.

RULE.
Divide the numerator by the denominator, and the
quotient will be the value sought.

EXAMPLES. 1. Find the value of 48

5)48(98

, Ans. 2. Find the value of 35.4

Ans. 1944 3. Find the value of 933

Ans. 84 4. Find the value of 22085

Ans. 613

360 5. Find the value of 7

Ans 8

3

T8

CASE IV. To reduce a whole number to an equivalent fraction, har

ing a given denominator.

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

EXAMPLES.

а

Ans. 10

TZ

100

90

1. Reduce 7 to a fraction whose denominator shall be 9,

Thus, 7x9=63, and the Ans. 2. Reduce 18 to a fraction whose denominator shall be 12.

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

Ans. 9°='=11°

CASE V. To reduce a compound fraction to a simple one of equal

value.

RULE. 1. Reduce al' whole and mixed numbers to their equivalent 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.

a

1. Reduce s off off of io to a simple fraction

1x2x3x4

==7 Ans,

2X3 X4X10 2. Reduce, of off to a single fraction. Ans. 3. Reduce of iof is to a single fraction.

Ans. 1986 4. Reduce # of of 8 to a simple fraction.

Ans. =3} 5. Reduce of 1 424 to a simple fraction.

Ans. 1966° =21 Note-If the denominator of any member of a com. Dound fraotion be equal to the numerator of another mer

36 T300

1

ber thereof, they may both be expunged, and the other
members continually multiplied (as by the rule) will pro-
duce the fraction required in lower terms.
6. Reduce of of to a simple fraction.

Thus 2x5
=ht. Ans.

.

4x7 7. Reduce of of of it to a simple fraction.

Ans. H

CASE VI. 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 denomi.

this written under the several now numerators will give the fractions required.

nator;

EXAMPLES.

1. Reduce to equivalent fractions, having a com mon denominator.

$ + f + 324 common denominator.

24 24 24 denominators. 2. Reduce f and 11 to a common denominator.

Ans. Ho fandila 8. Reduce } } and ; to a common denominator

Ans. fii ju Hi and

8

8

6 C 88

768 259 2 1980

4. Reduce and is to a common denominator. 800 300 400

and to it and t=146 Ans. 1000 1000 1000 5. Reduce } and 124 to a common denominator.

Ans. 44 6. Reduce and fof H to a common denominator.

Ans. 936 35 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..

! EXAMPLES.

1. Reduce 1 i and to their least common denominae tor.

4)2 4 8

2)2 1 2

1 1 1 4X2=8 the least com. denoininator.

84-2x1=4 the 1st. numerator.
8:4X3=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 41

2. Reduce if and í to their least common denomi: Dator.

Ans. ***

48 42

REDUCTION OF VULGAR

S. Reduce i and to their least common denom. inator.

Ans. is it 4. Reduce a if and 1to their least common denom. Mator.

Ans. Hit

3

16

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. mation

you would reduce it to; lastly, reduce this com pound fraction to a single one, by Case V.

EXAMPLES

20

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

Ans. 6 x 12 x 20 1440 2. Reduce Ta so of a pound to the fraction of a penny.

Compared thus, Toof of d. Then 5 x 20 x 12

190

Ans. '

а

а

440 1 1 3. Reduce f of a farthing to the fraction of a shiling 4. Reduce ; of a shilling to the fraction of a pound.

Ans. To 5. Reduce of a pwt. to the fraction of a pound troy.

Ans. Tot 6. Reduce of a pound avoirdupois to the fraction of 을

Ans. ticwt. 7. What part of a pound avoirdupois is of a cwt

Compounded thus, tio of 1 of =tit=, Ans. 8. What part of an hour is of a week.

Ans. 111

a cu't.

126

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