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ORgeIf you choose, you may take that easy method in Problem I. (page 74.)

EXAMPLES,

1

48

48
Os 48/6

Ans. *

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7596

1. Reduce to its lowest terms.

Operation. common mea. 8) = Ans.

Rem. 2. Reduce to its lowest terms. 3. Reduce is to its lowest terms. 4. Reduce 3798 to its lowest terms.

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

fi'action.

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.

Ans. **

1. Reduce 45% to its equivalent improper fraction.

45X8+7=397 Ans. 2. Reduce 1913 to its equivalent improper fraction. 3. Reduce 16.10% to an improper fraction.

Ans. 4618 4. Reduce 618 to its equivalent improper fraction.

Ans. 22089

137
CASE II.
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 18

5)48(9 Ans. 2. Find the value of 344

Ans. 1943 3. Find the value of 933

Ans. 849 4. Find the value of 27985

Ans. 6112 360 Find the value of 3

14

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

ing a given denominator.

RULE. Multiply the whole number by the given denominadas place the product over the said denominator, and it 1 form the fraction required.

EXAMPLES.

900

1. Reduce 7 to a fraction whose denoininator it 9.

Thus, 7x9=63, and 43 the ani 2. Reduce 18 to a fraction whose denominat 1 be 12.

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

ins: 9000

90

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

value.

RULE, 1. Reduce all whole and mixeil numbers to theisti valent fractions.'

2. Multiply all the numerators, together for at merator, and all the denonimators for a new des tor; and they will form the fraction required.

EXAMPLES.

1. Reduce i of' s off of ta to a simple questii.

1 X2 X3 X4

21 Ans.

2X3X4x10 2. Reduce of of to a single fraction. Ans. 3. Reduce of in of it to a single fraction.

Ans. 23 4. Reduce i of, of 8 to a simple fraction.

wins. 120 5. Reduce Off42} to a simple fraction.

atins. 126 60

1507

NOTE.-If the denominator of any member of bound fraction be equal to the numeretur of print

1

per thereof, they may both be expunged, and the 02?"wembers continually multiplied (as by the rule)

duce the fraction required in lower terms. Chedduce soft of to a simple fraction.

Thus, 2x5

=1= ns.

4X7 2. Leduce i of of of to a simple fraction.

Ans. =

CASE VI. conduce fractions of different denominations to contatant fractions having a common denoininator,

RILE 1. 1. Tieduce all fractions to simple terms.

3. ultiply each numerator into all the denominators Ceptits own, for a new numeratır; and all the denoinLiviors into each other continually for a common denomTrator; this written under the several new numerators, wil give the fractions required.

EXAMPLES.

1. Peace { to equivalent fractions, having a common denominator.

+ + + 4394 common denominator.

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16 new unce.tors

04 Henninatis. 2. Reducer and it to a compan denominator.

first and 8:9 3. Perluce and a Commen denominator.

.:15.

3:10. and the

4 Reduce to

2 5 9 2 1980 3756 3456 3453

and * to a common denominator. 800 300 400

and

= 1 and *=14 Ans. 1000 1000 1000 5. Reducer and 12} to a common denominator.

Ans. 54 90 888 6. Reduce and of into a common denominator.

Ans. 768 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 nume. rators being placed over the common denominator, will express the fractions required in their lowest terms.

EXAMPLES.

1. Reduce 1 1 and to their least common denominator.

4)2 4 8

2)2 1 2

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

8--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

2. Reduce the and ti to their least common denominator,

Ans.

S. Reduce and i to their least common de nominator.

Ans. 14 uu 4. Reduce 1 i and to their least common denom inator.

Ans. 1 H IG

CASE VII.

To reduce the fraction of one denomination to the fractio 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, reluce this come pound fraction to a single one, by Case V.

EXAMPLES.

5

1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of ' of z' of 'a pound. 5 X 1 X 1

Ans. 6 X 12 X 20 1440 2. Reduce of a pound to the fraction of a perny.

Compared thus, of 2 of 2 d. Then 5 x 20 x 12

1200

1

440

1 3. Reduce s of a farthing to the fraction of a shilling.

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

sis. ਨਰ 5. Reduce of a pwt. to the fraction of a pound troy.

Ans. 6. Reduce of a pound ürtirdupois to the fraction of

Jus. qd cout. 7. What part of a pound averlu;-is is of a cut. P

Compounded tiiva, płof 102=*ins. 8. What part of an luar O: 2 wees?

&?; 16 --

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