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Os, if you choose, you may take that easy method in Problem to page 09.)

EXAMPLES.
1. Reduce this to its lowest terms.

Operation.
common measure, 8):7= Ans.

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5) Rem.

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2. Reduce to its lowest terms.
3. Reduce is to its lowest terms.
4. Reduce 379 to its lowest terms.

Ans.
Ans. ti
Ans. }

CASE II.

To reduce a mixed number to its equivalent improper

fraction. Rule.-Multiply the whole number by the denominator of the giin en fraction, and to the product add the numerator, this sum writton bove the denoininator will form the fraction required

EXAMPLES,

1. Reduce 457 to its equivalent improper fraction :

45 X 8+7=397 Ans. 2. Reduce 1914 to its equivalent improper fraction.

Ans. 3. Reduce 161 to an improper fraction.

Ans, we
4 Reduce 61388 to its equivalent improper fraction.

Ans. 3+85
CASE III.
To find the value of an improper fraction.
RULE. --Divide the numerator by the denominator, and the quo
iend will be the value sought.

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CASE IV.

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To reduoo a whole number to an equivalent fraction, hay

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 traction required.

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EXAMPLES.

1. Reduce 7 to a fraction whose denominator will be 9.

Thus, 7x9=63, and 43 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. 988°='g'='1'

Ans.

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CASE V.

1 2

To reduce a compound fraction to a simple one of equal

value.

n

RULE.-1. Reduce all whole and mixed nurnbers to their equiva. lont fractions.

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

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EXAMPLES.

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1. Reduce of of off to a simple fraction.
1x2x3X4

= Ans.
2X3X4X10
2. Reduce of of to a single fraction.
3. Reduce of it of 1 to a single fraction.

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Ans. 838

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

Ans. W=3 5. Reduce of 14 of 42} to a simple fraction.

Ans. 12660=2176 NOTE.If the denominator of any member of a com. pound fraction be equal to the pumerator of another mem

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ber thereof, they may both be expunged, and the othes
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 2 x5

==it Ans. 4x7

7. Reduce of of 4 of 11 to a simple fraction.

Ans. It

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 cach 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 undor the several new numerators will give the fractions required.

EXAMPLES. 1. Reduce , , , to equivalent fractions, having a common denominator.

+ s + 124 common denominator.

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24 24 24 denominators.
2. Reduce 1, P, and li, to a common denominator,

Ans. if, 444, and HS
3. Reduce }, t, f, and y, to a common denominator.

Ans. 146. Hi, fit, and it

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8. I 4. Reduce , , and to, to a common denominatos. 800 300 400

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4.. -ando in and all Ans. 1000 1000 1000 5. Reduce 2, 6, and 12j, to a common denominator,

Ans.4. 19. . 6. Reduce , į, and of 14, to a common denominator.

To F

Ans. 268, 25.92, 1989. 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 follow. Bet ing Rule is much preferable.

wille:

it with RULE II.

natio. For reducing fractions to the least common denominator. poun

(By Rule, page 143) find the least common multiple of all the denominators of the given fractions, and it will he

1. the common denominator required, in which divide each

B 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 ox press the fractions required in their lowest terms.

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EXAMPLES.

T

1. Reduce 1, 2, and , to their least common denominator

4)2 48 2)2 1 2

3.

1 1 1 4x28 the least com. denominator.
8:-2.x1=4 the 1st numerator.

5.
8=4*3=6 the 2d numerator.
8;8x555 the 3d numerator.

6. These numbers placed over the denominator, give the cut answer , , , equal in value, and in much lower terms ī than the general Rule would produce 43, 44, 44

2. Reduce , f, and 15, to their least common denomina bor.

Ans. 43, 44, 46

8. Reduce it and in to their least common denomiNator.

Ans. 13H
4. Reduce and into their least common denomi
nator.

Ans. So H if
CASE VII.

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

RULE.

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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 denomie 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 t' of zy of a pound. 5 X 1 X 1

Ans. 6x 12 x 20

1440
2. Reduce tio of a pound to the fraction of a penny.

Compared thus tabo of 40 of yd.
Then 5 X 20 X 12

oth

1440

1 1 3. Reduce of a farthing to the fraction of a snilling.

Ans. o

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4. Reduse of a shilling to the fraction of a pouna.

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

Ans. Toto 6. Reduce of a pound avoirdupois to the fraction of

Ans. so cut.
7. What part of a pound avoirdupois is the of a cwts

Compounded thus tio of 4 of = Ans.
8. What
part of an hour is sic of a week.

Ans. 4 +

Cwt.

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