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E.-Division of a Fraction by an integer. Rule-1. If the fraction be a mixed number, reduce it to an improper fraction.

2. Form a fraction, whose numerator is the numerator of the dividend, and the denominator the product of the divisor and the denominator of the dividend.

3. Cancel any factors common to numerator and denominator, the resulting fraction is the quotient required.

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F.--Reduction of a Compound Fraction to a Simple Fraction.

Rule-1. Form a fraction, whose numerator is the product of all the nu. merators of the simple fractions, and whose denominator is the product of all the denominators. At first only indicate these products by writing the sign of multiplication between the factors.

2. Cancel all factors common to numerator and denominator.

3. Multiply all the remaining factors. The resulting fraction is that required.

4. If any of the simple fractions be mixed numbers, they must be reduced to improper fractions before applying the Rule.

EXAMPLES

1. Reduce { of of 14 of Å to a simple fraction.

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2. Reduce 4 of of 83 of 33 to a simple fraction.

1 4 3 23 9 4 43 23
4- of- of 8 - of - of of- of
2 9 5 43 2 9 5

43
9X4X43X23

2X9X 9X43
TX 2X 1X23

IXIX5X1 46 1

=95

G.-Multiplication of Fractions.

1. TO MULTIPLY FRACTIONS TOGETHER.

Rule--1. Reduce mixed numbers, if there be any, to improper fractions.

2. Form a fraction, whose numerator is the product of all the numerators, and denominator the product of all the denominators ; at first indicating only the multiplication by the proper sign.

3. Cancel all factors common to numerator and denominator.

4. Multiply together all the remaining factors, the resulting fraction is the product required.

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2. Multiply together 10, 207, 252.

1
4

9 81 184 309
10- x 204 X 25 -=-X--X-
8

12 8 9 12

81X184X309

8 X 9 X 12
9 X 23 X 103

1X1 X 4 21321 1

5330

II.

TO MULTIPLY A SIMPLE OR COMPOUND FRACTIONAL EXPRESSION BY
A SIMPLE FRACTION, OR BY ANOTHER COMPOUND EXPRESSION.

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Rule. Reduce each expression to a simple fraction, and then perform the multiplication

EXAMPLES. 1. Multiply ž - to, by 24.

3 3 35 — 12 11
X 2-

Х
8 10

40 4 23 11

253 -X

40 4 160 2. Simplify the expression (6} - - 3%+3)x (3h – 23+33) 1 7 5

7 1 11) 6- - 3-t Х

2 + 3 8 9

10 5
1 7 5

7 1
=3+ + x{1+ +
3 8

10 5 20
24 63 +40)

14 4+
x{1+
72

20
1 1
= 3-X2-

72 20
217 41

8897 257
Х

= 6-
72 20 1440 1440

20)

={3+

+

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Rule-1. Reduce mixed numbers, if any, to improper fractions. 2. Invert the divisor, and multiply the dividend by the inverted fraction.

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II. TO DIVIDE A SIMPLE OR COMPOUND FRACTIONAL EXPRESSION BY A

SIMPLE FRACTION, OR BY A COMPOUND EXPRESSION.

Rule. Reduce each expression to a simple fraction, and then perform the division.

EXAMPLES. 1. Divide 75 + — 44 by 41 — 3.

5 3

+7 8

5 3 4 8 = 3+:+

7 8 9

360 + 189 — 224
3+
7 X 8 X 9

7
325 7
+

X
7 X8 X9

5 1837 7 1837 37

Х 7X8X95 360 360

={s= {3

}

2. Multiply together 10%, 20%, 25%.

1 4

9 81 184 309
10- X 204 X 25 -=-X-X
8 9 12 8 9 12

81X184X309

8 X 9 X 12
9 X 23 X 103

1X1 X 4 21321

1 = 5330

4

II. TO MULTIPLY A SIMPLE OR COMPOUND FRACTIONAL EXPRESSION BY

A SIMPLE FRACTION, OR BY ANOTHER COMPOUND EXPRESSION.

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х

253

Rule. Reduce each expression to a simple fraction, and then perform the multiplication.

EXAMPLES. 1. Multiply } fo, by 24.

3

3 35 - 12 11
X 2-

40
23 11

Х

40 4 160 2. Simplify the expression (6} - 3} + %) X (3 - 2} + 30.)

7 5

7 1 11 + X3—

2-+8 9

10 5 1 7 5

7 1 11) ={3+

+ x{1+ + 3 8 9

10 5
24

14 4 + 11
X1+
72

20
] 1
= 3 X2-

72 20
217 41 8897 257
x

—6-
72 20 1440 1440

}

20$

{67
={3
={3+

63 +40

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3

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Rule-1. Reduce mixed numbers, if any, to improper fractions. 2. Invert the divisor, and multiply the dividend by the inverted fraction.

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