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COR. 3.- The product of two improper fractions is greater than either fraction.

EXAMPLES.

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1. Multiply 1, $, , , 1, 4, 3, , 10, 11, 1.

****************** }}x}} = 1'a. By analysis, $ of f = }, } off = 1, 4 of 4 = }, } of

1 b = 1, 1 off = 1, 4 of 3.= }, $ off = t; $ of = to, :

, 1 of 1 = 11, 11 of 11 = Te.

11 2. Multiply 3, Hf, and ; thus,

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=

2

x H x = 14, product.

3

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=

= 315

3. Multiply to and f.

XX= 44, product. 4. Multiply 35% by 9.

27 67 35 x 9

3214 = Product. Axiom 7%-If any number be both multiplied and divided by the same number, the value of the original number is not changed.

COR. 1.-If the multiplier is greater than the divisor, the product is greater than the number multiplied, but if the multiplier is less than the divisor, then the product is less than the multiplicand.

COR. 2.—Multiplying the numerator or dividing the denominator by any number, multiplies the fraction by the same number.

EXAMPLES.

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19

1. Multiply 1, 3, 4, 5, 5, 4, 3, 5, . Product = 1o. 2. Multiply 4, 6, 4, }, f.

Product = 3. Multiply ), it, is and 1. Product = 0 4. Multiply f, }, 11 and

Product = 語. 5. Multiply it x $*$* x 1. Product = d. 6. Multiply 454 by 15.

명품
451 x 15 = 225 x 15 = 910
45

455
6821

1365

= 6821. 2

7. Multiply 748 by 12.

3

744 x 12 = 29 x 12 = 897.
8. Multiply 271 by 33}.
111 x 196 = 18428 = 921% = 921%.

х

81

111 x 18 = 2913 = 921% = Product.

2

9. Multiply 541 by 37% = 42 x 4 = 24747. 10. Multiply 67 by 513. 11. Multiply 91 by 56%. 12. Multiply 5376] by 8214. 13. Multiply 6274 by 237%.

REM.—When one or both factors are mixed numbers, it is generally best to reduce them to improper fractions.

DIVISION OF FRACTIONS.

PROBLEMS.

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Ans.

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1. Divide 10 by 5.

Ans. 10 - 5= 1= 2. 2. Divide 6 by 3.

Ans. f = 2. 3. Divide 3 by 3.

Ans. = 1.

} 4. Divide 1 by 2.

Ans. 5. Divide 1 by 3. 6. Divide 2 by 3.

Ans. 7. Divide 3 by 4.

Ans. 8. Divide 5 by 4.

Ans. 4 = 11 9. Divide 1 by 2, or divide 4 into two equal parts.

1

Ans. 4x2 = 1 10. Divide by 2, or divide into two equal parts.

Ans. *2 = š 11. Divide by 2, or divide into two equal parts.

= : 12. Divide by , or how often is contained in

Ans. Evidently twice. 13. Divide by , or how often is contained in }=.

Ans. Evidently twice. 14. Divide f by $, or how often is contained in t.

Ans. = f and } =*;$;$= = 13. ]

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15. Divide } by 4, or how often is 4 contained in 3.

Ans. * = * and 1 = t; 2%= %.
}
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等。

Ans. $x2

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COR. 1.-The numerator of a fraction is a dividend, the denominator a divisor, and the fraction itself the quotient.

COR. 2.-To divide a fraction by a fraction, reduce both to a common denominator and then divide the

numerator of the dividend by the numerator of the divisor.

COR. 3.- Dividing the numerator or multiplying the denominator by any number, divides the fraction by the same number.

THEOREM.

To divide any number by a fraction, invert the divisor and multiply by it.

PROBLEMS,

1. Divide 24 by 6.

24
2, 2, 2, 3

= 2,2 = 4.
6

2, 3

8

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2. Divide 24 by 4.
24 2, 2, 2, 3
= 2, 2, 2 = 8 = 24 X

= 8.

& In the second division the divisor 6 is itself to be divided by 2; that is, its factor 2 is to be canceled.

Canceling a factor in the divisor multiplies the quotient by the same factor.

3. Divide 44 by .

x = 4,

or

24 = 12; and f 3; and

= 4. In this case a factor is to be canceled in both dividend and divisor.

Canceling a factor in the dividend divides the quotient by the same factor.

An integral number, or a fraction, is divided by a fraction by inverting the divisor and then multiplying by it.

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When one or both terms of a fraction are either fractions or mixed numbers, it is called a Complex Fraction ; thus,

31 1 3 374 1001 5' Ž 62 100*, etc., are complex fractions.

3

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