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

EXAMPLES.

1. Multiply, †, †, †, t, 4, 1, §, f‰, H, H.

= 12.

By analysis, of }=}, } of } = 1, 1 of 4 = }, of f = f, f of 4 = 4, 4 of 3.= }, } of &=t, of = 10,

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}, } 1%

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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.

1. Multiply,, t, t, b, t, b, t, fo. Product=10.

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411 × 138 = 2213 = 9213 = Product.

2

9. Multiply 542 by 37 = 212 × 13

10. Multiply 67% by 511.

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11. Multiply 91 by 56.

12. Multiply 53763 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.

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9. Divide

Ans.

=

11.

by 2, or divide into two equal parts.

Ans. x2 =

10. Divide by 2, or divide into two equal parts.

Ans. +2 = .

11. Divide by 2, or divide into two equal parts.

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12. Divide by, or how often is

ૐ.

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13. Divide by 1, or how often is contained in 1=4.

Ans.

Evidently twice.

14. Divide by , or how often is

Ans. =

contained in .

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and = 1; } ÷ 4 = } = 14.

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

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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.

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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.

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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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COMPLEX FRACTIONS.

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

31 13

3375

વર્ષ

1005

621 100, etc., are complex fractions.

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