The normal: or, Methods of teaching the common branches, orthoepy, orthography, grammar, geography, arithmetic and elocution .. by Holbrook Alfred

Author:Holbrook, Alfred. [from old catalog]
Language: eng
Format: epub, pdf
Tags: Teaching
Publisher: New York, Chicago, A. S. Barnes & company
Published: 1889-03-25T05:00:00+00:00

REDUCTION OF PRACXTC>tS TO LOWER TERMS

Demonstration^ Prop. 6.

REDUCTION OF FRACTIONS TO HIGHER TERii«.

Demonstration^ Prop. 3.

REDUCTION OF COMPOUND FRACTIONS TO SIMPLE.

Demonstration. Take J of |.

Since multiplication is taking one number as many times as there are units or parts of a unit in another, taking f of | is a case of multiplication; hence may be expressed thus : fx|. Then 3 times | (Prop. 1,) is y, but since the multiplier is J of 3, this product is four times too large, and ♦nust be divided by 4. But (Prop. 2.) yH-i=^j. By observing che two operations it is seen that the numerators have been multiplied together for a new numerator, and the denominators for a new denominator. Hence the ordinary rule is demonstrated.

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Remark 1. Beduction of Complex Fractions to Simple is demonstrated in a similar manner, after having first shown that it is a case of division.

Remark 2d. In examining classes this may be considered a test question, " Why does dividing the denominator multiply the fraction?" Such an answer as this is often given, " Because it shows that the fraction is divided into a less number of parts;" or this, " Because it increases the parts :' or this, " Because the number of the parts is less, therefore they must be greater." All these answers are worthless, the latter, which is more fre-

. J

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