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Such pupils if asked to add several fractions do so by first "clearing of frac- tions, " adding the numerators and having thrown away the common denominator proudly exhibit a polynomial as the result of their labors ! Board work. In putting work on the board for students terms should not be "transposed" from one side of the equation to the other by changing sign, but the step should be performed by adding the same expression to both sides. Instead of "clearing" of fractions it is better to redu...ce all the fractions to a common denominator and then make use of the fact that a fraction is zero when its numerator is zero, provided the denominator is not zero at the same time. All calculations should be made by passing from one step to the next by means of an identity familiar to the pupil. The solution of quadratics in the second year is best taught by the factor method, e. G. ax* +bx+c=a( x 2 +x+ )= a Thus the quadratic can be zero when and only when = or The question of equivalence of equations is the most difficult that the teacher of algebra has to contend with.
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