New Rudiments of Arithmetic Combining Mental And Slate Exercises for Intermedi
New Rudiments of Arithmetic Combining Mental And Slate Exercises for Intermedi
James B James Bates Thomson
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Divide JJ by ft DIVISION OF FRACTIONS. 121 To Divide a Fraction by a Fraction, when they have Different Denominators. i. At -J of a dime apiece, how many pears can be pur- chased for j of a dime ? Analysis. — \ dime will buy as many opebation. pears as \ dime is contained times in f 1X4 4 dime. Reducing \ and f to a common 3X5 ' denominator, they become jV and -, 2 2 -. , x ~ Their numerators are now like numbers, = t 9; ? > and one may be divided by the other. 7 4 Thus, 9-5-4=2! pears, the ans...wer re- T2~T2 — 9~4 > quired. (P. 120, Eem. ) 9-^4 = 2 iP- By inspecting the operation of redu- Or, |xf=|, or 2^. Cing the fractions to a common denomi- nator, it will be seen that the numerator of each is multiplied into the denominator of the other. This produces the same com- bination of terms and the same results as inverting the divisor and multiplying the terms of the dividend by it. Thus, |-* i i= £ x $=$, or z\ pears, the same as before. Remark. — In dividing, no use is made of the common denomi- nator ; hence, in practice, multiplying the denominators together may be omitted.
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