161
Fractions
This process can be continued until there are no whole numbers left which wiU divide both numerator and denominator and yield whole number quotients. No whole number will divide both numerator and denominator to give whole-number quotients in the case of such fractions as 7-2, 0/3, %" % 1%:;, and so on. Such fractions are said to be "reduced to lowest terms." In working with fractions, it is common to use them after they have been reduced to lowest terms, because then we are working wi th the smallest numbers possible. Why try to deal with 2%Q when we can just as well deal with lh? In adding and subtracting fractions, it is necessary to keep the denominators the same throughout. Thus (and I will use words to make the' si tuation clearer), 7i = %), one fifth plus one fifth equals two fifths (7'5 just as one apple plus one apple equals two apples. Again, seven twenty-fifths minus three twenty-fifths equals four twenty-fifths (%1'1 - %!5 = %5) just as seven oranges minus three oranges equal four oranges. However, one fifth cannot be added to seven twentyfifths directly, or subtracted from it directly, any more than you can add one apple to (or subtract one appLe from) seven oranges. What would your answer be if you tried? Fortunately, although one cannot change apples into oranges or oranges into apples, numbers at least can be manipulated. Fifths can be changed into twenty-fifths and twenty-fifths can be changed into fifths.
+