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Q&A #12670 |
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>If I divide the fraction 6/10 by 2/5 and simply divide across the top and >divide across the bottom like I do when I multiply, it gives me the same >answer as multiplying by the reciprocal (after simplifying). Why? Because division is the inverse operation of multiplication, so they should, and do, work according to the same principals. It is easy to show this always works by applying the usual multiply by the reciprocal of the divisor approach and then reorder the numerator and denominator factors. As an example if we look at 6/10 divided by 2/5 we would traditionally proceed by doing this... 6 5 --- * --- but that is 10 2 (6 * 5) / (10 * 2) If we apply the commutative property of multiplication to the denominator we have (6*5) / (2*10) and now breaking this back into products we get (6/2) * (5/10) and reversing the "multiply by the reciprocal rule" we can change this to a division problem that is (6/2)/(10/5) The problem with this method is that often you just exchange one problem for another... For example if we have (3/5) divided by (4/7) then using the top divided by top, bottom divided by bottom rule we would get (3/4) divided by (5/7) which is equal to the same value, but brings us no closer to a simplified rational answer. -Pat Ballew, for the T2T service
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