Question 131091This question is from textbook Prealgebra and Introductory Algebra
: Is this true or false? When dividing a fraction, the numerator is inverted and multiplied by the denominator.
This question is from textbook Prealgebra and Introductory Algebra
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Is this true or false? When dividing a fraction, the numerator is inverted and multiplied by the denominator.
I will assume that you are talking about fractions of the form (a/b)/(c/d). These are known as complex fractions and what we want to do is to make the denominator,(c/d), equal to 1. When we do that, we will have reduced the complex fraction to a simple fraction and I'm sure that you can easily deal with those. How do we do that? We simply multiply (c/d) by (d/c) and that equals 1. If we do that, though, we have to also multiply the numerator by (d/c) and when we do that, we have multiplied the complex fraction by (d/c)/(d/c) which equals 1 and that does not chance a thing. Lets do that and see what we get:
(a/b)*(d/c)/(c/d)*(d/c)=(a*d/b*c)/1 which equals (a/b)*(d/c) or ad/bc
SO THE ANSWER IS "FALSE". WHAT WE ACTUALLY DID WAS TO INVERT THE DENOMINATOR
AND MULTIPLY BUT HOPEFULLY YOU CAN NOW SEE WHY WE INVERTED THE DENOMINATOR AND MULTIPLIED
Hope this helps---ptaylor
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