Question 1130342
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Sometimes you have to ignore the preachings of tutor @maththerapy.  Obviously there is not only "1 CORRECT way" to solve this problem.  And the convoluted method he uses to solve the problem is DEFINITELY NOT the SIMPLEST.<br>
Tutor @theo provides several valid options, all of which are less work than what @maththerapy does.<br>
The easiest way to work this problem is to recognize that 2/5 is just half of 4/5 (listen to the words, if you don't see it in the written fractions).  Since 2/5 is half of 4/5, the 4/5 must have been divided by 2 to get the 2/5.<br>
That method of solution admittedly won't be seen by most people.  So the next best way to solve the problem, in my opinion, is to know that (a/c) divided by (b/c) is just a/b.  So (4/5) divided by (2/5) is just 4/2 = 2.<br>
It always works that way.  In elementary school you are told that, to divide fractions, you "flip" the second fraction and multiply.  When you do that with a problem like this, the denominators cancel:<br>
{{{(a/c)/(b/c) = (a/c)(c/b) = a/b}}}<br>
This method is equivalent to one of the methods suggested by @theo: multiply both fractions by their common denominator, 5:<br>
{{{(4/5)/(2/5) = (5(4/5))/(5(2/5)) = 4/2 = 2}}}<br>
And you can always use the straightforward process taught in elementary school, without realizing there is a shortcut:<br>
{{{(4/5)/(2/5) = (4/5)*(5/2) = 20/10 = 1}}}