Question 1208626
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The reciprocal of b/a divided by the reciprocal of {{{2b/a^2}}} multiplied by the reciprocal of 3/a is the reciprocal of what number?<br>
Dividing by the reciprocal of the fraction P/Q is the same as multiplying by the fraction P/Q.  So change the statement of the problem to<br>
The reciprocal of b/a multiplied by {{{2b/a^2}}} multiplied by the reciprocal of 3/a is the reciprocal of what number?<br>
The reciprocal of b/a is a/b; the reciprocal of 3/a is a/3.  So again change the statement of the problem to<br>
a/b multiplied by {{{2b/a^2}}} multiplied by a/3 is the reciprocal of what number?<br>
Now perform that multiplication:<br>
(a/b)(2b/a^2)(a/3) = (2a^2b)/(3a^2b) = 2/3<br>
2/3 is the reciprocal of 3/2<br>
ANSWER: 3/2<br>