SOLUTION: 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?

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Question 1208626: The reciprocal of b/a divided by the reciprocal of multiplied by the reciprocal of 3/a is the reciprocal of what number?
Answer by greenestamps(13198) (Show Source):
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The reciprocal of b/a divided by the reciprocal of multiplied by the reciprocal of 3/a is the reciprocal of what number?

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

The reciprocal of b/a multiplied by multiplied by the reciprocal of 3/a is the reciprocal of what number?

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

a/b multiplied by multiplied by a/3 is the reciprocal of what number?

Now perform that multiplication:

(a/b)(2b/a^2)(a/3) = (2a^2b)/(3a^2b) = 2/3

2/3 is the reciprocal of 3/2

ANSWER: 3/2