Need help with complex fraction interpretation

[Derekman]

I know how to solve a complex fraction but I don't understand the question here - the complex fraction 4/5 over 6 (four-fifths over 6) can be interpreted two different ways. What is the absolute value of the difference between the two interpretations? Express your answer as a common fraction.

I solve the complex fraction as 2/15 or 0.133 (0.8/6.0) but I don't understand what the two different interpretations are. Thanks.

 

[Derekman]

Thanks!

 

[soroban]

Hello, Derekman!

Where did this problem come from?
It seems to have been written by an amateur.
As stated, the premise is incorrect.

I know how to solve a complex fraction, but I don't understand the question here.
The complex fraction 4/5 over 6 (four-fifths over 6) can be interpreted two different ways. . ??

This is not true!

It says, "Four-fifths over six".
. . This can only be written: .\(\displaystyle \dfrac{\:\frac{4}{5}\;}{6}\)

The answer is: .\(\displaystyle \frac{4}{5} \div 6 \:=\:\frac{4}{5} \times \frac{1}{6} \:=\:\frac{2}{15}\)

There is no other interpretation.


If it has said "4 over 5 over 6" or \(\displaystyle 4 \div 5 \div 6\)
. . there is still only one interpretation.

The Order of Operations says:
. . multiplication and division are performed left to right.

Therefore, the problem must be: .\(\displaystyle (4\div5) \div 6 \)


The "other" interpretation would say: "Four over five-sixths"
. . and would be written: .\(\displaystyle 4 \div (5\div 6) \:=\:\dfrac{\,4\;}{\frac{5}{6}\,}\)