Simplify the complex fraction.
-$\frac{4+\frac{1}{3}}{3-\frac{2}{27}}$

A) $\frac{117}{79}$

B) $\frac{351}{158}$

C) $\frac{234}{79}$

D) $\frac{351}{79}$

Question

Simplify the complex fraction.
-$\frac{4+\frac{1}{3}}{3-\frac{2}{27}}$

A) $\frac{117}{79}$

B) $\frac{351}{158}$

C) $\frac{234}{79}$

D) $\frac{351}{79}$

Quizplus · Accepted Answer

To simplify the complex fraction, first simplify the numerator and the denominator separately. For the numerator, $4 + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{13}{3}$. For the denominator, $3 - \frac{2}{27} = \frac{81}{27} - \frac{2}{27} = \frac{79}{27}$. Then, divide the simplified numerator by the simplified denominator: $\frac{13/3}{79/27} = \frac{13}{3} \times \frac{27}{79} = \frac{351}{79}$. However, there seems to be a mistake in my explanation regarding the final simplification. Correcting that, the simplified fraction should indeed be $\frac{13}{3} \times \frac{27}{79} = \frac{13 \times 27}{3 \times 79}$, which simplifies correctly to $\frac{351}{237}$, but this is not among the options provided, indicating a mistake in my calculation or interpretation. The correct approach is to simplify the complex fraction directly: $\frac{4+\frac{1}{3}}{3-\frac{2}{27}}$, which simplifies to $\frac{4 \times 3 + 1}{3 \times 3 - \frac{2}{27} \times 27}$ leading to $\frac{12 + 1}{9 - 2}$, which is $\frac{13}{7}$, but this also does not match the provided options or the initial explanation. The correct simplification process should lead to a result that matches one of the given options, and the mistake in my explanation involves incorrect arithmetic or simplification steps. The correct simplification after re-evaluating should be: $\frac{4+\frac{1}{3}}{3-\frac{2}{27}} = \frac{\frac{12}{3}+\frac{1}{3}}{\frac{81}{27}-\frac{2}{27}} = \frac{\frac{13}{3}}{\frac{79}{27}}$, and when you multiply by the reciprocal, it should indeed simplify correctly to one of the provided options, taking into account the correct arithmetic operations and simplifications. My initial claim of the answer being A was incorrect due to a miscalculation. The correct answer, based on the proper simplification, should align with the options provided, and the correct simplification leads to $\frac{13}{3} \times \frac{27}{79} = \frac{351}{79}$, which matches option D, not A as initially stated. My explanation contained errors in the arithmetic process.

Simplify the Complex Fraction 4+133−227\frac{4+\frac{1}{3}}{3-\frac{2}{27}}3−272​4+31​​ A) 11779\frac{117}{79}79117​ B) 351158\frac{351}{158}158351​ C) 23479\frac{234}{79}79234​ D) 35179\frac{351}{79}79351​

Simplify the Complex Fraction $\frac{4+\frac{1}{3}}{3-\frac{2}{27}}$ A) $\frac{117}{79}$ B) $\frac{351}{158}$ C) $\frac{234}{79}$ D) $\frac{351}{79}$