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Evaluate and simplify the following complex fraction. ((2)/(3))/((4)/(-9))=

Evaluate and simplify the following complex fraction.\newline234−9=□ \frac{\frac{2}{3}}{\frac{4}{-9}}=\square

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Full solution

Q. Evaluate and simplify the following complex fraction.\newline234−9=□ \frac{\frac{2}{3}}{\frac{4}{-9}}=\square
  1. Find Reciprocal: First, let's find the reciprocal of the denominator 4−9\frac{4}{-9}.\newlineReciprocal: −94\frac{-9}{4}
  2. Multiply Numerator: Now, multiply the numerator 23\frac{2}{3} by the reciprocal of the denominator −94\frac{-9}{4}.23×−94\frac{2}{3} \times \frac{-9}{4}
  3. Perform Multiplication: Perform the multiplication.\newline(2×−9)/(3×4)=−18/12(2 \times -9) / (3 \times 4) = -18 / 12
  4. Simplify Fraction: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 66. \newline−1812=−32-\frac{18}{12} = -\frac{3}{2}

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