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Evaluate and simplify the following complex fraction. ((-2)/(-7))/((4)/(-9))=

Evaluate and simplify the following complex fraction.\newline−2−74−9=□ \frac{\frac{-2}{-7}}{\frac{4}{-9}}=\square

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Full solution

Q. Evaluate and simplify the following complex fraction.\newline−2−74−9=□ \frac{\frac{-2}{-7}}{\frac{4}{-9}}=\square
  1. Simplify Fraction: First, let's simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.−2−7×−94\frac{-2}{-7} \times \frac{-9}{4}
  2. Multiply Numerators and Denominators: Now, multiply the numerators and the denominators separately.\newlineNumerator: (−2)×(−9)=18(-2) \times (-9) = 18\newlineDenominator: (−7)×(4)=−28(-7) \times (4) = -28
  3. Write Result as Single Fraction: Next, write the result as a single fraction. 18−28\frac{18}{-28}
  4. Simplify Final Fraction: Finally, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 22. \newline18−28=(182)/(−282)=9−14\frac{18}{-28} = \left(\frac{18}{2}\right) / \left(-\frac{28}{2}\right) = \frac{9}{-14}

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