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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction. (-(4)/(7))/(-(5)/(8)) Answer:

Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.\newline−47−58 \frac{-\frac{4}{7}}{-\frac{5}{8}} \newlineAnswer:

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Full solution

Q. Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.\newline−47−58 \frac{-\frac{4}{7}}{-\frac{5}{8}} \newlineAnswer:
  1. Understand the problem: Understand the problem.\newlineWe need to divide two negative fractions: (−47)\left(-\frac{4}{7}\right) by (−58)\left(-\frac{5}{8}\right).\newlineWhen dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
  2. Find the reciprocal: Find the reciprocal of the second fraction.\newlineThe reciprocal of (−58)\left(-\frac{5}{8}\right) is (−85)\left(-\frac{8}{5}\right), because we swap the numerator and the denominator.
  3. Multiply fractions: Multiply the first fraction by the reciprocal of the second fraction.\newlineNow we multiply (−47)\left(-\frac{4}{7}\right) by (−85)\left(-\frac{8}{5}\right).
  4. Perform multiplication: Perform the multiplication.\newline(−47)×(−85)=47×85(-\frac{4}{7}) \times (-\frac{8}{5}) = \frac{4}{7} \times \frac{8}{5}, because the negatives cancel each other out.
  5. Multiply numerators and denominators: Multiply the numerators and the denominators separately.\newline(4×8)/(7×5)=32/35(4 \times 8) / (7 \times 5) = 32 / 35
  6. Check for simplification: Check if the fraction can be simplified further.\newlineThe fraction 3235\frac{32}{35} cannot be simplified further because 3232 and 3535 have no common factors other than 11.

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