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Evaluate the expression shown below and write your answer as a fraction in simplest form. \newline−37÷611×35-\frac{3}{7}\div\frac{6}{11}\times\frac{3}{5}

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Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form. \newline−37÷611×35-\frac{3}{7}\div\frac{6}{11}\times\frac{3}{5}
  1. Understand the problem: Understand the problem.\newlineWe need to simplify the expression −37÷611×35-\frac{3}{7} \div \frac{6}{11} \times \frac{3}{5}. This involves division and multiplication of fractions.
  2. Rewrite the division as multiplication: Rewrite the division as multiplication.\newlineTo divide by a fraction, we multiply by its reciprocal. So, −37÷611-\frac{3}{7} \div \frac{6}{11} becomes −37×116.-\frac{3}{7} \times \frac{11}{6}.
  3. Perform the multiplication: Perform the multiplication.\newlineNow we multiply −37×116×35-\frac{3}{7} \times \frac{11}{6} \times \frac{3}{5}. When multiplying fractions, we multiply the numerators together and the denominators together.\newline−3×11×37×6×5\frac{-3 \times 11 \times 3}{7 \times 6 \times 5}
  4. Calculate the numerator: Calculate the numerator.\newline−3×11×3=−9×11=−99-3 \times 11 \times 3 = -9 \times 11 = -99
  5. Calculate the denominator: Calculate the denominator. 7×6×5=42×5=2107 \times 6 \times 5 = 42 \times 5 = 210
  6. Write the fraction: Write the fraction.\newlineThe fraction is now −99210.-\frac{99}{210}.
  7. Simplify the fraction: Simplify the fraction.\newlineWe need to find the greatest common divisor (GCD) of 9999 and 210210 to simplify the fraction. The GCD of 9999 and 210210 is 33.
  8. Divide both the numerator and the denominator by the GCD: Divide both the numerator and the denominator by the GCD.\newline−99÷3=−33-99 \div 3 = -33\newline210÷3=70210 \div 3 = 70\newlineSo, the simplified fraction is −3370-\frac{33}{70}.

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