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Evaluate the expression shown below and write your answer as a fraction in simplest form (49−207)÷34\left(\frac{4}{9} - \frac{20}{7}\right)\div \frac{3}{4}

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Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form (49−207)÷34\left(\frac{4}{9} - \frac{20}{7}\right)\div \frac{3}{4}
  1. Find common denominator: Find a common denominator for the fractions 49\frac{4}{9} and 207\frac{20}{7} to subtract them.\newlineThe least common multiple (LCM) of 99 and 77 is 6363.
  2. Convert fractions: Convert the fractions to have the common denominator of 6363.(49)×(77)=2863\left(\frac{4}{9}\right) \times \left(\frac{7}{7}\right) = \frac{28}{63}(207)×(99)=18063\left(\frac{20}{7}\right) \times \left(\frac{9}{9}\right) = \frac{180}{63}
  3. Subtract fractions: Subtract the second fraction from the first fraction.\newline(2863)−(18063)=(28−18063)=−15263(\frac{28}{63}) - (\frac{180}{63}) = (\frac{28 - 180}{63}) = \frac{-152}{63}
  4. Divide by fraction: Divide the result by 34\frac{3}{4}.\newlineTo divide by a fraction, multiply by its reciprocal.\newline(−15263)÷(34)=(−15263)×(43)(-\frac{152}{63}) \div (\frac{3}{4}) = (-\frac{152}{63}) \times (\frac{4}{3})
  5. Multiply numerators and denominators: Multiply the numerators and denominators.\newline(−152×4)/(63×3)=−608/189(-152 \times 4) / (63 \times 3) = -608 / 189
  6. Simplify fraction: Simplify the fraction if possible.\newlineBoth the numerator and the denominator are divisible by 1919.\newline−608/189=(−32×19)/(9×21)=−32/9-608 / 189 = (-32 \times 19) / (9 \times 21) = -32 / 9

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