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

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Evaluate rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form

\left(\frac{4}{9} - \frac{20}{7}\right)\div \frac{3}{4}

Find common denominator: Find a common denominator for the fractions $\frac{4}{9}$ and $\frac{20}{7}$ to subtract them. $\newline$ The least common multiple (LCM) of $9$ and $7$ is $63$ .
Convert fractions: Convert the fractions to have the common denominator of $63$ . $\left(\frac{4}{9}\right) \times \left(\frac{7}{7}\right) = \frac{28}{63}$ $\left(\frac{20}{7}\right) \times \left(\frac{9}{9}\right) = \frac{180}{63}$
Subtract fractions: Subtract the second fraction from the first fraction. $\newline$ $(\frac{28}{63}) - (\frac{180}{63}) = (\frac{28 - 180}{63}) = \frac{-152}{63}$
Divide by fraction: Divide the result by $\frac{3}{4}$ . $\newline$ To divide by a fraction, multiply by its reciprocal. $\newline$ $(-\frac{152}{63}) \div (\frac{3}{4}) = (-\frac{152}{63}) \times (\frac{4}{3})$
Multiply numerators and denominators: Multiply the numerators and denominators. $\newline$ $(-152 \times 4) / (63 \times 3) = -608 / 189$
Simplify fraction: Simplify the fraction if possible. $\newline$ Both the numerator and the denominator are divisible by $19$ . $\newline$ $-608 / 189 = (-32 \times 19) / (9 \times 21) = -32 / 9$

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