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Evaluate the expression shown below and write your answer as a fraction in simplest form $-\frac{3}{7}\div\frac{6}{11}\times\frac{3}{5}$

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Roots of rational numbers

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

-\frac{3}{7}\div\frac{6}{11}\times\frac{3}{5}

Rewrite division as multiplication: Rewrite the division as multiplication by the reciprocal. $\newline$ To divide by a fraction, you multiply by its reciprocal. The reciprocal of $\frac{6}{11}$ is $\frac{11}{6}$ . $\newline$ So, $-\frac{3}{7} \div \frac{6}{11}$ becomes $-\frac{3}{7} \times \frac{11}{6}.$
Multiply first two fractions: Multiply the first two fractions. $\newline$ Now we multiply $−\frac{3}{7}$ by $\frac{11}{6}$ . $\newline$ $(−\frac{3}{7}) \times (\frac{11}{6}) = (−3 \times 11) / (7 \times 6) = −\frac{33}{42}$ .
Simplify the fraction: Simplify the fraction. $\newline$ Before we continue, let's simplify $\frac{-33}{42}$ . $\newline$ Both the numerator and the denominator are divisible by $3$ . $\newline$ $\frac{-33}{42} = \frac{(-33 \div 3)}{(42 \div 3)} = \frac{-11}{14}$ .
Multiply by third fraction: Multiply the simplified fraction by the third fraction. $\newline$ Now we multiply $\frac{-11}{14}$ by $\frac{3}{5}$ . $\newline$ $\left(\frac{-11}{14}\right) \times \left(\frac{3}{5}\right) = \frac{-11 \times 3}{14 \times 5} = \frac{-33}{70}$ .
Check for further simplification: Check if the final fraction can be simplified. $\newline$ The fraction $-\frac{33}{70}$ cannot be simplified further because $33$ and $70$ have no common factors other than $1$ .

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