Evaluate and simplify the following complex fraction. $\newline$ $\frac{\frac{-5}{7}}{\frac{2}{4}}=\square$

Full solution

Q. Evaluate and simplify the following complex fraction.

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\frac{\frac{-5}{7}}{\frac{2}{4}}=\square

Rewrite as division problem: First, let's rewrite the complex fraction as a division problem: $(-\frac{5}{7}) \div (\frac{2}{4})$ .
Use reciprocal: Now, remember that dividing by a fraction is the same as multiplying by its reciprocal. So, we'll take the reciprocal of $(\frac{2}{4})$ , which is $(\frac{4}{2})$ .
Multiply fractions: Next, we multiply $(-\frac{5}{7})$ by $(\frac{4}{2})$ . So, (-\frac{$5$}{$7$}) \times (\frac{$4$}{$2$}) = (\frac{$-5$ \times $4$}{$7$ \times $2$})\.
Perform multiplication: Now, let's do the multiplication: \((-5 \times 4) = -20 and $(7 \times 2) = 14$ .
Simplify fraction: So, we have $-\frac{20}{14}$ . We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .
Simplify fraction: So, we have $-20/14$ . We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .After simplifying, we get $-10/7$ .