Divide. Simplify your answer. 20d/9c^2 ÷ 16cd^2/19cd^2 ______

Rewrite division as multiplication: Write the division of the two fractions as a multiplication by the reciprocal of the second fraction. We have: (20d/9c^2) ÷ (16cd^2/19cd^2) This can be rewritten as: (20d/9c^2) * (19cd^2/16cd^2)Simplify second fraction: Simplify the second fraction before multiplying. The cd^2 terms in the numerator and denominator of the second fraction cancel each other out. So, (19cd^2/16cd^2) simplifies to (19/16)Multiply fractions: Multiply the first fraction by the simplified second fraction. (20d/9c^2) * (19/16) = (20d * 19)/(9c^2 * 16)Perform multiplication: Perform the multiplication in the numerator and the denominator. (20d * 19)/(9c^2 * 16) = (380d)/(144c^2)Simplify final fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, if possible. The greatest common divisor of 380 and 144 is 4. (380d)/(144c^2) = (95d)/(36c^2)

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Simplify your answer.

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\frac{20d}{9c^2} \div \frac{16cd^2}{19cd^2}

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______

Rewrite division as multiplication: Write the division of the two fractions as a multiplication by the reciprocal of the second fraction. $\newline$ We have: $(\frac{20d}{9c^2}) \div (\frac{16cd^2}{19cd^2})$ $\newline$ This can be rewritten as: $(\frac{20d}{9c^2}) \times (\frac{19cd^2}{16cd^2})$
Simplify second fraction: Simplify the second fraction before multiplying. $\newline$ The $cd^2$ terms in the numerator and denominator of the second fraction cancel each other out. $\newline$ So, $(19cd^2/16cd^2)$ simplifies to $(19/16)$
Multiply fractions: Multiply the first fraction by the simplified second fraction. $\newline$ $(\frac{20d}{9c^2}) \times (\frac{19}{16}) = \frac{20d \times 19}{9c^2 \times 16}$
Perform multiplication: Perform the multiplication in the numerator and the denominator. $\newline$ $(20d \times 19)/(9c^2 \times 16) = (380d)/(144c^2)$
Simplify final fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, if possible. $\newline$ The greatest common divisor of $380$ and $144$ is $4$ . $\newline$ $\frac{380d}{144c^2}$ = $\frac{95d}{36c^2}$