Divide. Simplify your answer. 5m^2n/10n^2 ÷ 10n ______

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, (5m^2n/10n^2) ÷ 10n = (5m^2n/10n^2) × (1/10n).Combine numerators and denominators: Combine the numerators and denominators. So, (5m^2n/10n^2) × (1/10n) = (5m^2n)/(10n^2 * 10n).Simplify the denominator: Simplify the denominator by multiplying the terms. So, 10n^2 * 10n = 100n^3.Place simplified denominator: Place the simplified denominator under the numerator. So, (5m^2n)/(100n^3).Reduce the fraction: Reduce the fraction by canceling out common factors. The number 5 goes into 100 twenty times, and n goes into n^3 n^2 times. So, (5m^2n)/(100n^3) = (m^2)/(20n^2).Check for further simplification: Check if further simplification is possible. Since there are no common factors left in the numerator and denominator, the fraction is in its simplest form.

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Divide. Simplify your answer. $\newline$ $\frac{5m^2n}{10n^2} \div 10n$

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Algebra 1

Multiply and divide rational expressions

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Q. Divide. Simplify your answer.

\newline

\frac{5m^2n}{10n^2} \div 10n

Rewrite as multiplication: Rewrite the division as a multiplication by taking the reciprocal of the second fraction. So, $(5m^2n/10n^2) \div 10n = (5m^2n/10n^2) \times (1/10n)$ .
Combine numerators and denominators: Combine the numerators and denominators. So, $(5m^2n/10n^2) \times (1/10n) = (5m^2n)/(10n^2 \times 10n)$ .
Simplify the denominator: Simplify the denominator by multiplying the terms. So, $10n^2 \times 10n = 100n^3$ .
Place simplified denominator: Place the simplified denominator under the numerator. So, $(5m^2n)/(100n^3)$ .
Reduce the fraction: Reduce the fraction by canceling out common factors. The number $5$ goes into $100$ twenty times, and $n$ goes into $n^3$ $n^2$ times. So, $(5m^2n)/(100n^3) = (m^2)/(20n^2)$ .
Check for further simplification: Check if further simplification is possible. Since there are no common factors left in the numerator and denominator, the fraction is in its simplest form.