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Divide.
Write your answer in simplest form.

(1)/(7)÷(2)/(5)=" ? "

Divide. $\newline$ Write your answer in simplest form. $\newline$ $\frac{1}{7} \div \frac{2}{5}=?$

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Multiply and divide rational expressions

Full solution

Q. Divide.

\newline

Write your answer in simplest form.

\newline

\frac{1}{7} \div \frac{2}{5}=?

Multiply fractions by reciprocal: To divide fractions, multiply the first fraction by the reciprocal of the second fraction. $\newline$ So, $(\frac{1}{7}) \div (\frac{2}{5})$ becomes $(\frac{1}{7}) \times (\frac{5}{2})$ .
Multiply numerators and denominators: Now, multiply the numerators together and the denominators together. $\newline$ $1 \times 5 = 5$ and $7 \times 2 = 14$ . $\newline$ So, $(\frac{1}{7}) \times (\frac{5}{2}) = \frac{5}{14}$ .
Check for simplification: Check if the fraction $\frac{5}{14}$ can be simplified. $\newline$ Since $5$ and $14$ have no common factors other than $1$ , the fraction is already in simplest form.

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