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$Simplify. Write your answer as a proper or improper fraction in simplest form. ((6)/(7))/((1)/(7))=(◻)/(◻)$

Simplify. Write your answer as a proper or improper fraction in simplest form. $\newline$ $\frac{\frac{6}{7}}{\frac{1}{7}}=\frac{\square}{\square}$

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Multiplication with rational exponents

Full solution

Q. Simplify. Write your answer as a proper or improper fraction in simplest form.

\newline

\frac{\frac{6}{7}}{\frac{1}{7}}=\frac{\square}{\square}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $(\frac{6}{7}) / (\frac{1}{7})$ . This involves dividing one fraction by another.
Rewrite as multiplication: Rewrite the division of fractions as multiplication. $\newline$ To divide by a fraction, we multiply by its reciprocal. The reciprocal of $(\frac{1}{7})$ is $(\frac{7}{1})$ . $\newline$ $(\frac{6}{7}) / (\frac{1}{7}) = (\frac{6}{7}) \times (\frac{7}{1})$
Perform the multiplication: Perform the multiplication. $\newline$ Now we multiply the numerators and the denominators separately. $\newline$ $(6 \times 7) / (7 \times 1) = 42 / 7$
Simplify the result: Simplify the result. $\newline$ Since $42$ divided by $7$ equals $6$ , we simplify the fraction to: $\newline$ $42 / 7 = 6$
Check for errors: Check for any possible math errors. $\newline$ We divided and multiplied correctly, and the final fraction is in its simplest form.

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