Identify Problem: Identify the division problem involving two fractions. We have (2/10) ÷ (1/7).Recall Rule: Recall the rule for dividing fractions: to divide by a fraction, multiply by its reciprocal. The reciprocal of (1/7) is 7/1. So, (2/10) ÷ (1/7) becomes (2/10) * (7/1).Perform Multiplication: Perform the multiplication of the two fractions. Multiply the numerators: 2 * 7 = 14. Multiply the denominators: 10 * 1 = 10. So, (2/10) * (7/1) = 14/10.Simplify Fraction: Simplify the fraction 14/10 if possible. Both the numerator and the denominator are divisible by 2. Divide both by 2 to simplify: 14 ÷ 2 = 7 and 10 ÷ 2 = 5. So, 14/10 simplifies to 7/5.Check Final Result: Check the final result for any possible simplification. The fraction 7/5 is already in simplest form and cannot be simplified further.

Precalculus

Operations with rational exponents

Full solution

\frac{2}{10} \div \frac{1}{7}

Identify Problem: Identify the division problem involving two fractions. $\newline$ We have $(\frac{2}{10}) \div (\frac{1}{7})$ .
Recall Rule: Recall the rule for dividing fractions: to divide by a fraction, multiply by its reciprocal. $\newline$ The reciprocal of $(\frac{1}{7})$ is $\frac{7}{1}$ . $\newline$ So, $(\frac{2}{10}) \div (\frac{1}{7})$ becomes $(\frac{2}{10}) \times (\frac{7}{1})$ .
Perform Multiplication: Perform the multiplication of the two fractions. $\newline$ Multiply the numerators: $2 \times 7 = 14$ . $\newline$ Multiply the denominators: $10 \times 1 = 10$ . $\newline$ So, $(\frac{2}{10}) \times (\frac{7}{1}) = \frac{14}{10}$ .
Simplify Fraction: Simplify the fraction $\frac{14}{10}$ if possible. $\newline$ Both the numerator and the denominator are divisible by $2$ . $\newline$ Divide both by $2$ to simplify: $14 \div 2 = 7$ and $10 \div 2 = 5$ . $\newline$ So, $\frac{14}{10}$ simplifies to $\frac{7}{5}$ .
Check Final Result: Check the final result for any possible simplification. $\newline$ The fraction $\frac{7}{5}$ is already in simplest form and cannot be simplified further.