\begin{tabular}{l} Question 2 \\ Divide. Write your answer in lowest tehms. Leave your answer as an improper fraction or whole number, \\ necessary. \\ \( \frac{3}{22} \div \frac{21}{2} \) \\ Question Help: \( \square \) Video \( 1 \square \) Video 2 \\ \hline Message instructor D Post to forum \end{tabular}

To solve the division of two fractions, follow these steps: **Problem:** \[ \frac{3}{22} \div \frac{21}{2} \] **Step 1: Rewrite the Division as Multiplication by the Reciprocal** Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{21}{2}\) is \(\frac{2}{21}\). \[ \frac{3}{22} \div \frac{21}{2} = \frac{3}{22} \times \frac{2}{21} \] **Step 2: Multiply the Numerators and the Denominators** Multiply the numerators (top numbers) together and the denominators (bottom numbers) together. \[ \frac{3 \times 2}{22 \times 21} = \frac{6}{462} \] **Step 3: Simplify the Fraction** To simplify \(\frac{6}{462}\), find the greatest common divisor (GCD) of 6 and 462 and divide both the numerator and the denominator by that number. 1. **Find the GCD of 6 and 462:** - The factors of 6 are 1, 2, 3, 6. - The factors of 462 are numerous, but the largest common factor with 6 is 6. 2. **Divide both numerator and denominator by the GCD (6):** \[ \frac{6 \div 6}{462 \div 6} = \frac{1}{77} \] **Final Answer:** \[ \frac{1}{77} \] This is the fraction in its lowest terms as an improper fraction.