Reduce the following ratio to its lowest terms and to an equivalent ratio having 1 as the smallest term. \( 69: 207: 161 \) a. Lowest terms: b. Lowest term is \( 1: \)

**Step 1. Find the Greatest Common Divisor (GCD)** The ratio is given as \[ 69:207:161. \] Factor each term: - \( 69 = 3 \times 23 \) - \( 207 = 3 \times 69 = 3 \times 3 \times 23 \) - \( 161 = 7 \times 23 \) Since each term has a common factor of \( 23 \), the GCD is \( 23 \). --- **Step 2. Reduce to Lowest Terms** Divide each term by \( 23 \): \[ \frac{69}{23} : \frac{207}{23} : \frac{161}{23} = 3:9:7. \] Thus, the ratio in lowest terms is \[ \boxed{3:9:7}. \] --- **Step 3. Express the Ratio with 1 as the Smallest Term** In the reduced ratio \( 3:9:7 \), the smallest term is \( 3 \). To get an equivalent ratio with \( 1 \) as the smallest term, divide every term by \( 3 \): \[ \frac{3}{3} : \frac{9}{3} : \frac{7}{3} = 1 : 3 : \frac{7}{3}. \] Thus, the equivalent ratio is \[ \boxed{1:3:\frac{7}{3}}. \] --- **Final Answers:** a. Lowest terms: \(3:9:7\) b. Ratio with \(1\) as the smallest term: \(1:3:\frac{7}{3}\)