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:

1. **Find the Greatest Common Divisor (GCD):** We start with the ratio \[ 69 : 207 : 161. \] Factor each term: - \(69 = 3 \times 23\) - \(207 = 9 \times 23 = 3^2 \times 23\) - \(161 = 7 \times 23\) The common factor is \(23\). Hence, the GCD is \(23\). 2. **Reduce the Ratio to its Lowest Terms:** Divide each term by \(23\): - \(\frac{69}{23} = 3\) - \(\frac{207}{23} = 9\) - \(\frac{161}{23} = 7\) Thus, the ratio in lowest terms is \[ 3 : 9 : 7. \] 3. **Normalize the Ratio so That the Smallest Term is 1:** In the lowest term ratio \(3:9:7\), the smallest term is \(3\). To convert this term to \(1\), divide each term by \(3\): - \(\frac{3}{3} = 1\) - \(\frac{9}{3} = 3\) - \(\frac{7}{3} = \frac{7}{3}\) The equivalent ratio with the smallest term as \(1\) is \[ 1 : 3 : \frac{7}{3}. \] **Final Answers:** a. Lowest terms: \(3 : 9 : 7\) b. Lowest term is \(1\): \(1 : 3 : \frac{7}{3}\)