Reduce the following ratio to its lowest terms and to an equivalent ratio having 1 as the smallest term.
69 : 207 : 161


To reduce the ratio \(69 : 207 : 161\) to its lowest terms, we first find the greatest common divisor (GCD) of the three numbers.

1. **Finding the GCD**:
   - The prime factorization of the numbers:
     - \(69 = 3 \times 23\)
     - \(207 = 3 \times 69 = 3^2 \times 23\)
     - \(161 = 7 \times 23\)
   - The common factor is \(23\).

2. **Dividing each term by the GCD (23)**:
   \[
   69 \div 23 = 3, \quad 207 \div 23 = 9, \quad 161 \div 23 = 7
   \]
   Therefore, the reduced ratio is:
   \[
   3 : 9 : 7
   \]

3. **Making 1 the smallest term**:
   To create an equivalent ratio with 1 as the smallest term, we can divide each term by 3 (the smallest number in the reduced ratio):
   \[
   3 \div 3 = 1, \quad 9 \div 3 = 3, \quad 7 \div 3 \approx 2.33
   \]
   Thus, the equivalent ratio is:
   \[
   1 : 3 : \frac{7}{3}
   \]
   (If you prefer whole numbers, we can also use a scaling factor.)

To summarize:
- The reduced ratio is \(3 : 9 : 7\).
- An equivalent ratio with 1 as the smallest term is \(1 : 3 : \frac{7}{3}\).

Would you like any further details or have any questions? Here are some follow-up questions:
1. How do you find the GCD of larger sets of numbers?
2. What are the applications of ratios in real life?
3. Can you provide an example of a ratio problem with different numbers?
4. How do you convert ratios into fractions?
5. What is the significance of reducing ratios? 

**Tip**: When working with ratios, always simplify to the lowest terms first for clarity.

Reduce the following ratio to its lowest terms and to an equivalent ratio having 1 as the smallest term: 69 : 207 : 161

Learn how to reduce the ratio 69 : 207 : 161 to its lowest terms and find an equivalent ratio with 1 as the smallest term. This solution includes GCD calculations and ratio simplification, suitable for students in Grades 6-8.

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