Question
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 \( 1: \)
Ask by Clarke Griffin. in Canada
Mar 10,2025
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Tutor-Verified Answer
Answer
a. Lowest terms: 3:9:7
b. Equivalent ratio with 1 as the smallest term: 1:3:7/3
Solution
**a. Lowest terms:**
We start with the ratio
\[
69:207:161
\]
Factor each term:
- \(69 = 3 \times 23\)
- \(207 = 9 \times 23\)
- \(161 = 7 \times 23\)
Since each term has a factor of \(23\), we divide by \(23\) to obtain the lowest terms:
\[
\frac{69}{23}:\frac{207}{23}:\frac{161}{23} = 3:9:7
\]
**b. Equivalent ratio having \(1\) as the smallest term:**
In the ratio \(3:9:7\), the smallest term is \(3\). To change the smallest term to \(1\), we divide each term by \(3\):
\[
\frac{3}{3}:\frac{9}{3}:\frac{7}{3} = 1:3:\frac{7}{3}
\]
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Simplify this solution Mind Expander
To reduce the ratio \( 69: 207: 161 \) to its lowest terms, we first find the greatest common divisor (GCD) of the three numbers. The GCD is 23, so we divide each term by 23: - \( 69 \div 23 = 3 \) - \( 207 \div 23 = 9 \) - \( 161 \div 23 = 7 \) Thus, the ratio in its lowest terms is \( 3: 9: 7 \). To express the ratio with 1 as the smallest term, we choose the smallest term which is 3. We divide each term by 3: - \( 3 \div 3 = 1 \) - \( 9 \div 3 = 3 \) - \( 7 \div 3 = \frac{7}{3} \) Therefore, the equivalent ratio with 1 as the smallest term is \( 1: 3: \frac{7}{3} \).
