To compare the mixed numbers \(1 \frac{1}{8}\), \(1 \frac{3}{12}\), and \(1 \frac{8}{11}\), we first convert each of the fractions to a common benchmark for easier comparison.
Step 1: Convert the fractions to decimals
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For \(1 \frac{1}{8}\): \[ 1 \frac{1}{8} = 1 + \frac{1}{8} = 1 + 0.125 = 1.125 \]
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For \(1 \frac{3}{12}\) (Note that \( \frac{3}{12} = \frac{1}{4} = 0.25\)): \[ 1 \frac{3}{12} = 1 + \frac{3}{12} = 1 + 0.25 = 1.25 \]
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For \(1 \frac{8}{11}\): \[ 1 \frac{8}{11} = 1 + \frac{8}{11} \approx 1 + 0.727 \approx 1.727 \quad (\text{using } \frac{8}{11} \approx 0.727) \]
Step 2: Compare the mixed numbers
Now we compare the decimal values:
- \(1 \frac{1}{8} \approx 1.125\)
- \(1 \frac{3}{12} \approx 1.25\)
- \(1 \frac{8}{11} \approx 1.727\)
Ordering these from greatest to least, we get:
- Greatest: \(1 \frac{8}{11}\) (1.727)
- Middle: \(1 \frac{3}{12}\) (1.25)
- Least: \(1 \frac{1}{8}\) (1.125)
Conclusion
Therefore, the order from greatest to least is: \[ 1 \frac{8}{11} > 1 \frac{3}{12} > 1 \frac{1}{8} \]
Benchmark Statement
Now, using your benchmark statement:
- You can fill in the blanks as follows: \[ 1 \frac{8}{11} > 1 \frac{4}{8} > 1 \frac{3}{12} > 1 \frac{1}{8} \]
This shows the ordering using the fraction \( \frac{4}{8} \) as a benchmark in your reference.