Question

Ordering 3 or More Mixed Numbers

Mixed number - a single value combining a whole number and a _ part of a whole
Order these mixed numbers from greatest to least: 1 1/8 , 1 3/12 , and 1 8/11
Since 4/8 = 1/2, use the benchmarks to order the fractions. |

_ > 1 4/8 > _

Answer 1

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

1. **For \(1 \frac{1}{8}\)**:
\[
1 \frac{1}{8} = 1 + \frac{1}{8} = 1 + 0.125 = 1.125
\]

2. **For \(1 \frac{3}{12}\)** (Note that \( \frac{3}{12} = \frac{1}{4} = 0.25\)):
\[
1 \frac{3}{12} = 1 + \frac{3}{12} = 1 + 0.25 = 1.25
\]

3. **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.