Question

greatest to least

11 26/40 11 5/20 -11 2/25

Answer 1

To compare the mixed numbers \(11 \frac{26}{40}\), \(11 \frac{5}{20}\), and \(-11 \frac{2}{25}\) from greatest to least, let's first convert them into improper fractions.

1. **Convert each mixed number to an improper fraction:**

- **For \(11 \frac{26}{40}\):**
\[
11 \frac{26}{40} = \frac{11 \times 40 + 26}{40} = \frac{440 + 26}{40} = \frac{466}{40}
\]

- **For \(11 \frac{5}{20}\):**
\[
11 \frac{5}{20} = \frac{11 \times 20 + 5}{20} = \frac{220 + 5}{20} = \frac{225}{20}
\]

- **For \(-11 \frac{2}{25}\):**
\[
-11 \frac{2}{25} = -\left(\frac{11 \times 25 + 2}{25}\right) = -\left(\frac{275 + 2}{25}\right) = -\left(\frac{277}{25}\right) = -\frac{277}{25}
\]

2. **Now, let's express all fractions with a common denominator to compare them easily.** The least common multiple (LCM) of 40, 20, and 25 is 200.

- **Convert \( \frac{466}{40} \):**
\[
\frac{466}{40} \times \frac{5}{5} = \frac{2330}{200}
\]

- **Convert \( \frac{225}{20} \):**
\[
\frac{225}{20} \times \frac{10}{10} = \frac{2250}{200}
\]

- **Convert \( -\frac{277}{25} \):**
\[
-\frac{277}{25} \times \frac{8}{8} = -\frac{2216}{200}
\]

3. **Now we have:**
- \( \frac{2330}{200} \) (for \(11 \frac{26}{40}\))
- \( \frac{2250}{200} \) (for \(11 \frac{5}{20}\))
- \(-\frac{2216}{200}\) (for \(-11 \frac{2}{25}\))

4. **Compare the values:**
- \( \frac{2330}{200} \)
- \( \frac{2250}{200} \)
- \(-\frac{2216}{200}\)

From greatest to least, the order is:

1. \(11 \frac{26}{40} \)
2. \(11 \frac{5}{20} \)
3. \(-11 \frac{2}{25} \)

So the final answer is:

\[ 11 \frac{26}{40} , 11 \frac{5}{20} , -11 \frac{2}{25} \]