To compare the numbers and put them in order from greatest to least, let's first convert each of them into improper fractions or decimal form for easier comparison.
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2 is simply 2.
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-2 6/40:
- Convert the mixed number to an improper fraction: \[ -2 \frac{6}{40} = -\left(2 + \frac{6}{40}\right) = -\left(\frac{80}{40} + \frac{6}{40}\right) = -\frac{86}{40} = -\frac{43}{20} \]
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2 9/36:
- Convert the mixed number to an improper fraction: \[ 2 \frac{9}{36} = 2 + \frac{9}{36} = \frac{72}{36} + \frac{9}{36} = \frac{81}{36} = \frac{27}{12} = \frac{9}{4} \]
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-2 24/32:
- Convert the mixed number to an improper fraction: \[ -2 \frac{24}{32} = -\left(2 + \frac{24}{32}\right) = -\left(\frac{64}{32} + \frac{24}{32}\right) = -\frac{88}{32} = -\frac{22}{8} = -\frac{11}{4} \]
Now we have three numbers in fractional form:
- 2 = \(2\)
- -2 6/40 = \(-\frac{43}{20}\)
- 2 9/36 = \(\frac{9}{4}\)
- -2 24/32 = \(-\frac{11}{4}\)
Next, we convert \(2\) and \(\frac{9}{4}\) into a common denominator for easier comparison. The common denominator for \(2\) (which can be written as \(\frac{8}{4}\)) and \(\frac{9}{4}\) is \(4\).
Thus, we can compare the values:
- \(2 = \frac{8}{4}\)
- \(-\frac{43}{20}\)
- \(\frac{9}{4}\)
- \(-\frac{11}{4}\)
Now let's rank these:
- \(2 = \frac{8}{4} \approx 2\) (greatest)
- \(\frac{9}{4} = 2.25\)
- \(-\frac{11}{4} = -2.75\)
- \(-\frac{43}{20} \approx -2.15\) (least negative)
Finally, writing them in order from greatest to least gives us:
2, 2 9/36, -2 6/40, -2 24/32.
In summary: \[ 2 \quad (greater) \quad 2 \frac{9}{36} \quad (greater) \quad -2 \frac{6}{40} \quad (greater) \quad -2 \frac{24}{32} \]
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