Put these numbers in order from greatest to least.

2

-2 6/40

2 9/36

-2 24/32

1 answer

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.

  1. 2 is simply 2.

  2. -2 6/40:

    • Convert the mixed number to an improper fraction: \[ -2 \frac{6}{40} = -\left(2 + \frac{6}{40}\right) = -\left(\frac{80}{40} + \frac{6}{40}\right) = -\frac{86}{40} = -\frac{43}{20} \]
  3. 2 9/36:

    • Convert the mixed number to an improper fraction: \[ 2 \frac{9}{36} = 2 + \frac{9}{36} = \frac{72}{36} + \frac{9}{36} = \frac{81}{36} = \frac{27}{12} = \frac{9}{4} \]
  4. -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:

  1. 2 = \(2\)
  2. -2 6/40 = \(-\frac{43}{20}\)
  3. 2 9/36 = \(\frac{9}{4}\)
  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: \[ 2 \quad (greater) \quad 2 \frac{9}{36} \quad (greater) \quad -2 \frac{6}{40} \quad (greater) \quad -2 \frac{24}{32} \]