Order −3

4
, 3
8
, −11
8
, −1
2
from least to greatest. Which is correct?

A number line going from negative 1 and StartFraction 3 Over 8 EndFraction to StartFraction 3 Over 8 EndFraction in increments of StartFraction 1 Over 8 EndFraction.
Negative 1 and StartFraction 1 Over 8 EndFraction, negative three-fourths, negative one-half, StartFraction 3 Over 8 EndFraction
Negative one-half, negative three-fourths, negative 1 and one-eighth, StartFraction 3 Over 8 EndFraction
StartFraction 3 Over 8 EndFraction, negative 1 and StartFraction 1 Over 8 EndFraction, Negative three-fourths, Negative one-half

1 answer

To order the numbers \(-\frac{3}{4}\), \(\frac{3}{8}\), \(-\frac{11}{8}\), and \(-\frac{1}{2}\) from least to greatest, let's first convert them into decimal or consistent fractional forms for easier comparison:

  1. \(-\frac{3}{4} = -0.75\)
  2. \(\frac{3}{8} = 0.375\)
  3. \(-\frac{11}{8} = -1.375\)
  4. \(-\frac{1}{2} = -0.5\)

Now we compare the numbers:

  • The smallest is \(-\frac{11}{8} = -1.375\)
  • Next is \(-\frac{3}{4} = -0.75\)
  • Then is \(-\frac{1}{2} = -0.5\)
  • Finally, the largest is \(\frac{3}{8} = 0.375\)

Putting these in order from least to greatest gives us:

\[ -\frac{11}{8}, , -\frac{3}{4}, , -\frac{1}{2}, , \frac{3}{8} \]

Now, checking the answer choices against this ordering:

  1. Negative 1 and \(\frac{3}{8}\), -1 and \(\frac{1}{8}\), negative three-fourths, negative one-half
  2. Negative one-half, negative three-fourths, negative 1 and one-eighth, \(\frac{3}{8}\)
  3. \(\frac{3}{8}\), negative 1 and \(\frac{1}{8}\), negative three-fourths, negative one-half

None of the provided answers directly present the correct ordering.

The correct order, as noted as \( -\frac{11}{8}, -\frac{3}{4}, -\frac{1}{2}, \frac{3}{8} \) can be summarized as:

  • An option isn't provided that matches this order.

If I had to choose the closest in terms of correct values:

-1 and \(\frac{3}{8}\), -1 and \(\frac{1}{8}\), negative three-fourths, negative one-half seems incorrect as it does not follow the order.

Thus, there seems to be an error or mismatch in the options provided against the correct ordering.

Final Ordering:

  • \(-\frac{11}{8}, -\frac{3}{4}, -\frac{1}{2}, \frac{3}{8}\) .