Question

Which set of rational numbers are ordered from least to greatest?

A number line going from negative 3 to positive 3 in increments of 1.

Negative 1, negative 1 and one-half, negative 1 and one-fourth, negative 1 and StartFraction 7 Over 8 EndFraction
Negative 1 and StartFraction 7 Over 8 EndFraction, negative 1 and one-half, negative 1 and one-fourth, negative 1
Negative 1, negative 1 and one-fourth, negative 1 and one-half, negative 1 and StartFraction 7 Over 8 EndFraction
Negative 1 and StartFraction 7 Over 8 EndFraction, negative 1 and one-fourth, negative 1 and one-half, negative 1

Answer 1

To order the given rational numbers from least to greatest, we will first convert all of them to improper fractions for easier comparison:

1. **Negative 1:** This is \(-1 = -\frac{1}{1}\).
2. **Negative 1 and one-half:** This is \(-1.5 = -\frac{3}{2}\).
3. **Negative 1 and one-fourth:** This is \(-1.25 = -\frac{5}{4}\).
4. **Negative 1 and \(\frac{7}{8}\):** This is \(-1.875 = -\frac{15}{8}\).

Now we have the following numbers as improper fractions:
- \(-1\) is \(-\frac{1}{1}\) or \(-\frac{8}{8}\)
- \(-1 \frac{1}{2}\) is \(-\frac{3}{2}\)
- \(-1 \frac{1}{4}\) is \(-\frac{5}{4}\)
- \(-1 \frac{7}{8}\) is \(-\frac{15}{8}\)

Next, we will compare and place these fractions on a number line:

1. \(-\frac{15}{8} \approx -1.875\) (Least)
2. \(-\frac{3}{2} = -1.5\)
3. \(-\frac{5}{4} = -1.25\)
4. \(-\frac{8}{8} = -1\) (Greatest)

Now we can order them from least to greatest:

1. \(-1 \frac{7}{8}\)
2. \(-1 \frac{1}{2}\)
3. \(-1 \frac{1}{4}\)
4. \(-1\)

So, the correct order from least to greatest is:

**Negative 1 and \(\frac{7}{8}\), negative 1 and one-half, negative 1 and one-fourth, negative 1.**

Thus, the answer is:

**Negative 1 and \(\frac{7}{8}\), negative 1 and one-half, negative 1 and one-fourth, negative 1.**