Answer :
To determine which set of rational numbers is ordered from least to greatest, we first need to understand the value of each fraction:
1. The number [tex]\(-1\)[/tex] is simply [tex]\(-1\)[/tex].
2. The number [tex]\(-1 \frac{1}{2}\)[/tex] can be written as [tex]\(-1 - \frac{1}{2} = -1.5\)[/tex].
3. The number [tex]\(-1 \frac{1}{4}\)[/tex] can be written as [tex]\(-1 - \frac{1}{4} = -1.25\)[/tex].
4. The number [tex]\(-1 \frac{7}{8}\)[/tex] can be written as [tex]\(-1 - \frac{7}{8} = -1.875\)[/tex].
With these conversions, we compare the decimal values to sort the numbers from least to greatest. Here are the decimal equivalents:
- [tex]\(-1\)[/tex] is [tex]\(-1\)[/tex]
- [tex]\(-1 \frac{1}{2}\)[/tex] is [tex]\(-1.5\)[/tex]
- [tex]\(-1 \frac{1}{4}\)[/tex] is [tex]\(-1.25\)[/tex]
- [tex]\(-1 \frac{7}{8}\)[/tex] is [tex]\(-1.875\)[/tex]
Ordering these from least to greatest:
- [tex]\(-1.875\)[/tex] (i.e., [tex]\(-1 \frac{7}{8}\)[/tex])
- [tex]\(-1.5\)[/tex] (i.e., [tex]\(-1 \frac{1}{2}\)[/tex])
- [tex]\(-1.25\)[/tex] (i.e., [tex]\(-1 \frac{1}{4}\)[/tex])
- [tex]\(-1\)[/tex] (i.e., [tex]\(-1\)[/tex])
Now let's compare this ordered sequence with the given sets:
1. [tex]\(-1, -1 \frac{1}{2}, -1 \frac{1}{4}, -1 \frac{7}{8}\)[/tex]
- This sequence is [tex]\(-1, -1.5, -1.25, -1.875\)[/tex], which is not in ascending order.
2. [tex]\(-1 \frac{7}{8}, -1 \frac{1}{2}, -1 \frac{1}{4}, -1\)[/tex]
- This sequence is [tex]\(-1.875, -1.5, -1.25, -1\)[/tex], which is correctly ordered in ascending order.
3. [tex]\(-1, -1 \frac{1}{4}, -1 \frac{1}{2}, -1 \frac{7}{8}\)[/tex]
- This sequence is [tex]\(-1, -1.25, -1.5, -1.875\)[/tex], which is not in ascending order.
4. [tex]\(-1 \frac{7}{8}, -1 \frac{1}{4}, -1 \frac{1}{2}, -1\)[/tex]
- This sequence is [tex]\(-1.875, -1.25, -1.5, -1\)[/tex], which is not in ascending order.
Based on this analysis, the set that is in ascending order is:
[tex]\[ \boxed{-1 \frac{7}{8},-1 \frac{1}{2},-1 \frac{1}{4},-1} \][/tex]
1. The number [tex]\(-1\)[/tex] is simply [tex]\(-1\)[/tex].
2. The number [tex]\(-1 \frac{1}{2}\)[/tex] can be written as [tex]\(-1 - \frac{1}{2} = -1.5\)[/tex].
3. The number [tex]\(-1 \frac{1}{4}\)[/tex] can be written as [tex]\(-1 - \frac{1}{4} = -1.25\)[/tex].
4. The number [tex]\(-1 \frac{7}{8}\)[/tex] can be written as [tex]\(-1 - \frac{7}{8} = -1.875\)[/tex].
With these conversions, we compare the decimal values to sort the numbers from least to greatest. Here are the decimal equivalents:
- [tex]\(-1\)[/tex] is [tex]\(-1\)[/tex]
- [tex]\(-1 \frac{1}{2}\)[/tex] is [tex]\(-1.5\)[/tex]
- [tex]\(-1 \frac{1}{4}\)[/tex] is [tex]\(-1.25\)[/tex]
- [tex]\(-1 \frac{7}{8}\)[/tex] is [tex]\(-1.875\)[/tex]
Ordering these from least to greatest:
- [tex]\(-1.875\)[/tex] (i.e., [tex]\(-1 \frac{7}{8}\)[/tex])
- [tex]\(-1.5\)[/tex] (i.e., [tex]\(-1 \frac{1}{2}\)[/tex])
- [tex]\(-1.25\)[/tex] (i.e., [tex]\(-1 \frac{1}{4}\)[/tex])
- [tex]\(-1\)[/tex] (i.e., [tex]\(-1\)[/tex])
Now let's compare this ordered sequence with the given sets:
1. [tex]\(-1, -1 \frac{1}{2}, -1 \frac{1}{4}, -1 \frac{7}{8}\)[/tex]
- This sequence is [tex]\(-1, -1.5, -1.25, -1.875\)[/tex], which is not in ascending order.
2. [tex]\(-1 \frac{7}{8}, -1 \frac{1}{2}, -1 \frac{1}{4}, -1\)[/tex]
- This sequence is [tex]\(-1.875, -1.5, -1.25, -1\)[/tex], which is correctly ordered in ascending order.
3. [tex]\(-1, -1 \frac{1}{4}, -1 \frac{1}{2}, -1 \frac{7}{8}\)[/tex]
- This sequence is [tex]\(-1, -1.25, -1.5, -1.875\)[/tex], which is not in ascending order.
4. [tex]\(-1 \frac{7}{8}, -1 \frac{1}{4}, -1 \frac{1}{2}, -1\)[/tex]
- This sequence is [tex]\(-1.875, -1.25, -1.5, -1\)[/tex], which is not in ascending order.
Based on this analysis, the set that is in ascending order is:
[tex]\[ \boxed{-1 \frac{7}{8},-1 \frac{1}{2},-1 \frac{1}{4},-1} \][/tex]
