To find the average of the three numbers [tex]\(2 \frac{1}{2}, -1 \frac{1}{2},\)[/tex] and [tex]\(3 \frac{1}{2}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions or decimal form:
- [tex]\(2 \frac{1}{2}\)[/tex] can be converted to an improper fraction:
[tex]\[2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\][/tex]
Alternatively, as a decimal:
[tex]\[2 \frac{1}{2} = 2.5\][/tex]
- [tex]\(-1 \frac{1}{2}\)[/tex] can be converted to an improper fraction:
[tex]\[-1 \frac{1}{2} = -1 + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2}\][/tex]
Alternatively, as a decimal:
[tex]\[-1 \frac{1}{2} = -1.5\][/tex]
- [tex]\(3 \frac{1}{2}\)[/tex] can be converted to an improper fraction:
[tex]\[3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}\][/tex]
Alternatively, as a decimal:
[tex]\[3 \frac{1}{2} = 3.5\][/tex]
2. Add the values in decimal form:
- Sum the numbers:
[tex]\[2.5 + (-1.5) + 3.5\][/tex]
- Calculate the sum step-by-step:
[tex]\[2.5 + (-1.5) = 1\][/tex]
[tex]\[1 + 3.5 = 4.5\][/tex]
So, the total sum is [tex]\(4.5\)[/tex].
3. Count the number of values:
- There are 3 values: [tex]\(2 \frac{1}{2}, -1 \frac{1}{2},\)[/tex] and [tex]\(3 \frac{1}{2}\)[/tex].
4. Calculate the average:
- The average is the total sum divided by the number of values:
[tex]\[\text{Average} = \frac{\text{Total sum}}{\text{Number of values}} = \frac{4.5}{3} = 1.5\][/tex]
Therefore, the average of the three numbers [tex]\(2 \frac{1}{2}, -1 \frac{1}{2},\)[/tex] and [tex]\(3 \frac{1}{2}\)[/tex] is [tex]\(1.5\)[/tex].
This corresponds to:
C) [tex]\(1 \frac{1}{2}\)[/tex]
