Question

What point on the number line is one fourth of the way from the point −2 to the point 5?

−0.25
−0.5
1.75
3.25

Answer 1

To find the point that is one fourth of the way from \(-2\) to \(5\), we can follow these steps:

1. **Calculate the distance between the two points, \(-2\) and \(5\)**:
\[
5 - (-2) = 5 + 2 = 7
\]

2. **Determine one fourth of this distance**:
\[
\frac{1}{4} \times 7 = \frac{7}{4} = 1.75
\]

3. **Calculate the point that is one fourth of the way from \(-2\)**:
This involves adding \(\frac{7}{4}\) to \(-2\):
\[
-2 + \frac{7}{4}
\]

First, convert \(-2\) to a fraction with a denominator of \(4\):
\[
-2 = -\frac{8}{4}
\]

Now, add:
\[
-\frac{8}{4} + \frac{7}{4} = \frac{-8 + 7}{4} = \frac{-1}{4} = -0.25
\]

Thus, the point on the number line that is one fourth of the way from \(-2\) to \(5\) is \(\boxed{-0.25}\).