To find the distance between the points [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex], follow these detailed steps:
1. Identify the Points:
- The first point is [tex]\(\frac{1}{4}\)[/tex].
- The second point is [tex]\(\frac{1}{2}\)[/tex].
2. Interpret the Problem:
- You're asked to determine the distance between these two points on a number line.
3. Distance Formula on a Number Line:
- The distance [tex]\(d\)[/tex] between two points [tex]\(a\)[/tex] and [tex]\(b\)[/tex] on a number line is given by the absolute value of their difference:
[tex]\[
d = |b - a|
\][/tex]
4. Substitute the Points into the Formula:
- Here, [tex]\(a = \frac{1}{4}\)[/tex] and [tex]\(b = \frac{1}{2}\)[/tex].
- Calculate the difference between [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
d = \left|\frac{1}{2} - \frac{1}{4}\right|
\][/tex]
5. Simplify the Expression:
- To subtract the fractions, you need a common denominator. The common denominator for [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex] is 4.
- Rewrite [tex]\(\frac{1}{2}\)[/tex] with the denominator of 4:
[tex]\[
\frac{1}{2} = \frac{2}{4}
\][/tex]
- Now subtract the fractions:
[tex]\[
d = \left|\frac{2}{4} - \frac{1}{4}\right|
\][/tex]
6. Perform the Subtraction:
- Subtract the numerators while keeping the denominator the same:
[tex]\[
d = \left|\frac{2 - 1}{4}\right| = \left|\frac{1}{4}\right|
\][/tex]
- Since the absolute value of [tex]\(\frac{1}{4}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex], we have:
[tex]\[
d = \frac{1}{4} = 0.25
\][/tex]
Thus, the distance between the points [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] is [tex]\(0.25\)[/tex] units.
