To solve the problem of subtracting fractions using the number line, let's carefully go through each step:
1. Define the given expression:
[tex]\[
-\frac{1}{3} - \left(-\frac{1}{2}\right)
\][/tex]
This expression involves subtracting the negative fraction [tex]\(-\frac{1}{2}\)[/tex] from [tex]\(-\frac{1}{3}\)[/tex].
2. Simplify the subtraction:
When we subtract a negative number, it's equivalent to adding its positive counterpart. So the expression can be rewritten as:
[tex]\[
-\frac{1}{3} + \frac{1}{2}
\][/tex]
3. Consider the values on the number line:
- [tex]\( -\frac{1}{6} \)[/tex]: This is a point to the left of zero.
- 0: This is the origin point on the number line.
- [tex]\( \frac{1}{6} \)[/tex]: This is a point slightly to the right of zero.
- [tex]\( \frac{1}{2} \)[/tex]: This is a point farther to the right of zero.
4. Performing the addition:
Adding [tex]\(\frac{1}{2}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex] may be understood as moving to the right on the number line from [tex]\(-\frac{1}{3}\)[/tex].
The calculation involves converting these fractions to have a common denominator:
[tex]\[
-\frac{1}{3} = -\frac{2}{6}
\][/tex]
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
Now, add the equivalent fractions:
[tex]\[
-\frac{2}{6} + \frac{3}{6} = \frac{1}{6}
\][/tex]
5. Identify the result on the number line:
- Zero (0) is our standard reference point.
- Moving [tex]\(-\frac{1}{3}\)[/tex] to the left, we use its equivalent fraction [tex]\(-\frac{2}{6}\)[/tex], which is the position two units left of zero when divided by 6.
- Moving [tex]\(\frac{3}{6}\)[/tex] to the right from [tex]\(-\frac{2}{6}\)[/tex] results in [tex]\(\frac{1}{6}\)[/tex], as shown in the calculation.
Therefore, the final position on the number line after performing the operation [tex]\(-\frac{1}{3} - \left(-\frac{1}{2}\right)\)[/tex] is:
[tex]\[
\boxed{\frac{1}{6}}
\][/tex]
