To solve the problem [tex]\(\frac{1}{3} - \frac{1}{6}\)[/tex], we need to find a common denominator for the fractions involved.
1. Identify the denominators:
The denominators are 3 and 6.
2. Find the least common denominator (LCD):
The least common denominator of 3 and 6 is 6. This is because 6 is the smallest number that both 3 and 6 can divide into without leaving a remainder.
3. Rewrite each fraction with the common denominator:
- For [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\][/tex]
- For [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{1}{6} = \frac{1}{6} \quad \text{(it is already in terms of the common denominator)}
\][/tex]
4. Perform the subtraction:
Now that both fractions have the same denominator, we can subtract them:
[tex]\[
\frac{2}{6} - \frac{1}{6} = \frac{2 - 1}{6} = \frac{1}{6}
\][/tex]
So, the difference between [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex] is [tex]\(\frac{1}{6}\)[/tex]. To express it numerically, [tex]\(\frac{1}{6}\)[/tex] is approximately 0.16666666666666666.
