To simplify the expression [tex]\(\frac{1}{3} - \frac{1}{2}\)[/tex], let's break it down step-by-step.
1. Express each fraction with a common denominator:
The fractions [tex]\(\frac{1}{3}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] have different denominators. The common denominator for 3 and 2 is 6.
2. Convert each fraction:
[tex]\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\][/tex]
[tex]\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\][/tex]
3. Subtraction of fractions with common denominators:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{2}{6} - \frac{3}{6} = \frac{2 - 3}{6} = \frac{-1}{6}
\][/tex]
4. Simplify the result:
The result, [tex]\(\frac{-1}{6}\)[/tex], is already in its simplest form.
So, [tex]\(\frac{1}{3} - \frac{1}{2} = \frac{-1}{6}\)[/tex].
The correct answer is:
C. [tex]\(\frac{1}{6}\)[/tex]
