To solve the given expression [tex]\(\frac{1}{3} + \frac{3}{4} - \frac{2}{6}\)[/tex], let's follow the steps in a detailed and structured manner.
First, simplify the fractions if possible:
- [tex]\(\frac{2}{6}\)[/tex] can be simplified. The greatest common divisor (GCD) of 2 and 6 is 2, so:
[tex]\[
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
Now, our expression looks like:
[tex]\[
\frac{1}{3} + \frac{3}{4} - \frac{1}{3}
\][/tex]
Next, notice that [tex]\(\frac{1}{3} - \frac{1}{3} = 0\)[/tex]. Therefore, we're left with:
[tex]\[
0 + \frac{3}{4}
\][/tex]
Adding zero to [tex]\(\frac{3}{4}\)[/tex] does not change its value:
[tex]\[
\frac{3}{4}
\][/tex]
So, the result of the given expression [tex]\(\frac{1}{3} + \frac{3}{4} - \frac{2}{6}\)[/tex] is:
[tex]\[
\frac{3}{4}
\][/tex]
Numerically, if we convert [tex]\(\frac{3}{4}\)[/tex] to a decimal, it equals [tex]\(0.75\)[/tex].
Therefore, the final answer is:
[tex]\[
0.75
\][/tex]
