To solve the equation [tex]\(\frac{3}{8}+\frac{1}{4}+\frac{1}{2}-\frac{2}{3}\)[/tex]:
1. Convert all fractions to decimals:
- [tex]\(\frac{3}{8} = 0.375\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{2}{3} = 0.6666666666666666\)[/tex]
2. Perform the addition and subtraction step-by-step:
- First, add [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
0.375 + 0.25 = 0.625
\][/tex]
- Next, add [tex]\(\frac{1}{2}\)[/tex] to the result:
[tex]\[
0.625 + 0.5 = 1.125
\][/tex]
- Finally, subtract [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
1.125 - 0.6666666666666666 = 0.45833333333333337
\][/tex]
3. Interpret the result:
The calculated result of the operation [tex]\(\frac{3}{8} + \frac{1}{4} + \frac{1}{2} - \frac{2}{3}\)[/tex] yields approximately 0.4583.
4. Comparison to given options:
- [tex]\(\frac{11}{24} \approx 0.4583 \)[/tex]
- [tex]\(\frac{3}{11} \approx 0.2727 \)[/tex]
- [tex]\(\frac{1}{8} = 0.125 \)[/tex]
- [tex]\(1 \frac{19}{24} = 1 + \frac{19}{24} \approx 1.7917 \)[/tex]
The result corresponds to [tex]\(\frac{11}{24}\)[/tex]. Thus, the correct answer is:
[tex]\[
\boxed{\frac{11}{24}}
\][/tex]
