To simplify the expression [tex]\( \left(11 \frac{1}{13} - 1 \frac{3}{8}\right) + 2 \frac{7}{8} \)[/tex]:
1. Convert the mixed numbers to improper fractions:
- For [tex]\( 11 \frac{1}{13} \)[/tex]:
[tex]\[
11 \frac{1}{13} = 11 + \frac{1}{13} \approx 11.076923076923077
\][/tex]
- For [tex]\( 1 \frac{3}{8} \)[/tex]:
[tex]\[
1 \frac{3}{8} = 1 + \frac{3}{8} = 1.375
\][/tex]
- For [tex]\( 2 \frac{7}{8} \)[/tex]:
[tex]\[
2 \frac{7}{8} = 2 + \frac{7}{8} = 2.875
\][/tex]
2. Perform the subtraction [tex]\( 11 \frac{1}{13} - 1 \frac{3}{8} \)[/tex]:
[tex]\[
11.076923076923077 - 1.375 = 9.701923076923077
\][/tex]
3. Add the results:
[tex]\[
9.701923076923077 + 2.875 = 12.576923076923077
\][/tex]
Thus, the simplified result of [tex]\( \left(11 \frac{1}{13} - 1 \frac{3}{8}\right) + 2 \frac{7}{8} \)[/tex] is [tex]\( 12.576923076923077 \)[/tex].
