Alright, let's solve this step-by-step.
1. Combine the fractions [tex]\( \frac{1}{4} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex]:
- First, find a common denominator for 4 and 8. The least common multiple (LCM) of 4 and 8 is 8.
- Convert [tex]\( \frac{1}{4} \)[/tex] to a fraction with a denominator of 8:
[tex]\[
\frac{1}{4} = \frac{2}{8}
\][/tex]
- Now, we can add [tex]\( \frac{2}{8} \)[/tex] and [tex]\( \frac{1}{8} \)[/tex]:
[tex]\[
\frac{2}{8} + \frac{1}{8} = \frac{3}{8}
\][/tex]
2. Add [tex]\( \frac{3}{8} \)[/tex] to [tex]\( \frac{5}{12} \)[/tex]:
- Find a common denominator for 8 and 12. The LCM of 8 and 12 is 24.
- Convert [tex]\( \frac{3}{8} \)[/tex] to a fraction with a denominator of 24:
[tex]\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\][/tex]
- Convert [tex]\( \frac{5}{12} \)[/tex] to a fraction with a denominator of 24:
[tex]\[
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
\][/tex]
- Now we can add [tex]\( \frac{9}{24} \)[/tex] and [tex]\( \frac{10}{24} \)[/tex]:
[tex]\[
\frac{9}{24} + \frac{10}{24} = \frac{19}{24}
\][/tex]
So the final result of adding [tex]\( \frac{1}{4} + \frac{1}{8} \)[/tex] and then adding [tex]\( \frac{5}{12} \)[/tex] to the result is:
[tex]\[
\frac{19}{24}
\][/tex]
