Let's solve the given expression step-by-step.
The given expression is:
[tex]\[ 104 \frac{5}{8}{ }^{15} + 2 \frac{2}{3} \frac{16}{24} \][/tex]
1. Convert the mixed numbers to improper fractions and calculate their decimal equivalents:
- For [tex]\(104 \frac{5}{8}\)[/tex]:
[tex]\[
104 \frac{5}{8} = 104 + \frac{5}{8}
\][/tex]
Since [tex]\(\frac{5}{8} = 0.625\)[/tex],
[tex]\[
104 + 0.625 = 104.625
\][/tex]
- For [tex]\(2 \frac{2}{3} \frac{16}{24}\)[/tex], we break it down further:
[tex]\[
2 \frac{2}{3} \frac{16}{24}
\][/tex]
Simplify [tex]\(\frac{16}{24}\)[/tex] to its simplest form (which is [tex]\(\frac{2}{3}\)[/tex]):
[tex]\[
\frac{16}{24} = \frac{2}{3}
\][/tex]
Therefore, the new expression is:
[tex]\[
2 \frac{2}{3} \frac{2}{3}
\][/tex]
Combine the fractions:
[tex]\[
2 + \frac{2}{3} + \frac{2}{3}
\][/tex]
Since [tex]\(\frac{2}{3} + \frac{2}{3} = \frac{4}{3}\)[/tex], we get:
[tex]\[
2 + \frac{4}{3}
\][/tex]
Converting this to a decimal form:
[tex]\[
2 + \frac{4}{3} = 2 + 1.333333333 = 3.333333333
\][/tex]
2. Summarize the fractional part:
We have:
[tex]\[
104.625 \, \text{and} \, 3.333333333
\][/tex]
- For [tex]\( \frac{16}{24}\)[/tex], which we simplified earlier:
[tex]\[
\frac{16}{24} = 0.666666666
\][/tex]
Thus, the results are:
[tex]\[ 104.625 \][/tex]
[tex]\[ 3.333333333333333 \][/tex]
[tex]\[ \text{Simplified } \frac{16}{24} = 0.6666666666666666 \][/tex]
So, the detailed step-by-step solution to the given problem shows the numerical results:
[tex]\[ 104.625 \, \text{and} \, 3.333333333333333 \][/tex]
And the simplified form of [tex]\( \frac{16}{24} \)[/tex] is:
[tex]\[ 0.6666666666666666 \][/tex]
