To add the fractions [tex]\(\frac{5}{8} + \frac{1}{16}\)[/tex], we first need to make sure the denominators are the same. Here is a detailed, step-by-step solution:
1. Find a common denominator:
- The denominators of the given fractions are 8 and 16.
- The least common denominator (LCD) of 8 and 16 is 16.
2. Convert the first fraction to have this common denominator:
- [tex]\(\frac{5}{8}\)[/tex] can be rewritten with a denominator of 16. Since [tex]\(8 \times 2 = 16\)[/tex], we multiply both the numerator and the denominator of [tex]\(\frac{5}{8}\)[/tex] by 2:
[tex]\[
\frac{5 \times 2}{8 \times 2} = \frac{10}{16}
\][/tex]
3. Write both fractions with the common denominator:
[tex]\[
\frac{5}{8} = \frac{10}{16} \quad \text{and} \quad \frac{1}{16} = \frac{1}{16}
\][/tex]
4. Add the fractions:
[tex]\[
\frac{10}{16} + \frac{1}{16} = \frac{10 + 1}{16} = \frac{11}{16}
\][/tex]
5. Simplify the fraction:
- The fraction [tex]\(\frac{11}{16}\)[/tex] is already in its simplest form because the greatest common divisor (GCD) of 11 and 16 is 1.
So, the detailed solution to [tex]\(\frac{5}{8} + \frac{1}{16}\)[/tex] is:
[tex]\[
\begin{aligned}
\frac{5}{8}+\frac{1}{16} & = \frac{10}{16} + \frac{1}{16} \\
& = \frac{11}{16}
\end{aligned}
\][/tex]
Therefore, the answer is [tex]\(\frac{11}{16}\)[/tex].
