By copying and completing the working below, work out [tex]\frac{5}{8}+\frac{1}{16}[/tex].

Give your answer as a fraction in its simplest form.

[tex]
\begin{aligned}
\frac{5}{8}+\frac{1}{16} & =\frac{\square}{16}+\frac{\square}{16} \\
& =\frac{\square}{\square}
\end{aligned}
[/tex]



Answer :

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].