Sure, let's go through the problem step-by-step.
### Step 1: Addition Problem
We start with the given fractions:
[tex]\[
\frac{3}{16} + \frac{5}{16}
\][/tex]
### Step 2: Unsimplified Sum
Since both fractions have the same denominator, we can add the numerators directly and keep the denominator the same.
- Numerator: [tex]\(3 + 5 = 8\)[/tex]
- Denominator: [tex]\(16\)[/tex]
Thus, the unsimplified sum is:
[tex]\[
\frac{8}{16}
\][/tex]
### Step 3: Simplified Sum
Next, we reduce the fraction [tex]\(\frac{8}{16}\)[/tex] to its lowest terms. This involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.
- The GCD of 8 and 16 is 8.
- Simplified numerator: [tex]\(\frac{8}{8} = 1\)[/tex]
- Simplified denominator: [tex]\(\frac{16}{8} = 2\)[/tex]
Therefore, the simplified sum is:
[tex]\[
\frac{1}{2}
\][/tex]
### Summary
Combining these steps, we fill in the table as follows:
[tex]\[
\begin{tabular}{|c|l|l|}
\hline
Addition Problem & Unsimplified Sum & Simplified Sum \\
\hline
$\frac{3}{16}+\frac{5}{16}$ & $\frac{8}{16}$ & $\frac{1}{2}$ \\
\hline
\end{tabular}
\][/tex]
