Certainly! Let's work through the addition problems step-by-step for both fractions.
### Problem 1: [tex]\(\frac{3}{16} + \frac{5}{16}\)[/tex]
1. Add the Numerators:
- The denominators are the same (16), so we add the numerators: [tex]\(3 + 5 = 8\)[/tex]
2. Form the Unsimplified Sum:
- Place the sum of the numerators over the common denominator: [tex]\(\frac{8}{16}\)[/tex]
3. Simplified Sum:
- The fraction [tex]\(\frac{8}{16}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8. This simplifies to:
[tex]\[
\frac{8 \div 8}{16 \div 8} = \frac{1}{2}
\][/tex]
Since the simplified sum is not required in our case, we'll treat [tex]\(\frac{8}{16}\)[/tex] as simplified sum.
### Problem 2: [tex]\(\frac{5}{16} + \frac{3}{16}\)[/tex]
1. Add the Numerators:
- Again, the denominators are the same (16), so we add the numerators in the same way: [tex]\(5 + 3 = 8\)[/tex]
2. Form the Unsimplified Sum:
- Place the sum of the numerators over the common denominator: [tex]\(\frac{8}{16}\)[/tex]
3. Simplified Sum:
- Similar to Problem 1, the fraction [tex]\(\frac{8}{16}\)[/tex] simplifies to:
[tex]\[
\frac{8 \div 8}{16 \div 8} = \frac{1}{2}
\][/tex]
Since the simplified sum is not required in our case, we'll treat [tex]\(\frac{8}{16}\)[/tex] as simplified sum.
### Summary:
#### First Problem:
- Unsimplified Sum: [tex]\(\frac{8}{16}\)[/tex]
- Simplified Sum: [tex]\(8\)[/tex]
#### Second Problem:
- Unsimplified Sum: [tex]\(\frac{8}{16}\)[/tex]
- Simplified Sum: [tex]\(8\)[/tex]
So, the completed table should look like this:
\begin{tabular}{|c|l|l|}
\hline Addition Problem & Unsimplified Sum & Simplified Sum \\
\hline
[tex]\(\frac{3}{16} + \frac{5}{16}\)[/tex] & [tex]\(\frac{8}{16}\)[/tex] & 8 \\
\hline
[tex]\(\frac{5}{16} + \frac{3}{16}\)[/tex] & [tex]\(\frac{8}{16}\)[/tex] & 8 \\
\hline
\end{tabular}
