Answer :
Sure, let's carefully fill out the table step-by-step using the given results. The first column and the first row provide the basis for each division. Here is the table that needs to be filled in:
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|} \hline \div & 8 & \frac{1}{8} & -3 \pi & \sqrt{7} & 0 & -\sqrt{13} \\ \hline 8 & 1 & 64 & -0.8488 & 3.0237 & \text{undefined} & -2.2188 \\ \hline \frac{1}{8} & 0.0156 & 1 & -0.0133 & 0.0472 & \text{undefined} & -0.0347 \\ \hline -3 \pi & -1.1781 & -75.3982 & 1 & -3.5622 & \text{undefined} & 2.6140 \\ \hline \sqrt{7} & 0.3307 & 21.1660 & -0.2807 & 1 & \text{undefined} & -0.7338 \\ \hline 1 & 0.125 & 8 & -0.1061 & 0.3780 & \text{undefined} & -0.2774 \\ \hline -\sqrt{13} & -0.4507 & -28.8444 & 0.3826 & -1.3628 & \text{undefined} & 1 \\ \hline \end{tabular} \][/tex]
Here is the filled-out table, including all the step-by-step division results:
1. 8 divided by each value in the top row:
- [tex]\( 8 \div 8 = 1 \)[/tex]
- [tex]\( 8 \div \frac{1}{8} = 64 \)[/tex]
- [tex]\( 8 \div -3\pi \approx -0.8488 \)[/tex]
- [tex]\( 8 \div \sqrt{7} \approx 3.0237 \)[/tex]
- [tex]\( 8 \div 0 \)[/tex] is undefined
- [tex]\( 8 \div -\sqrt{13} \approx -2.2188 \)[/tex]
2. [tex]\(\frac{1}{8}\)[/tex] divided by each value in the top row:
- [tex]\( \frac{1}{8} \div 8 = 0.0156 \)[/tex]
- [tex]\( \frac{1}{8} \div \frac{1}{8} = 1 \)[/tex]
- [tex]\( \frac{1}{8} \div -3\pi \approx -0.0133 \)[/tex]
- [tex]\( \frac{1}{8} \div \sqrt{7} \approx 0.0472 \)[/tex]
- [tex]\( \frac{1}{8} \div 0 \)[/tex] is undefined
- [tex]\( \frac{1}{8} \div -\sqrt{13} \approx -0.0347 \)[/tex]
3. [tex]\(-3 \pi\)[/tex] divided by each value in the top row:
- [tex]\( -3\pi \div 8 \approx -1.1781 \)[/tex]
- [tex]\( -3\pi \div \frac{1}{8} \approx -75.3982 \)[/tex]
- [tex]\( -3\pi \div -3\pi = 1 \)[/tex]
- [tex]\( -3\pi \div \sqrt{7} \approx -3.5622 \)[/tex]
- [tex]\( -3\pi \div 0 \)[/tex] is undefined
- [tex]\( -3\pi \div -\sqrt{13} \approx 2.6140 \)[/tex]
4. [tex]\(\sqrt{7}\)[/tex] divided by each value in the top row:
- [tex]\( \sqrt{7} \div 8 \approx 0.3307 \)[/tex]
- [tex]\( \sqrt{7} \div \frac{1}{8} \approx 21.1660 \)[/tex]
- [tex]\( \sqrt{7} \div -3\pi \approx -0.2807 \)[/tex]
- [tex]\( \sqrt{7} \div \sqrt{7} = 1 \)[/tex]
- [tex]\( \sqrt{7} \div 0 \)[/tex] is undefined
- [tex]\( \sqrt{7} \div -\sqrt{13} \approx -0.7338 \)[/tex]
5. 1 divided by each value in the top row:
- [tex]\( 1 \div 8 = 0.125 \)[/tex]
- [tex]\( 1 \div \frac{1}{8} = 8 \)[/tex]
- [tex]\( 1 \div -3\pi \approx -0.1061 \)[/tex]
- [tex]\( 1 \div \sqrt{7} \approx 0.3780 \)[/tex]
- [tex]\( 1 \div 0 \)[/tex] is undefined
- [tex]\( 1 \div -\sqrt{13} \approx -0.2774 \)[/tex]
6. [tex]\(-\sqrt{13}\)[/tex] divided by each value in the top row:
- [tex]\( -\sqrt{13} \div 8 \approx -0.4507 \)[/tex]
- [tex]\( -\sqrt{13} \div \frac{1}{8} \approx -28.8444 \)[/tex]
- [tex]\( -\sqrt{13} \div -3\pi \approx 0.3826 \)[/tex]
- [tex]\( -\sqrt{13} \div \sqrt{7} \approx -1.3628 \)[/tex]
- [tex]\( -\sqrt{13} \div 0 \)[/tex] is undefined
- [tex]\( -\sqrt{13} \div -\sqrt{13} = 1 \)[/tex]
By completing these steps, we have successfully filled out the table based on the division results.
[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|} \hline \div & 8 & \frac{1}{8} & -3 \pi & \sqrt{7} & 0 & -\sqrt{13} \\ \hline 8 & 1 & 64 & -0.8488 & 3.0237 & \text{undefined} & -2.2188 \\ \hline \frac{1}{8} & 0.0156 & 1 & -0.0133 & 0.0472 & \text{undefined} & -0.0347 \\ \hline -3 \pi & -1.1781 & -75.3982 & 1 & -3.5622 & \text{undefined} & 2.6140 \\ \hline \sqrt{7} & 0.3307 & 21.1660 & -0.2807 & 1 & \text{undefined} & -0.7338 \\ \hline 1 & 0.125 & 8 & -0.1061 & 0.3780 & \text{undefined} & -0.2774 \\ \hline -\sqrt{13} & -0.4507 & -28.8444 & 0.3826 & -1.3628 & \text{undefined} & 1 \\ \hline \end{tabular} \][/tex]
Here is the filled-out table, including all the step-by-step division results:
1. 8 divided by each value in the top row:
- [tex]\( 8 \div 8 = 1 \)[/tex]
- [tex]\( 8 \div \frac{1}{8} = 64 \)[/tex]
- [tex]\( 8 \div -3\pi \approx -0.8488 \)[/tex]
- [tex]\( 8 \div \sqrt{7} \approx 3.0237 \)[/tex]
- [tex]\( 8 \div 0 \)[/tex] is undefined
- [tex]\( 8 \div -\sqrt{13} \approx -2.2188 \)[/tex]
2. [tex]\(\frac{1}{8}\)[/tex] divided by each value in the top row:
- [tex]\( \frac{1}{8} \div 8 = 0.0156 \)[/tex]
- [tex]\( \frac{1}{8} \div \frac{1}{8} = 1 \)[/tex]
- [tex]\( \frac{1}{8} \div -3\pi \approx -0.0133 \)[/tex]
- [tex]\( \frac{1}{8} \div \sqrt{7} \approx 0.0472 \)[/tex]
- [tex]\( \frac{1}{8} \div 0 \)[/tex] is undefined
- [tex]\( \frac{1}{8} \div -\sqrt{13} \approx -0.0347 \)[/tex]
3. [tex]\(-3 \pi\)[/tex] divided by each value in the top row:
- [tex]\( -3\pi \div 8 \approx -1.1781 \)[/tex]
- [tex]\( -3\pi \div \frac{1}{8} \approx -75.3982 \)[/tex]
- [tex]\( -3\pi \div -3\pi = 1 \)[/tex]
- [tex]\( -3\pi \div \sqrt{7} \approx -3.5622 \)[/tex]
- [tex]\( -3\pi \div 0 \)[/tex] is undefined
- [tex]\( -3\pi \div -\sqrt{13} \approx 2.6140 \)[/tex]
4. [tex]\(\sqrt{7}\)[/tex] divided by each value in the top row:
- [tex]\( \sqrt{7} \div 8 \approx 0.3307 \)[/tex]
- [tex]\( \sqrt{7} \div \frac{1}{8} \approx 21.1660 \)[/tex]
- [tex]\( \sqrt{7} \div -3\pi \approx -0.2807 \)[/tex]
- [tex]\( \sqrt{7} \div \sqrt{7} = 1 \)[/tex]
- [tex]\( \sqrt{7} \div 0 \)[/tex] is undefined
- [tex]\( \sqrt{7} \div -\sqrt{13} \approx -0.7338 \)[/tex]
5. 1 divided by each value in the top row:
- [tex]\( 1 \div 8 = 0.125 \)[/tex]
- [tex]\( 1 \div \frac{1}{8} = 8 \)[/tex]
- [tex]\( 1 \div -3\pi \approx -0.1061 \)[/tex]
- [tex]\( 1 \div \sqrt{7} \approx 0.3780 \)[/tex]
- [tex]\( 1 \div 0 \)[/tex] is undefined
- [tex]\( 1 \div -\sqrt{13} \approx -0.2774 \)[/tex]
6. [tex]\(-\sqrt{13}\)[/tex] divided by each value in the top row:
- [tex]\( -\sqrt{13} \div 8 \approx -0.4507 \)[/tex]
- [tex]\( -\sqrt{13} \div \frac{1}{8} \approx -28.8444 \)[/tex]
- [tex]\( -\sqrt{13} \div -3\pi \approx 0.3826 \)[/tex]
- [tex]\( -\sqrt{13} \div \sqrt{7} \approx -1.3628 \)[/tex]
- [tex]\( -\sqrt{13} \div 0 \)[/tex] is undefined
- [tex]\( -\sqrt{13} \div -\sqrt{13} = 1 \)[/tex]
By completing these steps, we have successfully filled out the table based on the division results.
