Let's match each division problem to its correct quotient step-by-step:
1. [tex]$0 \div 8$[/tex]:
- When you divide zero by any non-zero number, the result is always zero.
- Hence, [tex]$0 \div 8 = 0$[/tex].
2. [tex]$3 \div 0$[/tex]:
- Division by zero is undefined in mathematics.
- Hence, [tex]$3 \div 0$[/tex] is "Undefined".
3. [tex]$\frac{7}{0}$[/tex]:
- Similar to the previous case, division by zero is undefined.
- Hence, [tex]$\frac{7}{0}$[/tex] is "Undefined".
4. [tex]$0 \div 16$[/tex]:
- Again, dividing zero by any non-zero number yields zero.
- Therefore, [tex]$0 \div 16 = 0$[/tex].
5. [tex]$42 \div 0$[/tex]:
- Division by zero is always undefined.
- Hence, [tex]$42 \div 0$[/tex] is "Undefined".
6. [tex]$\frac{0}{23}$[/tex]:
- Dividing zero by any non-zero number results in zero.
- Therefore, [tex]$\frac{0}{23} = 0$[/tex].
7. [tex]$\frac{0}{100}$[/tex]:
- Finally, dividing zero by any non-zero number results in zero.
- Therefore, [tex]$\frac{0}{100} = 0$[/tex].
Given all the calculations, we can now match the problems with their respective quotients:
[tex]\[
\begin{array}{ll}
0 \div 8 & \text{Zero} \\
3 \longdiv { 0 } & \text{Undefined} \\
\frac{7}{0} & \text{Undefined} \\
0 \longdiv { 1 6 } & \text{Zero} \\
42 \div 0 & \text{Undefined} \\
\frac{0}{23} & \text{Zero} \\
\frac{0}{100} & \text{Zero} \\
\end{array}
\][/tex]
