To determine which demonstration correctly shows that [tex]\(34.4 \div a = 8\)[/tex] is true when [tex]\(a = 4.3\)[/tex], let's go through each option step-by-step:
### Option 1
[tex]\[
\begin{array}{l}
34.4 \div a = 8 \\
34.4 + (4.3) = 42.7 \\
42.7 = 42.7
\end{array}
\][/tex]
This option is incorrect. The second line, [tex]\(34.4 + 4.3 = 42.7\)[/tex], does not demonstrate division. It adds [tex]\(34.4\)[/tex] and [tex]\(4.3\)[/tex], which is not relevant to verifying [tex]\(34.4 \div 4.3\)[/tex].
### Option 2
[tex]\[
\begin{array}{l}
34.4 \div a = 8 \\
(4.3) \div 34.4 = \frac{1}{8} \\
\frac{1}{8} = \frac{1}{8}
\end{array}
\][/tex]
While this option results in a true statement ([tex]\(\frac{1}{8} = \frac{1}{8}\)[/tex]), it does not directly verify that [tex]\(34.4 \div 4.3\)[/tex] equals 8. It shows the reciprocal relationship without directly addressing the original division.
### Option 3
[tex]\[
\begin{array}{l}
34.4 \div a = 8 \\
34.4 - (4.3) = 30.1 \\
30.1 = 30.1
\end{array}
\][/tex]
This option is incorrect. The subtraction [tex]\(34.4 - 4.3 = 30.1\)[/tex] does not help verify the division statement [tex]\(34.4 \div 4.3 = 8\)[/tex].
### Option 4
[tex]\[
\begin{array}{l}
34.4 \div a = 8 \\
34.4 \div (4.3) = 8 \\
8 = 8
\end{array}
\][/tex]
This option is correct. It directly performs the division:
[tex]\[
34.4 \div 4.3 = 8
\][/tex]
and then confirms that 8 equals 8.
Thus, the correct demonstration is option 4:
[tex]\[
\begin{array}{l}
34.4 \div a = 8 \\
34.4 \div(4.3) = 8 \\
8 = 8
\end{array}
\][/tex]
