Sure, let's follow the steps to solve the problem.
### Step 1: Estimate the Product by Rounding and Multiplying
Estimate the product of [tex]\(82 \times 16\)[/tex] by rounding the numbers to the nearest ten:
- Round 82 to the nearest ten: 80
- Round 16 to the nearest ten: 20
Now, multiply the rounded numbers:
[tex]\[ 80 \times 20 = 1600 \][/tex]
So, our estimated answer is 1600.
### Step 2: Calculate the Correct Answer
Now, let's calculate the exact product of 82 and 16:
[tex]\[ 82 \times 16 = 1312 \][/tex]
### Step 3: Find the Difference Between the Estimated Answer and the Correct Answer
Finally, let's find the difference between the estimated answer and the correct answer:
[tex]\[ 1312 - 1600 = -288 \][/tex]
### Summary Table
Here is the completed table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
EQUATION & \begin{tabular}{c}
ESTIMATE \\
ANSWER
\end{tabular} & \begin{tabular}{c}
CORRECT \\
ANSWER
\end{tabular} & \begin{tabular}{c}
DIFFERENCE BETWEEN \\
ANSWER AND CORRECT ANSWER
\end{tabular} \\
\hline
$34 \times 61$ & 800 & 2074 & $2074 - 800 = 1274$ \\
\hline
$82 \times 16$ & 1600 & 1312 & $1312 - 1600 = -288$ \\
\hline
\end{tabular}
\][/tex]
Therefore, the estimate for [tex]\(82 \times 16\)[/tex] is 1600, the correct answer is 1312, and the difference is -288.
