Estimating a product Deandre and Karen are trying to estimate this product. \[ \begin{array}{l}9 \times 83 \\ \text { Answer the questions below. } \\ \begin{array}{l}\text { (a) Deandre estimates this product by computing } 9 \times 80 \text {. } \\ \text { What is his estimate? } \\ 9 \times 80=\square \\ \text { What is her estimate? } \\ 9 \times 90=\square \\ \text { (b) Karen estimates this product by computing } 9 \times 90 \text {. } \\ \text { (c) Whose estimate is closer to } 9 \times 83 \text { ? } \\ \text { Deandre's estimate is closer } \\ \text { Karen's estimate is closer } \\ \text { Their estimates are equally close }\end{array}\end{array} . \begin{array}{l}\text { Ther }\end{array} \]

To solve the problem, we will follow the steps outlined in the prompt. ### Step 1: Calculate Deandre's Estimate Deandre estimates the product by computing \( 9 \times 80 \). \[ 9 \times 80 = 720 \] ### Step 2: Calculate Karen's Estimate Karen estimates the product by computing \( 9 \times 90 \). \[ 9 \times 90 = 810 \] ### Step 3: Calculate the Actual Product Now, we need to calculate the actual product \( 9 \times 83 \). \[ 9 \times 83 = 747 \] ### Step 4: Determine the Differences Next, we will find the differences between the actual product and each estimate. - **Difference for Deandre's estimate:** \[ |720 - 747| = 27 \] - **Difference for Karen's estimate:** \[ |810 - 747| = 63 \] ### Step 5: Compare the Differences Now we compare the differences: - Deandre's difference: 27 - Karen's difference: 63 Since 27 is less than 63, Deandre's estimate is closer to the actual product. ### Final Answers - (a) Deandre's estimate: \( 720 \) - (a) Karen's estimate: \( 810 \) - (c) Deandre's estimate is closer. Thus, the answers are: - \( 9 \times 80 = 720 \) - \( 9 \times 90 = 810 \) - Deandre's estimate is closer.