Question
\begin{tabular}{l}\( 7 \times 538 \) \\ nswer the questions below. \\ \( \begin{array}{l}\text { (a) Rachel estimates this product by computing } 7 \times 500 \text {. } \\ \text { What is her estimate? } \\ 7 \times 500=\square \\ \text { (b) Brian estimates this product by computing } 7 \times 600 \text {. } \\ \text { What is his estimate? } \\ 7 \times 600=\square \\ \text { (c) Whose estimate is closer to } 7 \times 538 \text { ? } \\ 0 \text { Rachel's estimate is closer } \\ \text { Brian's estimate is closer } \\ \text { Their estimates are equally close }\end{array} \) \\ \hline\end{tabular}
Ask by Hardy Morrison. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) 3500
(b) 4200
(c) Rachel's estimate is closer
Solution
Let's solve each part step by step.
(a) Rachel estimates by computing 7 × 500.
7 × 500 = 3500
(b) Brian estimates by computing 7 × 600.
7 × 600 = 4200
(c) To see whose estimate is closer, first compute the actual product:
7 × 538 = 7 × (500 + 38) = (7 × 500) + (7 × 38) = 3500 + 266 = 3766
Now, compare the differences from the actual product:
Rachel's difference: |3766 − 3500| = 266
Brian's difference: |4200 − 3766| = 434
Since 266 < 434, Rachel's estimate is closer.
Final Answers:
(a) 3500
(b) 4200
(c) Rachel's estimate is closer
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Rachel's estimate is \( 7 \times 500 = 3500 \). She's rounding down to the nearest hundred, which is a common technique used in estimation! Brian's estimate is \( 7 \times 600 = 4200 \). By rounding up, he's aiming for a higher product, which can sometimes lead to larger errors if the actual number is much lower. To determine whose estimate is closer to \( 7 \times 538 \) (which equals \( 3766 \)), we see that Rachel's estimate is off by \( 266 \) (from \( 3500 \)), while Brian's is off by \( 434 \) (from \( 4200 \)). Therefore, Rachel's estimate is closer!
