\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}
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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!
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