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Part 1 of 2 Error Analysis Chetsea needed to compare the absolute values ol -136 and -132 She incorrectly said that the absolute value of - 136 is less than the absolute value of -132 How do you know that \( |-136|>|-132| \) ? What mistake might Chelsea have mado? How do you know that \( |-136|>|-132| \) ? The distance from -136 to zero is less than the distance from -132 to zero B. The number -136 is located to the left of -132 on a number line C. The number -136 is located to the right of -132 on a number line D. The distance from -136 to zero is greater than the distance from -132 to zero D. 130

Ask by Cruz Campbell. in the United States
Mar 20,2025

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The absolute value of -136 is greater than that of -132 because -136 is farther from zero on the number line.

Solución

1. The absolute value of a number represents its distance from zero on the number line. In this case, \[ |-136| = 136 \quad \text{and} \quad |-132| = 132. \] 2. Since 136 is greater than 132, we have \[ |-136| > |-132|. \] 3. The correct explanation is that the distance from \(-136\) to zero is greater than the distance from \(-132\) to zero. This corresponds to option D. 4. Chelsea's mistake might have been confusing the order of numbers on the number line with the comparison of their absolute values. Although \(-136\) is to the left of \(-132\) (which means it is a smaller number), its absolute value (or distance from zero) is actually larger.

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Mind Expander

Chetsea’s misunderstanding about absolute values is a common pitfall! Absolute value measures distance from zero, disregarding direction. So, |-136| equals 136 and |-132| equals 132. Since 136 is indeed greater than 132, Chelsea mistakenly assessed the distances based solely on the numbers’ positions. To improve her understanding, Chelsea should visualize a number line. Placing -136 and -132 helps highlight that -136 is farther from zero. Next time she compares absolute values, her number line should guide her decision—helping dissolve potential confusion about these pesky negative numbers!

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