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Look at the integers −8, 3, −1 and 9. Which one is the smallest, and which one is farthest from zero?

Class 6IntegersIntegers
  • ASmallest −8, farthest from zero −8
  • BSmallest −1, farthest from zero 9
  • CSmallest 3, farthest from zero −8
  • DSmallest −8, farthest from zero 9

Step-by-Step Solution

Smallest means furthest left, which is −8. Farthest from zero means the largest absolute value: |−8| = 8, |3| = 3, |−1| = 1 and |9| = 9, so 9 wins that one. The trap is assuming the smallest integer must also be the one farthest from zero — that only happens when the negatives reach further out than the positives.
Answer: D) Smallest −8, farthest from zero 9

Key idea: Adding integers — different signs

When two integers have **different signs**, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value. So 7 + (−3) = 4 (|7| > |−3|, so the answer is positive 4), and (−7) + 3 = −4 (|−7| > |3|, so the answer is negative 4). On the number line: a positive number moves right, a negative number moves left — they partially cancel.

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