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In a school sports tally, Neelgiri House stands at −18 points and Aravalli House at +15 points. Which house's tally is further from zero, and by how much further?

Class 7Integers (Extended)Integers
  • AAravalli, by 3 points
  • BBoth are equally far from zero.
  • CAravalli, by 33 points
  • DNeelgiri, by 3 points

Step-by-Step Solution

'How far from zero' is absolute value: |−18| = 18 and |+15| = 15. So Neelgiri is further, by 18 − 15 = 3 points. The trap is that Aravalli has the greater tally (15 > −18) yet the smaller distance from zero — greater and further apart are different questions. Answering 33 adds the two distances instead of comparing them.
Answer: D) Neelgiri, by 3 points

Key idea: Dividing integers

The sign rule for division is **the same as for multiplication**: same signs → positive, different signs → negative.

12 ÷ 4 = 3
(−12) ÷ (−4) = 3
12 ÷ (−4) = −3
(−12) ÷ 4 = −3

Also: integer ÷ 1 = the integer; integer ÷ itself = 1; **never divide by 0** — division by zero is undefined.

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