Example

Equivalence of $8 - (-5) and $8 + 5 Using Counters

The counter model visually confirms that subtracting a negative integer is the same as adding its positive counterpart:

  • **$8 - (-5):Startwith:** Start with {8}positive(blue)counters.Toremovepositive (blue) counters. To remove{5}negatives,firstintroducenegatives, first introduce{5}neutralpairs(eachconsistingofoneblueandoneredcounter),whichdonotchangethetotalvalue.Nowremovetheneutral pairs (each consisting of one blue and one red counter), which do not change the total value. Now remove the{5}redcountersrepresentingred counters representing{-5}.The. The {5}bluecountersfromtheneutralpairsremainalongsidetheoriginalblue counters from the neutral pairs remain alongside the original{8},giving, giving {13} positives. So $8 - (-5) = 13.
  • **$8 + 5:Startwith:** Start with {8}positivecountersandcombinethemwithpositive counters and combine them with{5}morepositivecounters,givingmore positive counters, giving{13} positives. So $8 + 5 = 13.

Both approaches produce 13{13}, confirming that $8 - (-5) = 8 + 5$.

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Updated 2026-04-21

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