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Absolute value, step by step

Absolute value is a distance, and a distance is never negative.

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The question

Work out the value.

|−5| + |11|

|−5| + |11|
|−5| = 5|11| = 11
5+11=16
  1. The two bars ask for a DISTANCE: how far the thing between them is from zero. A distance is never negative, and that is a fact about distance rather than a rule about minus signs.
  2. There are two sets of bars here, and each one is finished before they meet: |−5| is 5, and |11| is 11.
  3. Only then add them: 5 + 11 = 16. Adding −5 and 11 FIRST would have given 6, which is the answer to a question nobody asked.

How it works.

  1. 01

    The two bars ask for a DISTANCE: how far the thing between them is from zero. A distance is never negative, and that is a fact about distance rather than a rule about minus signs.

  2. 02

    There are two sets of bars here, and each one is finished before they meet: |−5| is 5, and |11| is 11.

  3. 03

    Only then add them: 5 + 11 = 16. Adding −5 and 11 FIRST would have given 6, which is the answer to a question nobody asked.

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