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Several properties are used to evaluate this expression. Identify the property used in each step.

21 + (36 + 0 + 19)

21 + (36 + 19):
21 + (19 + 36):
(21 + 19) + 36:

40 + 36

76

1 answer

Let's identify the properties used in each step of the expression:

  1. Step: \( 21 + (36 + 0 + 19) \)

    • Property used: Identity Property of Addition (adding 0 doesn't change the value)

  2. Step: \( 21 + (36 + 19) \)

    • Property used: Associative Property of Addition (changing the grouping of the numbers does not change the sum)

  3. Step: \( 21 + (19 + 36) \)

    • Property used: Commutative Property of Addition (changing the order of the numbers being added does not change the sum)

  4. Step: \( (21 + 19) + 36 \)

    • Property used: Associative Property of Addition (changing the grouping of the numbers again)

  5. Step: \( 40 + 36 \)

    • This step is just simplifying \( (21 + 19) \) to get 40.

  6. Step: \( 76 \)

    • Property used: Addition (calculating the sum of 40 and 36)

So, the properties identified for each step are as follows:

  1. Identity Property
  2. Associative Property
  3. Commutative Property
  4. Associative Property
  5. Simplification
  6. Addition/Calculation.