CALCULATE WITH CONFIDENCE

Arithmetic Operations

Associative Property Calculator

Compare both valid groupings of three values under addition or multiplication and verify that they match exactly.

Exact arithmetic

Compare two groupings

Addition or multiplication

Common exact result

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Choose addition or multiplication.
  2. Enter values a, b, and c.
  3. Compare the left-grouped and right-grouped expressions.

Calculation method

Regrouping does not change the result

Addition and multiplication are associative: (a + b) + c = a + (b + c), and (a × b) × c = a × (b × c).

Subtraction and division are deliberately unavailable because changing their grouping can change the answer.

Worked example

Regroup an addition

Both ways of grouping 5, 0.4, and 0.6 produce the same exact value.

(5 + 0.4) + 0.6 = 5 + (0.4 + 0.6) = 6.0

Supported inputs

Precision and limits

Exact decimal input

Each value may contain up to 200 digits, including up to 100 decimal places.

Supported operations

This property applies here only to addition and multiplication.

Exact verification

Both groupings are calculated independently and compared as exact values.

Private by default

Your entries are calculated in this browser and are not submitted with the calculation.