How this calculator works
The associative property says that regrouping a sum or product does not change its exact mathematical value. Parentheses show which pair is combined first. Very large or tiny decimal inputs may show small floating-point differences between the two evaluation orders.
Formula
(a + b) + c = a + (b + c); (a × b) × c = a × (b × c).
Worked example
(2 + 3) + 4 = 5 + 4 = 9 and 2 + (3 + 4) = 2 + 7 = 9. For multiplication, (2 × 3) × 4 and 2 × (3 × 4) both give 24.
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Frequently asked questions
Does this work for subtraction?
No. (8 - 3) - 2 is 3, whereas 8 - (3 - 2) is 7.
Is regrouping the same as reordering?
Regrouping changes parentheses. Reordering changes the position of terms and uses the commutative property.
Why might the displayed results differ for extreme decimals?
Finite computer arithmetic can lose small terms. The algebraic identity still holds for exact real numbers.