Which property allows regrouping numbers in a sum or product without changing the result?

Which property allows regrouping numbers in a sum or product without changing the result?

• A. Commutative Property
• B. Distributive Property
• C. Associative Property
• D. Identity Property

Answer: (C)

Regrouping numbers in a sum or product without changing the result comes from the associative property. This property says that the way you group numbers doesn’t affect the outcome, as long as you don’t change the order of the terms. For addition, (a + b) + c = a + (b + c). For multiplication, (ab)c = a(bc). For example, with addition, (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. With multiplication, (2 × 3) × 4 equals 6 × 4, which is 24, and 2 × (3 × 4) equals 2 × 12, which is also 24. This demonstrates that regrouping preserves the result. Other properties deal with different ideas: changing the order of terms (commutative) or distributing a factor over a sum (distributive), or using identity elements like 0 or 1.

Regrouping numbers in a sum or product without changing the result comes from the associative property. This property says that the way you group numbers doesn’t affect the outcome, as long as you don’t change the order of the terms. For addition, (a + b) + c = a + (b + c). For multiplication, (ab)c = a(bc).

For example, with addition, (2 + 3) + 4 equals 5 + 4, which is 9, and 2 + (3 + 4) equals 2 + 7, which is also 9. With multiplication, (2 × 3) × 4 equals 6 × 4, which is 24, and 2 × (3 × 4) equals 2 × 12, which is also 24. This demonstrates that regrouping preserves the result.

Other properties deal with different ideas: changing the order of terms (commutative) or distributing a factor over a sum (distributive), or using identity elements like 0 or 1.