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Which property is illustrated by ?

Class 7Integers (Extended)Integers
  • AAssociative property of multiplication
  • BCommutative property of multiplication
  • CDistributive property
  • DIdentity property

Step-by-Step Solution

Regrouping the factors without changing their order or the product is the associative property: (a × b) × c = a × (b × c).
Answer: A) Associative property of multiplication

Key idea: Properties — same as for whole numbers, mostly

Integers obey:
- **Commutative** for addition and multiplication: a + b = b + a; a × b = b × a.
- **Associative** for addition and multiplication: (a + b) + c = a + (b + c); (a × b) × c = a × (b × c).
- **Distributive**: a × (b + c) = a × b + a × c — and this is true even when a, b, c are negative.

Subtraction and division are NOT commutative or associative for integers (they aren't for whole numbers either). Order and grouping matter.

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Find the integer x such that x × (−7) = −49.Evaluate: (−2) × (−3) × (−4) × (−5) ÷ (−6).Look at the pattern: 3 × (−4) = −12, 2 × (−4) = −8, 1 × (−4) = −4, 0 × (−4) = 0.…The bars in |a| mean 'distance of a from 0 on the number line', so |−6| = 6. Evaluate…Which statement correctly compares |−7 + 3| with |−7| + |3|?