- A
- B
- C(−7) × 4 is an integer
- D
Step-by-Step Solution
but : subtraction is not commutative. Addition and multiplication are commutative, and is an integer (closure).
Answer: D)
Kiran uses the two number cards with the operation chips. Which statement is FALSE?
Class 7Integers (Extended)Integers
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.
- **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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