Answer:
- commutative property of multiplication
- associative property of addition
- additive inverse property
- multiplication property of zero
Explanation:
You are asked to identify the real number properties that justify various changes in the way an expression is written.
Properties of numbers
In general, there are associative, commutative, identity, and inverse properties of addition and multiplication. You can use these properties to simplify and rewrite expressions, and to help perform arithmetic.
This is basically a vocabulary question, to see if you know the names associated with the behaviors these properties describe.
Commutative properties
When an operation (such as addition or multiplication) has the commutative property, it means the order of its operands does not matter
addition: a + b = b + a
multiplication: a × b = b × a
Associative properties
When an operation has the associative property, it means that grouping of operands does not matter.
addition: (a + b) + c = a + (b + c)
multiplication: (ab)c = a(bc)
Identity properties
When an operation is performed using its identity element, the value of the other operand is not changed:
addition: a + 0 = a
multiplication: a × 1 = a
Inverse properties
When an operation has an inverse, performing the operation with the inverse produces the identity element.
addition: a + (-a) = 0
multiplication: a × (1/a) = 1
Note: these last two properties are used to simplify and solve algebraic expressions. They let you "undo" operations done to variables or expressions.
Questions at hand
You can match the given expressions to the example expressions shown above. The "multiplication property of zero" is also known as the "zero product rule": a product is zero if and only if a factor is zero.
