Question

. Identify the correct definitions and models. Select all that apply. * 3 points Commutative property of addition (lessons 3 & 6): the property of operations that says addends can be in any order and it will NOT change the sum; a + b = b + a Distributive property of multiplication over addition (lessons 3 & 4): the property of operations that says multiplying the sum of two or more addends by a number is the same as multiplying the number by each of the addends individually and adding the products; a(b + c) = ab + ac and ab + ac = a(b + c) Identity Property of Multiplication (lesson 6) – the property of operations that says that the product of any number and 1 is that same number; a ∙ 1 = a

Answer 1

Here are the correct definitions and models based on the properties you've described:

1. Commutative property of addition: Correctly defined as the property of operations that states addends can be in any order without changing the sum. The equation \( a + b = b + a \) correctly represents this property.

2. Distributive property of multiplication over addition: This property is defined accurately as it states that multiplying the sum of two or more addends by a number is equivalent to multiplying the number by each of the addends individually and then adding the products. Both forms \( a(b + c) = ab + ac \) and \( ab + ac = a(b + c) \) are correct representations.

3. Identity Property of Multiplication: Correctly defined as the property that states that the product of any number and 1 is that same number. The equation \( a \cdot 1 = a \) accurately represents this property.

All three definitions and corresponding models provided are correct.