4. Identify the correct definitions and models. Select all that apply. *
o - 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
o - 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)
- o 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
- Associative property of addition (lesson 3): the property of operations that says the grouping of addends does not affect the sum; (a + b) + c = a + (b + c)
- Identity Property of Addition (lesson 2): the property of operations that says the sum of any number and 0 is that same number; a + 0 = a
can you give me a selected answer?
Sure! Based on the given options, the correct definitions and models are:
- 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
The selected answers are the ones that have the letter "o" in front of them. So, the correct selections would be:
- o 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
- o 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)
- o 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
The correct definitions and models are as follows:
- Commutative property of addition: This property states that addends can be in any order, and it will not change the sum. In other words, if you switch the order of the addends, the result will be the same. The equation representing this property is a + b = b + a.
- Distributive property of multiplication over addition: This property states that 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. There are two equivalent equations that represent this property: a(b + c) = ab + ac and ab + ac = a(b + c).
- Identity Property of Multiplication: This property states that the product of any number and 1 is the same number itself. In other words, when you multiply a number by 1, the result is the original number. This property can be represented by the equation a ∙ 1 = a.
To identify the correct definitions and models, you can check the options provided and select all the statements that are true. In this case, the correct options are:
- 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