30 points! first to answer
1. identify the property shown by the equation 14 x 6 = 6 x 14
a. commutative property
b. associative property
c. identity property
d. distributive property
2. identify the property shown by the equation 7 + (5 + 8) = (7 + 5 + 8
a. commutative property
b. associative property
c. identity property
d. distributive property
3. identify the property shown by the equation 15+0=15
a. commutative property
b. associative property
c. identity property
d. distributive property

1. A. Commutative Property

2. B. Associative Property

3. C. Identity Property

Step-by-step explanation:

3. The Identity Property of Addition states that any number added by 0 is THAT NUMBER.

2. The Associative Property of Addition states that with the use of GROUPING SYMBOLS, no matter how you write your answer out\in-side them, you will ALWAYS get the exact same result.

1. The Commutative Property of Multiplication states that no matter the order of how you write your factors, you will ALWAYS get the exact same product.

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Here we want to work with different axioms of the sum and product operations.

First, let's write a brief description of these, so we can understand how they work:

Sum:

Commutative property: the order of the sum does not matter

A + B = B + A

Associative property: When we add we can group the numbers as we want

A + B + C = (A + B) + C = A + (B + C)

Identity property: When we add a given number to zero, the outcome is the given number

N + 0 = N

Product

Commutative property: the order of the factors does not matter

A*B = B*A

Associative property: When we add we can group the numbers as we want

A*B*C = (A*B)*C = A*(B*C)

Identity property: The product between any number N and 1, is equal to N.

N*1 = N

Distributive property: In the addition of two numbers that share a common factor, we can take the common factor out.

C*A + C*B = C*(A + B)

Now let's solve the question:

1)  14 x 6 = 6 x 14

We have a product where the order of the factors changes, we know that this is the Commutative property of the product.

2) 7 + (5 + 8) = (7 + 5) + 8

Here we grouped the numbers in a different way in addition, then this is the Associative property of the addition.

3) 15+0=15

Here we have a number plus zero that equals the original number, we know that this is the Identity property of the addition.

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step-by-step explanation:

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