Question

Match each property with the appropriate example.

1.
4(x - 2) = 4x - 8

2.
(4+2) + 8 = 4 + (2+8)

3.
4 * 2 = 2 * 4

4.
4 * 1 = 4



a.
Commutative property

b.
Distributive property

c.
Associative property

d.
Identity property

Answer 1

1. Distributive property 2. Associative property

3. Identity property 4. Commutative property

Answer 2

1. Distrubutive 2. Associative 3. Commutative 4. Identity

Explanation:

Answer 3

For this case we have that by definition:

• the distributive property establishes that:

`a (b + c) = ab + ac`

So:

`4 (x-2) = 4x-8`

State the distributive property.

• The associative property states:

`a + (b + c) = (a + b) + c`

So:

`(4 + 2) + 8 = 4 + (2 + 8)`

Enunciates the associative property

• The commutative property establishes that the order of the factors does not alter the product.

`a * b = b * a`

So:

`4 * 2 = 2 * 4`

Enunciates the commutative property

• The Identity property establishes that every number multiplied by 1 gives the same number. So:

`4 * 1 = 4`

State identity property

Answer:

Distributive property

Associative property

Commutative property

Identity property