## Mandy

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The Commutative Property states:

For any real numbers a and b:

a + b = b + c

ab = ba

The Commutative Property is when the ORDER CHANGES but the result remains the same.

For any real number a,

a + 0 = 0 + a = a

a * 1 = 1 * a = a

Notes: An easy way to remember this is that the Identity Property leaves the IDENTITY of a real number unchanged. Adding 0 to any number or multiplying any number times a does not change the value of the number in any way.

EXAMPLES:

12m + m

= 12m + 1m

= (12 + 1)m

= 13m

For any real number \( a \neq 0 :\)

\( a + (-a) = 0 \ \) and,

\( a \left( \frac{1}{a} \right) = 1.\)

That is, any number times its reciprocal equals 1.

The reciprocal of zero is not defined.

Very simply stated, the Distributive Property is easy to understand when seen like this:

a(b+c) = ab + ac

OR

(b+c)a = ba + ca

In more complex examples, the Distributive Property can be applied to equations like this one, though the same principles still apply:

EXAMPLES:

**3(x + y)**

= 3x + 3y

**-2(5 + k)**

= -2(5) + (-2)(k)

= -10 - 2k

**4x + 8x**

= (4 + 8)x

= 12x