# MandysNotes

## Mandy

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### Commutative Property

20 March 2010

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.

### Identity Properties

20 March 2010

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

### Inverse Properties

20 March 2010

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.

### The Distributive Property, Explanation & Examples

20 March 2010

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

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