# MandysNotes

## 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

## Sets of Numbers Examples Sets: Natural Numbers, Whole numbers, Integers

20 March 2010

Counting Numbers:

### {1, 2, 3, 4, 5, 6, ...}

BY THE WAY, "..." notates continuation going up infinitely.

The set of Natural Numbers $$\mathbb{N}\ \$$ = {0, 1, 2 3, 4, 5, 6...}.

The set of Integers, $$\mathbb{Z}\ \$$   = {..., -3, -2, -1, 0, 1, 2, 3}.

The set of Rational numbers, $$\mathbb{Q}\ \$$  is the set of ratios of integers.

That is, every $$q \in \mathbb{Q}\$$

is of the form:

$$q = \frac{n}{m} \$$

With $$n, m \in \mathbb{Z}\$$ .

The set of Real Numbers $$\mathbb{R}\ \$$  is the set of limits of sequences of rational numbers.

## Sets of Numbers

20 March 2010

A set is a collection of "elements," or "members," and each set is entirely determined by its members. If $x$is a member of a set $U,$ we write $x \in U.$ In basic algebra, the elements of a set are usually numbers.

We can also designate a set by enclosing its members in  braces , {   }.