MandysNotes

20 March 2010 In Properties of Real Numbers

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:

distributive property, Mandy's Notes

 

EXAMPLES:

3(x + y)

= 3x + 3y


-2(5 + k)

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

= -10 - 2k

 

4x + 8x

= (4 + 8)x

= 12x

20 March 2010 In Basics & Number Properties

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.

 

20 March 2010 In Basics & Number Properties

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 , {   }.

NOTRad