**Unit 6: Number Systems and Algebra Concepts**

**if the product of two numbers equals one, then the numbers are reciprocals of each other. Here are two web-sites to illustrate reciprocal.**

__Vocabulary:__

Reciprocal:Math is Fun, reciprocal definition.

Math is Fun, reciprocal example.

The reciprocal is used in dividing fractions. Most parents learned the rule of "invert and multiply", this is still what we are doing, the reciprocal just explains why.

*Reciprocals are not always just a fraction turned "upside down", for example the reciprocal of 4 is 1/4 or 0.25.

Opposite of a number-example: 5, the opposite is -5.

Math is Fun, opposite of a number, adding and subtracting.

**Multiplication property of -1:**When multiplying or dividing with positve and negative numbers. If you have two negative numbers the answer will be positive. If you have a negative and a positive the answer will be negative.

Also, with more than just two numbers: an even number of negative numbers will make the answer positive. An odd number of negative numbers will make the answer negative.

Math is Fun, multiplying positive and negatives numbers.

**Counting numbers:**The numbers used to count things (1, 2, 3, 4, ...), 0 is sometimes included.

**Whole numbers:**Any of the numbers 0, 1, 2, 3, 4, and so on.

**Integers:**A number in the set {...-4, -3, -2, -1, 0, 1, 2, 3, 4, ...}

**Rational numbers:**Any number that can be represented in the form a/b, where a and b are intergers and b does not equal 0.

**Terminating decimals:**A decimal that ends. Example: 0.15; 0.035

**Repeating decimals:**A decimal in which one digit, or a group of digits, is repeated without end. Example: 0.333; 0.147

**Irrational numbers:**Numbers that cannot be written as fractions. Example: pi, the square root of 2.

**Real numbers:**Any rational or irrational number. For every real number there is a corresponding point on the number line.

Math is Fun, numbers.

**Order of operations:**PEMDAS or

__Please excuse my dear Aunt Sally__.

Rules for orders of operations.

1. Do the operations inside the parentheses.

2. Do all the calculations wtih exponents.

3. Do all multiplication and division in order from left to right.

4. Do all additions and subtraction in order from left to right.

Math is Fun, order of operations.