When determining the place each digit has in a number, start from the right and separate each group of three digits (sometimes called a period or grouping) by commas. **Example: 2,345,456.**

If you write or say a number, start from the left with the largest grouping or period. Continue naming each group except for the ones place (it’s not stated). Thus,** 2,345,456** is read “Two million three hundred forty five thousand four hundred fifty six“.

Changing the order numbers are added in does not change the sum. This is known as the **Commutative Property of Addition**.

Changing the grouping of numbers when adding does not change the sum. This is known as the **Associative Property of Addition**.

Zero is the **additive identity** because adding zero to any number gives that number.

The order two numbers are subtracted in does matter (ie., not commutative).

An addition problem can be changed into a subtraction problem. For example** 6 + 2 = 8**.

There are two possible subtraction problems: **8 – 2 = 6 or 8 – 6 = 2**.

Subtracting zero from any number results in that number.

Changing the order numbers are multiplied in does not change the product. This is known as the **Commutative Property of Multiplication**.

Changing the grouping of numbers when multiplying does not change the product. This is known as the **Associative Property of Multiplication**.

One is the **multiplicative identity** because multiplying one times any number gives that number.

Zero times any number results in a product of zero.

Dividing zero by any nonzero number is zero.

However, dividing any number by zero **cannot be done**. This type of division is known as **undefined**. It is impossible to compute or find the answer for the problem.

Any nonzero number divided by itself is one.

**Divisibility Test:**

A number is divisible in the following cases below.

- Two if it is an even number
- Three if the sum is divisible by three
- Five if it ends in zero or five
- Nine if the sum is divisible by nine
- Zero if it ends in zero

- When adding two fractions with the same denominators, add the numerators and place the result over the denominator. For example:
**1/5 + 3/5 = ( 1 + 3)/5 =4/5** - Proper fractions are written such that the
__denominator is never zero__**(a/b, where b is not equal to zero). Example:****2/5** - A whole number can be written as a fraction by placing the whole number over 1
**(Therefore 3= 3/1)**. The reciprocal (inverse) is the number 1 over the whole number.**So, 4= 4/1 and the reciprocal is ¼.**

- Dividing by any power of 10 (10, 100, 1000, etc.) means that you move the decimal to the left the same number of spaces that you have zeros
**. So, 456.7/100 = 4.567** - A Repeating decimal is a decimal that repeats a number of times (in a series) indefinitely. Write the number by placing a bar over the repeating series.
**So, 10.454545… means that a bar is written over 45 because that is the series that repeats.** - When rounding a number up, you have to look at the place to the right of the number you are rounding.
**If the number is 5 or greater, round the number up to the next number.**

- The symbol % means “divided by 100”.
**So, 35% = 35/100= 0.35** - To change a percent to a decimal, move the decimal two places to the left.
**So, 42% = .42 or 0.42**

- Rectangles, squares, parallelograms, trapezoids, and triangles are all polygons (“poly” means many sides).
- A circle is a simple closed curve that divides a plane into two regions (“interior” or inside and “exterior” or outside).
- A triangle is a polygon with three sides.
- All four angles of a rectangle and square are 90 degrees.
- A trapezoid has four sides but only two of them are parallel to each other.