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.
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.