Summary of Key Concepts

Positive and Negative Numbers ((Reference))

A number is denoted as positive if it is directly preceded by a " + + " sign or no sign at all. A number is denoted as negative if it is directly preceded by a " − − " sign.

Opposites ((Reference))

Opposites are numbers that are the same distance from zero on the number line but have opposite signs.

Double-Negative Property ((Reference))

−(−a)=a −(−a)=a

Absolute Value (Geometric) ((Reference))

The absolute value of a number a a , denoted | a | | a | , is the distance from a a to 0 on the number line.

Absolute Value (Algebraic) ((Reference))

| a |={ a if a≥0 −a if a<0 | a |={ a if a≥0 −a if a<0

Addition of Signed Numbers ((Reference))

To add two numbers with
like signs, add the absolute values of the numbers and associate the common sign with the sum.
unlike signs, subtract the smaller absolute value from the larger absolute value and associate the sign of the larger absolute value with the difference.

Addition with 0 ((Reference))

0+any number=that particular number 0+any number=that particular number , that is, 0+a=a 0+a=a for any real number a a .

Additive Identity ((Reference))

Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity.

Definition of Subtraction ((Reference))

a−b=a+(−b) a−b=a+(−b)

Subtraction of Signed Numbers ((Reference))

To perform the subtraction a−b a−b , add the opposite of b b to a a , that is, change the sign of b b and add.

Multiplication and Division of Signed Numbers ((Reference))

(+) (+)=+ (+) (+) = + (+) (−) =− (−) (−)=+ (+) (−)=− (−) (+)=− (−) (−) =+ (−) (+) =− (+) (+)=+ (+) (+) = + (+) (−) =− (−) (−)=+ (+) (−)=− (−) (+)=− (−) (−) =+ (−) (+) =−

Reciprocals ((Reference))

Two numbers are reciprocals of each other if their product is 1. The numbers 4 and 1 4 1 4 are reciprocals since (4) ( 1 4 )=1 (4) ( 1 4 )=1 .

Negative Exponents ((Reference))

If n n is any natural number and x x is any nonzero real number, then x −n = 1 x n x −n = 1 x n .

Writing a Number in Scientific Notation ((Reference))

To write a number in scientific notation:

Converting from Scientific Notation:
positive exponent ((Reference))

To convert a number written in scientific notation to a number in standard form when there is a positive exponent as the power of 10, move the decimal point to the right the number of places prescribed by the exponent on the 10.

Negative Exponent ((Reference))

To convert a number written in scientific notation to a number in standard form when there is a negative exponent as the power of 10, move the decimal point to the left the number of places prescribed by the exponent on the 10.