Negatives

a negative number is a number that is less than zero

negative numbers are used...  

                                                           in banking to show debt (aka: in the red)

                                                as opposed to having credit

                                        in measuring temperatures below 0℃

                                        in measuring the distance below sea level

we can add or subtract positive and negative numbers by moving to the left or right on the number line

                                                    move to the right → when you add

move to the left ← when you subtract

the key to multiplying and dividing with negatives is the following...

( − ) x ( − ) =  +       or     ( negative ) ÷ ( negative ) = positive

( + ) x ( + ) =  +       or     ( positive )  ÷  ( positive ) = positive

        &

( − ) x ( + ) =  −       or     ( negative ) ÷ ( positive ) = negative

( + ) x ( − ) =  −       or     ( positive ) ÷ ( negative ) = negative

Absolute numbers  cannot be negative

and are expressed as a number between two straight vertical lines

| 4 |  =  4       | - 4 |  =  4

Further hints...

negative numbers squared are always positive

(-2)2 = (-2) x (-2) = 4