Negative Number

Negative Number

Tips for negative number

Commonly, plus and minus signs are used to indicate addition and subtraction, respectively. Those signs can also be used to indicate directed distances and specific points on a number line. A positive number means a move to the right on the number line, while a negative number means a move to the left. These concepts are key to mastering computation with negative numbers. The rules for operations with negative numbers may seem arbitrary and mysterious but they are not as arbitrary as they seem. To understand the rules, you first need to understand what it means to do operations with negative numbers. A number line is one of the most useful models for understanding negative numbers.

Integers

negative whole numbers (...,-4, -3, -2, -1) and 
0; and positive whole numbers (1, 2, 3, ...). 
We represent them on the number line thus:

On the number line, LEFT is LESS.

So -4 < 2 and -103 < -45.

Also, 2 > -2 and 3 > -150

Uses:

Temperatures (below zero) 
Bank balances which are overdrawn 
Golf 
Engineering 
Science 

Absolute Value

The distance from 0 to an integer is its absolute 
value (written using vertical line brackets around 
the number.

Examples:
|-4| = 4

|3| = 3

Opposite of an Integer

The opposite of an integer is obtained by changing 
its sign (i.e. change - to + or change + to -).

Examples: 
The opposite of -3 is 3 and the opposite of 4 is -4.

Integer Addition

Use the number line and think of "journeys".

-2 + 5 means "start at -2 and go 5 in the positive 
direction"

3 + -6 means "start at 3 and go 6 in the negative 
direction"

-5 + 12 means "start at -5 and go 12 in the positive 
direction"


Problem: It is -4?and snowing. The forecast for 
tomorrow is for a rise in temperature of 6? What 
will it be tomorrow?

Answer: -4 + 6 = 2. It will be 2?tomorrow.

Integer Subtraction

We can change the subtraction into a more familiar 
addition by realising subtracting an integer is the same 
as adding its opposite.

Examples:
-4 - -3 = -4 + +3 = -1

5 - +7 = 5 + -7 = -2.

Integer Multiplication

We can summarise the results thus:

positive ?positive = positive

+ ?+ = +

signs the same: positive answer
negative ?positive = negative

- ?+ = -

signs different: negative answer

positive ?negative = negative

+ ?- = -

signs different: negative answer
negative ?negative = positive

- ?- = +

signs the same: positive answer

Examples:

-2 ?5 = -10
7 ?-2 = -14
-3 ?-6 = 18