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negative numbers
 Number Addition Subtraction Multiplication Division Mixed Operation Decimal Fraction negative numbers Percentage Coordinate Time Equation Geometry Word Problems
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# negative numbers

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## Tips for negative numbers

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 numbers means a move to the left. These concepts are key to mastering computation with negative numberss. The rules for operations with negative numberss 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 numberss. A number line is one of the most useful models for understanding negative numberss.

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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.

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

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

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

Integer Multiplication

We can summarise the results thus:

positive ?positive = positive

+ ?+ = +

negative ?positive = negative

- ?+ = -

positive ?negative = negative

+ ?- = -

negative ?negative = positive

- ?- = +