Positive and Negative Numbers

Numbers Can be Positive or Negative

Negative sign
+Positive sign

No Sign Means Positive

If a number has no sign it usually means that it is a positive number.

Any numbers greater than zero are described as positive numbers. Usually, we don’t put a plus sign in front of positive numbers because the general understanding is that numbers without a sign are positive.

Example

4 is really +4

Adding a Positive Number

Adding positive numbers is just simple addition.

Example

4 + 3 = 7

is really saying

“Positive 4 plus Positive 3 equals Positive 7”

We could write it as (+4) + (+3) = (+7)

Subtracting A Positive Number

Subtracting positive numbers is just simple subtraction.

Example

4 − 3 = 1

is really saying

“Positive 4 minus Positive 3 equals Positive 1”

We could write it as (+4) − (+3) = (+1)

Adding A Negative Number

Numbers that are less than zero are known as negative numbers.

These numbers have a minus sign in front of them to indicate that they are less than zero (for example, -7 or ‘minus 7’).

Subtracting a positive is the same as adding a negative.

So these have the same result:

Example

(+5) − (+2) = (+3), is saying “Positive 5 minus positive 2 equals Positive 3”

Is same with

(+5) + (−2) = (+3), is saying “Positive 5 plus Negative 2 equals Positive 3”

Subtracting A Negative Number

If you subtract a negative number, the two negatives combine to make a positive.

Example

What is 3 − (−6) ?

3−(−6) = 3 + 6 = 9

Subtracting a Negative is the same as adding!

Two Negatives make a Positive

Multiplying & Dividing Positive & Negative Numbers

First, ignore the signs, multiply or divide the numbers as if they were both positive.

After you have the numerical answer, apply a very simple rule to decide the sign of the answer:

When the signs of the 2 numbers are different, the answer will be negative.

When the signs of the 2 numbers are the same, the answer will be positive.

So:

(negative number) × (negative number) = positive number

(positive number) × (positive number) = positive number

But:

(negative number) × (positive number) = negative number

You cannot multiply a number by itself to get a negative number. To get a negative number, you need 1 positive & 1 negative number.

The rule works the same way when you have more than 2 numbers to divide or multiply. An odd number of negative numbers will give a negative answer. An even number of negative numbers will give a positive answer.

It can all be put into 2 rules:

 Rule Examples
+(+)
-(-)
2 same signs become a positive sign +4 + (+3) = 4 + 3 = 7
3−(−6) = 3 + 6 = 9
+(-)
-(+)
2 different signs become a negative sign 7 + (-4) = 7 – 4 = 3
9−(+5) = 9 – 5 = 4

So, all you have to remember is:

  • 2 same signs become a positive sign
  • 2 different signs become a negative sign

Learn More

Even and Odd Numbers

Cardinal and Ordinal Numbers Chart

Complex Numbers

Irrational Numbers

Numbers Index

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