Numbers Can be Positive or Negative
| – | Negative sign |
| + | Positive sign |
Table of Contents
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.
4 is really +4
Adding a Positive Number
Adding positive numbers is just simple addition.
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.
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:
(+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.
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