Rules for Adding and Subtracting Positive and Negative Numbers
Here are some thoughts about negatives:
First the rules for adding negatives:
(1) If you are adding two positive numbers, just add the numbers and keep the positive sign.
Example: +5 + (+4) = +9
(2) If you are adding two negative numbers, add the two numbers, and keep the negative sign.
Example: -7 + (-8) = -15
(3) If you adding one positive and one negative number,
subtract the two numbers and keep the sign of the larger.
Examples:
-8 + (+6) = -2
-8 + (+16) = +8
In dealing with negative numbers, it is often easy to think of a negative sign as the "opposite of."
And you can think of good as POSITIVE and bad as NEGATIVE.
You can think of wining as POSITIVE and losing as NEGATIVE.
You can think of earning money as POSITIVE and spending money as NEGATIVE.
You can think of gaining as POSITIVE and losing as NEGATIVE.
What is the opposite of good? Answer: Bad. So, - (+3) = -3
What is the opposite of bad?
Answer: Good. So, - (-3) = +3
What is the opposite of winning? Answer: Losing. So, - (+3) = -3
What is the opposite of losing 3 yards in football?
Answer: Gaining 3 yards.
So, - (-3) = +3
What is the opposite of gaining 3 yards?
Answer: Losing 3 yards.
So, - (+3) = -3
I always used the football field to help visualize the addition of signed numbers.
If you on the 25 yard line and you lose 7 yards, then you are on the 18 yard line:
25 + (-7) = +18
Or, if you are at the line of scrimmage and you lose 6 yards and then lose 7 more yards,
you will have lost 13 yards:
-6 + (-7) = -13
Or you can just use the number line to show additions and subtractions.
For addition, you move to the right; for subtraction, you move to the left.
Additionally, if a number is positive, you move in the direction above;
But if the number is negative, you move in the opposite direction from what is normal.
Example: 4 -(-9) = 13.
You are subtracting a negative number from a positive number.
You start at spot 4 on the number line.
You go back negative 9 times. Meaning, you go to the right 9 times.
This sends you to spot 13.
Example: 4 + (-9) = -5
Start at the number 4 on the number line.
Then you move 9 units to the left because you are adding a negative number.
That puts you at -5.
Think in terms of money:
IF you have $22 and you spend $6, then you have 22 +(-6) = 22 - (6) = 16
If you have $22 and you spend $30, then you must borrow money to make the transaction.
22 - 30 = -8 (you owe somebody $8)
Here is an example I have heard used to help you remember what sign the answer will be when adding and subtracting negatives:
First of all, positive numbers are Love and negative number are Hate.
Positive + Positive = Love to Love = Answer is Love or Positive (If I love to love, I love.)
Positive + Negative = Love to Hate = Answer is Hate or Negative (If I love to hate, I hate.)
(Your answer may not always be negative, but it will be subtracting and will end up being less then the original number.
Example: 5 + (-2) = 5 - 2 = 3
Example: 5 + (-12) = -7
Negative + Negative = Hate to Hate = Answer is Love or Positive (If I hate to hate, I love.)
(Again, your answer may not always be positive, but it will be adding and will end up being more than the original number.
Example: -5 - (-3) = -5 + 3 = -2; -3 - (-5) = -3 + 5 = 2