Negative and positive rules addition and subtraction

The Rules of Using Positive and Negative Integers

Table of Contents Show

The Rules of Using Positive and Negative Integers
Tips for Success
Addition
Subtraction
Multiplication
Division
What is the rule for negative and positive numbers?
What are the two rules for adding positive and negative numbers?
What is the rule for subtracting with negatives?

Illustration by Hugo Lin. ThoughtCo.

Updated on January 26, 2020

Whole numbers, figures that do not have fractions or decimals, are also called integers. They can have one of two values: positive or negative.

Positive integers have values greater than zero.
Negative integers have values less than zero.
Zero is neither positive nor negative.

The rules of how to work with positive and negative numbers are important because you'll encounter them in daily life, such as in balancing a bank account, calculating weight, or preparing recipes.

Tips for Success

Like any subject, succeeding in mathematics takes practice and patience. Some people find numbers easier to work with than others do. Here are a few tips for working with positive and negative integers:

Context can help you make sense of unfamiliar concepts. Try and think of a practical application like keeping score when you're practicing.
Using a number line showing both sides of zero is very helpful to help develop the understanding of working with positive and negative numbers/integers.
It's easier to keep track of the negative numbers if you enclose them in brackets.

Addition

Whether you're adding positives or negatives, this is the simplest calculation you can do with integers. In both cases, you're simply calculating the sum of the numbers. For example, if you're adding two positive integers, it looks like this:

5 + 4 = 9

If you're calculating the sum of two negative integers, it looks like this:

(–7) + (–2) = -9

To get the sum of a negative and a positive number, use the sign of the larger number and subtract. For example:

(–7) + 4 = –3
6 + (–9) = –3
(–3) + 7 = 4
5 + (–3) = 2

The sign will be that of the larger number. Remember that adding a negative number is the same as subtracting a positive one.

Subtraction

The rules for subtraction are similar to those for addition. If you've got two positive integers, you subtract the smaller number from the larger one. The result will always be a positive integer:

5 – 3 = 2

Likewise, if you were to subtract a positive integer from a negative one, the calculation becomes a matter of addition (with the addition of a negative value):

(–5) – 3 = –5 + (–3) = –8

If you're subtracting negatives from positives, the two negatives cancel out and it becomes addition:

5 – (–3) = 5 + 3 = 8

If you're subtracting a negative from another negative integer, use the sign of the larger number and subtract:

(–5) – (–3) = (–5) + 3 = –2
(–3) – (–5) = (–3) + 5 = 2

If you get confused, it often helps to write a positive number in an equation first and then the negative number. This can make it easier to see whether a sign change occurs.

Multiplication

Multiplying integers is fairly simple if you remember the following rule: If both integers are either positive or negative, the total will always be a positive number. For example:

3 x 2 = 6
(–2) x (–8) = 16

However, if you are multiplying a positive integer and a negative one, the result will always be a negative number:

(–3) x 4 = –12
3 x (–4) = –12

If you're multiplying a larger series of positive and negative numbers, you can add up how many are positive and how many are negative. The final sign will be the one in excess.

Division

As with multiplication, the rules for dividing integers follow the same positive/negative guide. Dividing two negatives or two positives yields a positive number:

12 / 3 = 4
(–12) / (–3) = 4

Dividing one negative integer and one positive integer results in a negative number:

(–12) / 3 = –4
12 / (–3) = –4

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

What is the rule for negative and positive numbers?

If both numbers are positive, the result is positive. If both numbers are negative, the result is positive. (Basically, the two negative values cancel each other out). If one number is positive and the other is negative, the result is negative.

What are the two rules for adding positive and negative numbers?

Adding Positive and Negative Numbers.

Rule 1: Adding positive numbers to positive numbers—it's just normal addition..

Rule 2: Adding positive numbers to negative numbers—count forward the amount you're adding..

Rule 3: Adding negative numbers to positive numbers—count backwards, as if you were subtracting..

What is the rule for subtracting with negatives?

Subtracting a number is the same as adding its opposite. So, subtracting a positive number is like adding a negative; you move to the left on the number line. Subtracting a negative number is like adding a positive; you move to the right on the number line.