Adding and Subtracting Positive and Negative Numbers (2024)

Numbers Can be Positive or Negative

This is the Number Line:


Negative Numbers (−)	Positive Numbers (+)


"−" is the negative sign.	"+" is the positive sign

No Sign Means Positive

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

Example: 5 is really +5

Play with it!

On the Number Line positive goes to the right and negative to the left.

Try the sliders below and see what happens:

numbers/images/number-line-add.js?sub=n

Balloons and Weights

Let us think about numbers as balloons (positive) and weights (negative):

This basket has balloons and weights tied to it:

The balloons pull up (positive)
And the weights drag down (negative)

Adding a Positive Number

Adding positive numbers is just simple addition.

We can add balloons (we are adding positive value)

the basket gets pulled upwards (positive)

Example: 2 + 3 = 5

is really saying

"Positive 2 plus Positive 3 equals Positive 5"

We could write it as (+2) + (+3) = (+5)

Subtracting A Positive Number

Subtracting positive numbers is just simple subtraction.

We can take away balloons (we are subtracting positive value)

the basket gets pulled downwards (negative)

Example: 6 − 3 = 3

is really saying

"Positive 6 minus Positive 3 equals Positive 3"

We could write it as (+6) − (+3) = (+3)

Adding A Negative Number

Now let's see what adding and subtracting negative numbers looks like:

Example: 6 + (−3) = 3

is really saying

"Positive 6 plus Negative 3 equals Positive 3"

We could write it as (+6) + (−3) = (+3)

The last two examples showed us that taking away balloons (subtracting a positive) or adding weights (adding a negative) both make the basket go down.

So these have the same result:

(+6) − (+3) = (+3)
(+6) + (−3) = (+3)

In other words subtracting a positive is the same as adding a negative.

Subtracting A Negative Number

Lastly, we can take away weights (we are subtracting negative values)

the basket gets pulled upwards (positive)

Example: What is 6 − (−3) ?

6−(−3) = 6 + 3 = 9

Yes indeed! Subtracting a Negativeis the same as adding!

Two Negatives make a Positive

What Did We Find?

Adding a positive number is simple addition ...

Adding a Positive is Addition

Positive and Negative Together ...

Subtracting a Positive
or
Adding a Negative
is
Subtraction

Example: What is 6 − (+3) ?

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

5+(−7) = 5 − 7 = −2

Subtracting a negative ...

Subtracting a Negative is the same as Adding

Example: What is 14 − (−4) ?

14−(−4) = 14 + 4 = 18

The Rules:

It can all be put into two rules:

	Rule	Example
+(+)	Two like signs become a positive sign	3+(+2) = 3 + 2 = 5
−(−)	Two like signs become a positive sign	6−(−3) = 6 + 3 = 9

+(−)	Two unlike signs become a negative sign	7+(−2) = 7 − 2 = 5
−(+)	Two unlike signs become a negative sign	8−(+2) = 8 − 2 = 6

They are "like signs" when they are like each other (in other words: the same).

So, all you have to remember is:

Two like signs become a positive sign

Two unlike signs become a negative sign

Example: What is 5+(−2) ?

+(−) are unlike signs (they are not the same), so they become a negative sign.

5+(−2) = 5 − 2 = 3

Example: What is 25−(−4) ?

−(−) are like signs, so they become a positive sign.

25−(−4) = 25+4 = 29

Starting Negative

What if we start with a negative number?

Using The Number Line can help:

Example: What is −3+(+2) ?

+(+) are like signs, so they become a positive sign.

−3+(+2) = −3 + 2

Start at −3 on the number line,
move forward 2 and you end up at −1

−3+(+2) = −3 + 2 = −1

Example: What is −3+(−2) ?

+(−) are unlike signs, so they become a negative sign.

−3+(−2) = −3 − 2

Start at −3 on the number line,
move back 2 and you end up at −5

−3+(−2) = −3 − 2 = −5

Now Play With It!

Adding and Subtracting Positive and Negative Numbers (16)

Try playing Casey Runner, you need to know the rules of positive and negative to succeed!

A Common Sense Explanation

And there is a "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive)

If I say "Do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).

So, two negatives make a positive, and if that satisfies you, then you are done!

Another Common Sense Explanation

A friend is +, an enemy is −

+ + ⇒ +		a friend of a friend is my friend
+ − ⇒ −		a friend of an enemy is my enemy
− + ⇒ −		an enemy of a friend is my enemy
− − ⇒ +		an enemy of an enemy is my friend

A Bank Example

Example: Last year the bank subtracted $10 from your account by mistake, and they want to fix it.

So the bank must take away a negative $10.

Let's say your current balance is $80, so you will then have:

$80−(−$10) = $80 + $10 = $90

So you get $10 more in your account.

A Long Example You Might Like

Ally's Points

Ally can be naughty or nice. So Ally's parents have said

"If you are nice we will add 3 points (+3).
If you are naughty, we take away 3 points (−3).
When you reach 30 Points you get a toy."

Ally starts the day with 9 Points:		9
Ally's Mom discovers spilt milk:		9 − 3 = 6
Then Dad confesses he spilt the milk and writes "undo". How do we "undo" a minus 3? We add 3 back again!
So Mom calculates:		6 − (−3) = 6 + 3 = 9

So when we subtract a negative, we gain points
(i.e. the same as adding points).

So Subtracting a Negative is the same as Adding

A few days later. Ally has 12 points.

Mom adds 3 points because Ally's room is clean.		12 + 3 = 15

Dad says "I cleaned that room" and writes "undo" on the chart. Mom calculates:		15 − (+3) = 12

Dad sees Ally brushing the dog. Writes "+3" on the chart. Mom calculates:		12 + (+3) = 15

Ally throws a stone against the window. Dad writes "−3" on the chart. Mom calculates:		15 + (−3) = 12

See: both "15 − (+3)" and "15 + (−3)" result in 12.

So:

It doesn't matter if you subtract positive points
or add negative points,
you still end up losing points.

So Subtracting a Positive
or
Adding a Negative
is
Subtraction

Try These Exercises ...

Now try This Worksheet, and see how you go.

And also try these questions:

11715, 11716, 11717, 11718, 11719, 11720, 11721, 3445, 3446

Number Line Using The Number Line Whole Numbers and Integers Multiplying Negatives Number Index Algebra Index

FAQs

Adding and Subtracting Positive and Negative Numbers? ›

Adding two positive integers results in positive integers, whereas adding two negative integers will result in the sum with a negative sign. But, the addition of two different signed integers will result in subtraction only and the sign of the result will be the same as the larger number has.

Read On ›

What is the rule for adding and subtracting positive and negative numbers? ›

The grid below can help to work out whether to add or subtract with a positive or negative number. If you have two signs next to each other, change them to a single sign. If the signs are the same, add. If the signs are different, subtract.

How do you add positive and negative numbers examples? ›

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.

Get More Info ›

Do two negatives make a positive when adding and subtracting? ›

If you subtract a negative number, the two negatives combine to make a positive. −10−(−10) is not −20. Instead, you can think of it as turning one of the negative signs upright, to cross over the other, and make a plus. The sum would then be −10+10 = 0.

Get More Info ›

How do you add and subtract positive and negative decimals? ›

Adding and Subtracting Two Signed Decimals

When adding a positive and a negative decimal, subtract the number with a smaller absolute value from the number with the greatest absolute value, and the sign of the final answer is the same as the number whose absolute value is the greatest.

Read The Full Story ›

What is the plus and minus rule in maths? ›

When two signs are written next to each other, the rules for adding and subtracting numbers are: two signs that are different become a negative sign. two signs that are the same become a positive sign.

Get More Info Here ›

Why do you add when subtracting a negative number? ›

Another way to think of a negative sign is as an OPPOSITE sign. So when you are subtracting a negative, it's really telling you to do the opposite of subtracting, which ends up being adding.

See Details ›

What is the law of negative and positive numbers? ›

Multiplication and Division of Integers. RULE 1: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.

Learn More Now ›

What happens if you subtract two positives? ›

Rule 1: Subtracting a positive number from a positive number – it's just normal subtraction.

What is an example of addition and subtraction? ›

The symbol to represent addition is '+' (plus sign) and subtraction is '-' (minus sign). Both addition and subtraction are inverse operations of each other. For example, if 9 + 1 = 10, then 10 – 1 = 9. That shows if 1 is added to 9 then the result is 10, whereas if 1 is subtracted from 10, then the result is 9.

Tell Me More ›

How do you subtract positive and negative? ›

Subtracting a Negative from a Positive: Positive Minus Negative. Remember, a minus sign with another minus sign results in a plus sign. In other words, subtracting a negative number from a positive number is the same as adding two positive numbers.

Find Out More ›

What is the rule of signs in math? ›

Descartes' Rule of Signs states that the possible number of the positive roots of a polynomial is equal to the number of sign changes in the coefficients OR less than the number of sign changes by a multiple of 2. For example, a polynomial with 3 sign changes could have 3 positive roots or 1 positive root.

What is the law of signs in addition and subtraction? ›

When adding two numbers with like signs, add the values and keep the common sign. When adding two numbers with unlike signs, subtract the values and use the sign of the larger-valued number. Change the subtraction operator to addition and change the sign of the number that immediately follows.

Know More ›

What are the rules of integers? ›

Rule 1: Multiplying integers with the same sign results in a positive product. Positive x Positive = Positive and Negative x Negative = Positive. Rule 2: Multiplying integers with opposite signs results in a negative product. Positive x Negative = Negative. Rule 3: Multiplying by zero always results in zero.