What is the rule for 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.

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 . 6 + (–9) = –3.

Do two negatives make a positive when adding and subtracting?

Two negatives cancel out and make a positive , in maths as well as in speech.

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.

How to add two negative numbers?

When we add two or more negative numbers together, add the numbers and keep the negative sign . In multiplication and division, if the signs are the same, the product or quotient is positive. In multiplication and division, if the signs are different, the product or quotient is negative.

Do you subtract two positive numbers?

Rule 1: Subtracting a positive number from a positive number – it's just normal subtraction . For example: this is what you have learned before. 6 – 3 are two positive numbers. So solve this equation the way you always have: 6 – 3 = 3.

What is the rule with adding and subtracting negatives?

The rules for adding and subtracting negative numbers are as follows: To add two negative numbers, we ignore the negatives on each of the numbers, and add them. After this, we simply make the result negative. To subtract two negative numbers, we turn the problem into an addition problem by adding the opposite.

What is the rule of negative and positive?

Remember that two plus signs or two minus signs make a positive . One plus and one minus make a negative. Part of MathsNumber and number processes.

What are the rules for positive and negative integers?

RULE 1: The quotient of a positive integer and a negative integer is negative . RULE 2: The quotient of two positive integers is positive. RULE 3: The quotient of two negative integers is positive. If the signs are different the answer is negative.

What is the bodmas rule?

BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics . BODMAS stands for B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction.

What is the rule for minus and plus in math?

Adding and multiplying combinations of positive and negative numbers can cause confusion and so care must be taken. Two 'pluses' make a plus, two 'minuses' make a plus. A plus and a minus make a minus . If two positive numbers are multiplied together or divided, the answer is positive.

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.

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

Adding and Subtracting Positive and Negative Numbers (2024)

Numbers Can be Positive or Negative

No Sign Means Positive

Play with it!

Balloons and Weights

Adding a Positive Number

Example: 2 + 3 = 5

Subtracting A Positive Number

Example: 6 − 3 = 3

Adding A Negative Number

Example: 6 + (−3) = 3

Subtracting A Negative Number

Example: What is 6 − (−3) ?

What Did We Find?

Adding a positive number is simple addition ...

Positive and Negative Together ...

Example: What is 6 − (+3) ?

Example: What is 5 + (−7) ?

Subtracting a negative ...

Example: What is 14 − (−4) ?

The Rules:

Example: What is 5+(−2) ?

Example: What is 25−(−4) ?

Starting Negative

Example: What is −3+(+2) ?

Example: What is −3+(−2) ?

Now Play With It!

A Common Sense Explanation

Another Common Sense Explanation

A Bank Example

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

A Long Example You Might Like

Ally's Points

Try These Exercises ...

FAQs

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

What is the rule for minus and plus in math? ›