Adding and Subtracting Positive and Negative Numbers (2024)

Table of Contents

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 References

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)

FAQs

What is the rule for adding and subtracting negative and positive 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.

When adding a negative and a positive, what is the answer? ›

If one is positive and the other negative, the answer will be negative. When more integers are involved work the calculations from left to right.

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What is the answer when you subtract a positive from a negative? ›

Thus, positive minus negative equals positive.

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Does subtracting a positive number give the same result as adding the number which is its opposite is the opposite positive or negative? ›

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

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What is the formula for adding positive and negative numbers? ›

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.

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How to remember negative and positive rules? ›

When adding and subtracting numbers it's important to be consistent with positive and negative values. Remember that two plus signs or two minus signs make a positive. One plus and one minus make a negative.

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How to teach adding positive and negative numbers? ›

One way to think of adding positive and negative numbers is to imagine that you're standing at ground level. If you add a positive, you'll go up as if you climbed up a ladder. If you add a negative, you'll dig a hole down into the ground.

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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.

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What is the law of positive and negative signs? ›

A plus and a minus make a minus. If two positive numbers are multiplied together or divided, the answer is positive. If two negative numbers are multiplied together or divided, the answer is positive. If a positive and a negative number are multiplied or divided, the answer is negative.

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When adding two numbers with different signs will the answer be positive, negative, or it depends? ›

When adding two rational numbers with different signs, the sign of the sum depends on their absolute values. If the absolute value of the positive number is greater, the sum is positive; if the absolute value of the negative number is greater, the sum is negative; if the absolute values are equal, the sum is zero.

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When you subtract two positive numbers the answer is positive? ›

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 happens if you add a positive and a negative number? ›

The rules for adding negative and positive numbers are: A positive integer plus a smaller negative integer equals a positive integer smaller than the original positive integer. A positive integer plus a larger negative integer equals a negative integer closer to 0 than the original negative integer.

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Is adding a positive number the same as subtracting a negative number True or false? ›

Expert-Verified Answer

Subtracting a negative number is the same as adding a positive number.

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What is the bodmas rule? ›

The BODMAS rule states we should calculate the Brackets first (2 + 4 = 6), then the Orders (5² = 25), then any Division or Multiplication (3 x 6 (the answer to the brackets) = 18), and finally any Addition or Subtraction (18 + 25 = 43).

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What is the rule for adding and subtracting? ›

The rules to add and subtract numbers are given below: Addition of two positive numbers is always positive. Addition of two negative numbers is always negative. Subtraction of two positive numbers can be either positive or negative. Subtraction of two negative numbers can be either positive or negative.

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