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Adding negative numbers (practice) | Khan Academy

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Add and Subtract Fractions Word Problems 

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Add/Subtract Positive and Negative Decimals 

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How To Add And Subtract Negative Numbers

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Adding and Subtracting Integers: A Step-By-Step Review | How to Add and Subtract Integers

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Add and Subtract Positive and Negative Numbers  Help

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Add and Subtract Positive and Negative Numbers  Help

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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.

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:

We can add weights (we are adding negative values)

the basket gets pulled downwards (negative)

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:

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 Negative is 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 ...

Example: What is 6 − (+3) ?

6−(+3) = 6 − 3 = 3

Example: What is 5 + (−7) ?

Subtracting a negative ...

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

−(−)

6−(−3) = 6 + 3 = 9

+(−)

Two unlike signs become a negative sign

7+(−2) = 7 − 2 = 5

−(+)

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.

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.

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

Example: What is −3+(−2) ?

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

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

Now Play With It!

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 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."

Then Dad confesses he spilt the milk and writes "undo".

How do we "undo" a minus 3?
We add 3 back again!

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

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.

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

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Adding and Subtracting Positive and Negative Numbers

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This is the Number Line: Negative Numbers (−) Positive Numbers (+) "−" is the negative sign. "+" is the positive sign If a number has no sign it usually means that it is a positive number. On the Number Line positive goes to the right and negative to the left.