How To Add And Subtract With Negative Numbers

How to Add together and Subtract
Positive and Negative Numbers

Numbers Tin exist Positive or Negative

This is the Number Line:

Negative Numbers (−)	Positive Numbers (+)

No Sign Means Positive

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

Instance: 5 is actually +5

Play with it!

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

Endeavor the sliders below and see what happens:

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

Balloons and Weights

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

This handbasket has balloons and weights tied to it:

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

Adding a Positive Number

Adding positive numbers is just simple addition.

We can add balloons (we are adding positive value)

the handbasket gets pulled up (positive)

Example: 2 + 3 = 5

is really maxim

"Positive 2 plus Positive 3 equals Positive 5"

We could write information technology as (+2) + (+3) = (+5)

Subtracting A Positive Number

Subtracting positive numbers is merely simple subtraction.

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

the handbasket gets pulled downwards (negative)

Case: vi − 3 = iii

is really proverb

"Positive 6 minus Positive 3 equals Positive three"

We could write it as (+half-dozen) − (+iii) = (+3)

Calculation A Negative Number

Now let'due south see what adding and subtracting negative numbers looks similar:

We can add weights (we are adding negative values)

the basket gets pulled downwards (negative)

Example: 6 + (−3) = iii

is really saying

"Positive 6 plus Negative 3 equals Positive 3"

Nosotros could write it equally (+6) + (−three) = (+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.

Then these accept the same result:

• (+half-dozen) − (+iii) = (+3)
• (+6) + (−iii) = (+three)

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

Subtracting A Negative Number

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

the handbasket gets pulled upward (positive)

Example: What is half-dozen − (−3) ?

6−(−3) = 6 + 3 = 9

Yes indeed! Subtracting a Negative is the same as adding!

2 Negatives make a Positive

What Did We Discover?

Adding a positive number is elementary addition ...

Calculation a Positive is Addition

Positive and Negative Together ...

Subtracting a Positive
or
Calculation a Negative
is
Subtraction

Example: What is six − (+3) ?

6−(+3) = 6 − three = 3

Instance: What is 5 + (−seven) ?

v+(−7) = 5 − 7 = −2

Subtracting a negative ...

Subtracting a Negative is the same as Adding

Example: What is xiv − (−4) ?

14−(−4) = 14 + 4 = 18

The Rules:

It can all exist put into ii rules:

	Rule				Example
+(+)	Ii like signs get a positive sign				3+(+2) = 3 + ii = 5
−(−)					6−(−3) = vi + 3 = 9
+(−)	Two different signs become a negative sign				seven+(−2) = 7 − 2 = five
−(+)					viii−(+two) = 8 − 2 = half dozen

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

So, all y'all have to remember is:

2 similar signs become a positive sign

2 unlike signs get a negative sign

Case: What is 5+(−2) ?

+(−) are unlike signs (they are non the same), so they get a negative sign.

v+(−two) = 5 − 2 = iii

Example: What is 25−(−4) ?

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

25−(−iv) = 25+4 = 29

Starting Negative

What if we showtime with a negative number?

Using The Number Line can assistance:

Example: What is −iii+(+ii) ?

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

−three+(+ii) = −3 + two

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

−3+(+2) = −3 + ii = −1

Case: What is −3+(−2) ?

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

−iii+(−ii) = −3 − ii

Start at −iii on the number line,
move dorsum ii and yous end upward at −5

−3+(−2) = −3 − 2 = −five

Now Play With It!

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

A Common Sense Caption

And in that location 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 "Practice 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

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

So the bank must have away a negative $10.

Let'south say your current balance is $lxxx, then you will then have:

$80−(−$x) = $80 + $10 = $xc

So y'all get $10 more in your account.

A Long Example Yous Might Like

Marry's Points

Marry tin be naughty or nice. So Marry's parents accept said

"If you are prissy we will add together 3 points (+3).
If y'all are naughty, we take abroad 3 points (−3).
When you lot attain thirty Points you lot get a toy."

Ally starts the day with nine Points:		ix
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? Nosotros add iii dorsum again!
So Mom calculates:		6 − (−three) = 6 + 3 = 9

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

So Subtracting a Negative is the same as Adding

A few days subsequently. Marry 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 domestic dog. Writes "+3" on the chart. Mom calculates:		12 + (+3) = xv
Ally throws a stone against the window. Dad writes "−3" on the nautical chart. Mom calculates:		fifteen + (−3) = 12

See: both "fifteen − (+three)" and "15 + (−three)" event in 12.

So:

It doesn't matter if yous subtract positive points
or add negative points,
you yet cease upwardly losing points.

So Subtracting a Positive
or
Calculation a Negative
is
Subtraction

Try These Exercises ...

Now try This Worksheet, and run across how you go.

And also try these questions:

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

How To Add And Subtract With Negative Numbers,

Source: https://www.mathsisfun.com/positive-negative-integers.html

Posted by: kentunclefor.blogspot.com

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