RULES OF ADDING POSITIVE AND NEGATIVE NUMBERS

Rule 1 :

Positive + Positive  =  Add

The result will be positive

Example :

2 + 1  =  3

Rule 2 :

Negative + Negative  =  Add

The result will be negative

Example :

-3 + (-5)  =  -8

Rule 3 : 

Negative + Positive  =  Subtract

Take sign of number with largest absolute value

Example :

-3 + 5  =  2

Rule 4 : 

Positive + Negative  =  Subtract

Take sign of number with largest absolute value

Example :

3 + (-5)  =  -2

Practice Problems

Problem 1 : 

Simplify : 

3 + 6

Solution :

Rule 1 :

Positive + Positive  =  Add

The result will be positive

Then, 

3 + 6  =  9

Problem 2 : 

Simplify : 

-5 + 2

Solution :

Rule 3 : 

Negative + Positive  =  Subtract

Take sign of number with largest absolute value

Then, 

-5 + 2  =  -3

Problem 3 : 

Simplify : 

5 + (-3)

Solution :

Rule 4 : 

Positive + Negative  =  Subtract

Take sign of number with largest absolute value

Then, 

5 + (-3)  =  2

Problem 4 : 

Simplify : 

- 5 + (-7)

Solution :

Rule 2 :

Negative + Negative  =  Add

The result will be negative

Then,

-5 + (-7)  =  -10

Problem 5 : 

Simplify : 

2 + (-3) + 7 + 2 + (-5) + (-7)

Solution :

Group the numbers with positive sign and negative sign. 

2 + (-3) + 7 + 3 + (-5)  =  [2 + 7 + 3] + [(-3) + (-5)]

Apply Rule 1 for the group of numbers with positive sign and  Rule 2 for the group numbers with negative sign. 

2 + (-3) + 7 + 3 + (-5)  =  12 + (-8)

Use Rule 4.

2 + (-3) + 7 + 3 + (-5)  =  4

Problem 6 : 

Simplify : 

-2 + (-7) + 4 + (-1) + 5

Solution :

Group the numbers with positive sign and negative sign. 

-2 + (-7) + 4 + (-1) + 5  =  [4 + 5] + [-2 + (-7) + (-1)]

Apply Rule 1 for the group of numbers with positive sign and  Rule 2 for the group numbers with negative sign. 

-2 + (-7) + 4 + (-1) + 5  =  9 + (-10)

Use Rule 4.

-2 + (-7) + 4 + (-1) + 5  =  -1

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