# ADDING AND SUBTRACTING POSITIVE AND NEGATIVE NUMBERS

To simplify two or more numbers which are having same or different signs, we follow the steps given below.

If two numbers are having same signs, +  and +  (or) - and -, we have to add them and put greater number's sign for the answer.

If two numbers are having different signs, + and -  (or) - and +, we have to subtract them and put greater number's sign for the answer.

Simplify the following :

Problem 1 :

(-12) + (-1)

Solution :

(-12) + (-1)

Since these are having same signs, we add them and put greater number's sign for the answer.

= -12 – 1

= -13

Problem 2 :

(-9) + 11

Solution :

Since the given two numbers are having different signs, subtract the smaller from larger and use the sign of the larger number to the answer.

(-9) + 11 = 2

Problem 3 :

(-4) + (-8) + 11

Solution :

(-4) + (-8) + 11

Simplify the numbers which are same signs first.

= -4 – 8 + 11

= -12 + 11

Now we have different signs, so we subtract them and put greater number's sign for the answer.

= -1

Problem 4 :

3 + (-11) + 8

Solution :

= 3 + (-11) + 8

Combine the numbers which are having same signs first.

= 3 + 8 - 11

= 11 - 11

= 0

Problem 5 :

(-4) + 6 + (-3)

Solution :

(-4) + 6 + (-3)

= -4 + 6 – 3

= 2 – 3

= -1

Problem 6 :

1 + (-4) + 10

Solution :

1 + (-4) + 10

First combine the terms which are having same signs.

= 1 + 10 - 4

=  11 - 4

Since they are having different signs, subtract 4 from 11 and put positive sign for the answer.

= 7

Problem 7 :

(-5) + (-5) + 1

Solution :

(-5) + (-5) + 1

First combine the terms which are having same signs.

= -5 - 5 + 1

= -10 + 1

Since they are having different signs, subtract 1 from 10 and put negative sign for the answer.

= -9

Problem 8 :

1 + (-3) + 11

Solution :

1 + (-3) + 11

First combine the terms which are having same signs.

= 1 + 11 - 3

= 12 - 3

Since they are having different signs, subtract 3 from 12 and put positive sign for the answer.

= 9

Problem 9 :

(-9) + 4 + 7

Solution :

First combine the terms which are having same signs.

= (-9) + 4 + 7

= -9 + 11

Since they are having different signs, subtract 3 from 12 and put positive sign for the answer.

= 2

Problem 10 :

(-12) + 4 + 8

Solution :

(-12) + 4 + 8

= -12 + 12

= 0

Problem 11 :

3 + (-10) + 6

Solution :

= 3 + (-10) + 6

= 9 - 10

= -1

Problem 12 :

(-3) + 3 + 12

Solution :

= (-3) + 3 + 12

= -3 + 15

= 12

Problem 13 :

(-4) – (-8) - 2

Solution :

(-4) – (-8) - 2

= -4 + 8 – 2

= -4 - 2 + 8

= -6 + 8

= 2

Problem 14 :

(-2) – (-1) - (-7)

Solution :

= (-2) – (-1) - (-7)

= -2 + 1 + 7

= -2 + 8

= 6

Problem 15 :

2 – (-5) - 3

Solution :

= 2 – (-5) - 3

= 2 + 5 – 3

= 7 – 3

= 4

Problem 16 :

(-7) – (-7) - 4

Solution :

= (-7) – (-7) – 4

= -7 + 7 – 4

= -7 - 4 + 7

= -11 + 7

= -4

Problem 17 :

(-6) – 4 – (-4)

Solution :

= (-6) – 4 – (-4)

= -6 – 4 + 4

= -10 + 4

= -6

Problem 18 :

(-8) – (-8) - 5

Solution :

= (-8) – (-8) - 5

= -8 + 8 – 5

= -8 - 5 + 8

= -13 + 8

= -5

Problem 19 :

(-5) – 6 - (-6)

Solution :

= (-5) – 6 - (-6)

= -5 – 6 + 6

= -11 + 6

= -5

Problem 20 :

6 – (-3) - 1

Solution :

= 6 – (-3) - 1

= 6 + 3 – 1

= 9 – 1

= 8

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