Addition and Subtraction Example

The addition or addition is a mathematical operation in which several numbers they accumulate with each other. It occurs differently between:

• Numbers of the same sign
• Opposite sign numbers

Sum between numbers of the same sign

In the sum, if the numbers are of the same sign, whether positive or negative, your values are going to add to each other, having a cumulative result. To make this operation easier, the absolute value of each number is used. The absolute value is the one that the number has just because of its numerical character.

For example, the absolute value of -2 is: | -2 | = 2. The sign only indicates where on the number line it would be placed.

Positive signs

1 + 4 + 9 = 14

(+1) + (+4) + (+9) = (+14)

|+1| + |+4| + |+9| = |+14|

In the first line, the sum of 1, 4 and 9 is represented, which results in a cumulative of 14. In the second line the explanation is given more detailed of its signs. They are all positive. They are put in parentheses to distinguish the number signs from the addition signs. Both lines are spelled correctly.

In the third line, the absolute values ​​are used as a reference. When they are all of the same sign, the 1, 4 and 9 are simply added, meeting a final value of 14. After this accumulation, the sign is put on that everyone had the same.

Negative signs

(-2) + (-5) + (-3) = (-10)

|-2| + |-5| + |-3| = |-10|

|-2| = 2, |-5| = 5, |-3| = 3

In the first line, represents the sum of -2, -5 and -3, which results in a cumulative of -10. In the second line, the absolute values ​​are used as a reference. When they are all of the same sign, the 2, 5 and 3 are simply added, meeting the final value of 10. Later, the sign is put on that everyone had the same.

Sum between numbers of different signs

In addition, when the numbers have different signs, there are two steps to follow:

• Accumulate everyonethose with the same sign. It will have a positive value and a negative value.
• Counteract values positive and negative, to have a final value.

Example:

(-6) + (+7) + (-2) + (-5) + (+1) + (+2) = -3

Step 1:

The negatives are added: (-6) + (-2) + (-5) = |-6| + |-2| + |-5| = -13

The positives are added: (+7) + (+1) + (+2) = +10

Step 2:

The results are counteracted: (-13) + (+10) = -3

You get a result of (-3). It is negative because the highest absolute value is 13: | -13 | - | +10 | = 13-10 = 3; and the negative sign is put on it.

The substraction

The subtraction or subtraction It is the mathematical operation in which two or more numbers are going to counteract each other, to arrive at a final number, which can be positive or negative. In this operation you have to be especially careful with the signs, since a minus sign (-) modifies the sign of the number.

To do the subtraction of the numbers, you have to follow three simple steps:

• Change the sign of the numbers that follow each sign from "-" and separate them with "+" signs.
• Accumulate all the positives with each other, and all the negatives with each other.
• Counter the positive result with the negative result.

Example:

(-6) – (+2) – (-9) – (-4) – (+8) – (+3) = -6

Step 1:

(-6) – (+2) – (-9) – (-4) – (+8) – (+3) =

Change of signs: (-6), (-2), (+9), (+4), (-8), (-3)

Separate with "+" signs: (-6) + (-2) + (+9) + (+4) + (-8) + (-3)

Step 2:

Accumulate positives with each other: (+9) + (+4) = +13

Accumulate negatives with each other: (-6) + (-2) + (-8) + (-3) = |-6| + |-2| + |-8| + |-3| = -19

Step 3:

Counteract the positive and negative result: (-19) + (+13) = |-19| - |+13| = 19 – 13 = 6, but since 19 (the largest) is negative, that sign is put to the result.

Addition examples

1.- 4 + 5 + 8 + 10 = |+4| + |+5| + |+8| + |+10| = +27

2.- 2 + 9 + 10 + 16 = |+2| + |+9| + |+10| + |+16| = +37

3.- 1 + 12 + 5 + 6 = |+1| + |+12| + |+5| + |+6| = +24

4.- 18 + 5 + 7 + 3 = |+18| + |+5| + |+7| + |+3| = +33

5.- 13 + 4 + 1 + 8 = |+13| + |+4| + |+1| + |+8| = +26

6.- (-12) + (-7) + (-20) = |-12| + |-7| + |-20| = -39

7.- (-8) + (-5) + (-4) = |-8| + |-5| + |-4| = -17

8.- (-10) + (+8) + (-6) + (+4) = (-10) + (-6) + (+8) + (+4) = (-16) + (+12) = -4 

9.- (-5) + (-20) + (-12) + (+9) = (-5) + (-20) + (-12) + (+9) = -37 + 9 = -28

10.- (+8) + (-2) + (-6) + (+3) = (+8) + (+3) + (-2) + (-6) = +11 -8 = +3

Examples of subtraction

1.- (+20) – (-4) – (+6) = (+20) + (+4) + (-6) = +24 -6 = +18

2.- (+16) – (-1) – (+3) = (+16) + (+1) + (-3) = +17 -3 = +14

3.- (+14) – (-5) – (+9) = (+14) + (+5) + (-9) = +19 -9 = +10

4.- (+10) – (-8) – (+2) = (+10) + (+8) + (-2) = +18 -2 = +16

5.- (+8) – (-9) – (+1) = (+8) + (+9) + (-1) = +17 -1 = +16

6.- (-11) – (-4) – (+2) = (-11) + (+4) + (-2) = -13 +4 = -9

7.- (-6) – (+1) – (+8) = (-6) + (-1) + (-8) = -15

8.- (-9) – (+10) – (+3) = (-9) + (-10) + (-3) = -22

9.- (-5) – (-10) – (+6) = (-5) + (+10) + (-6) = +10 -11 = -1

10.- (-19) – (-7) – (+5) = (-19) + (+7) + (-5) = -24 + 7 = -17