##### Operations with positive and negative numbers

What are positive and negative numbers?
Positive numbers are numbers that are greater then zero.
Negative numbers are numbers that are less then zero.

Visualizing positive and negative numbers on a number line

Positive numbers are written without a sign or with a “+” in front of them. Meanwhile negative numbers are always written with a “-“sign in front of them. Negative numbers represent opposite, so if positive numbers represent a movement to the right then negative represent a movement to the left.

Be careful! “The number 0 is neither positive or negative”.

We know that the four basic operations in mathematics are adding, subtracting, multiplying and dividing.
Interaction of positive and negative numbers with this four basic operations.

1. Adding two positive numbers it’s just normal addition, the sign is always positive.

2 + 3 = 5
13 + 21 = 34

2. Adding two negative numbers it becomes subtraction, where you start from a negative point on the number line and moves to the left. The sign is always negative.

(-6) + (-3) = -9
(-3) + (-2) =-5

3. Adding a positive and a negative number, subtract the numbers and put the sign of the greater absolute value. The sign depends on the number that has the greater absolute value.

9 + (-5) = 4, we keep the sign of the number 9 since |9|>|-5|

(-7) + 2 = -5, we keep the sign of the number -5 since |-7|>|2|

### Rules of Subtracting Numbers

1. Subtracting two positive numbers it’s just normal subtraction, but be careful the sign of the subtraction depends on the numbers we subtract.

If the first number is bigger than the second one the sign is positive:
10 – 6 = 4
12 – 3 = 9

If the first number is smaller than the second one the sign is negative:
3 – 8 = – 5
5 – 13 = -8

2. Subtracting a positive number from a negative number is equivalent to adding the negative of that number. The sign is always negative.

-12 – 7 = -12 + (-7) = -19
-5 – 6 = -5 + (-6) = -11

3. Subtracting a negative number from a positive number is equivalent to turning the subtraction sign followed by a negative sign both into a positive one.

8 – (-5) = 8 + 5 = 13
2 – (-1) = 2 + 1 = 3

4. Subtracting a negative number from a negative number is equivalent to turning the subtraction sign followed by a negative sign both into a positive one. Then we go to the rule 3 of adding a positive and negative number.

(-7) – (-3) = (-7) + 3 = -4, we keep the sign of the number (-7) since |-7|>|3|
(-3) – (-7) = (-3) + 7 = 4, we keep the sign of the number (7) since |7|>|-3|

### Rules of Multiplying Numbers

1. Multiplying two positive numbers or two negative numbers the product is always a positive number.

• Multiplying two positive numbers
2 x 6 = 12
4 x 11 = 44

• Multiplying two negative numbers
(-3) x (- 4) = 12
(-2) x (-3) = 6

2. Multiplying a positive number with a negative number or a negative with a positive number the product is always negative.

• Multiplying a positive with a negative number
3 x (-6) = -18
2 x (-5) = -10

• Multiplying a negative with a positive number
-5 x (3) = -15
-7 x (4)= -28

### Rules of Dividing Numbers

1. Dividing two positive numbers or two negative numbers the quotient is always a positive number.

• Dividing two positive numbers
8 ÷ 2 = 4
12 ÷ 6= 2
• Dividing two negative numbers
(-9) ÷ (-3) = 3
(-14) ÷ (-7) = 2

2. Dividing a positive number with a negative number or a negative with a positive number the quotient is always negative.

• Dividing a positive with a negative number
18 ÷ (-2) = -9
36 ÷ (- 6)= -6

• Dividing a negative with a positive number
(-5) ÷ (5) = -1
(-20) ÷ 4 = -5
Next article

### Roman numbers

Roman Numerals are a number system that originated in the ancient Rome that are written by combinations of letters from Latin alphabet.

Next article

### Roman numbers

Roman Numerals are a number system that originated in the ancient Rome that are written by combinations of letters from Latin alphabet.