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# Positive and Negative Integers

When children start to mumble, they come across with numbers. The usage of numbers is found everywhere in our surroundings. Children also learn operations with numbers in their early grades of school. In middle school, the students come to know different types of numbers in detail, which are - real numbers. integers, whole numbers, natural numbers, even numbers, odd numbers, prime numbers, composite numbers etc. In this page, we are going to learn about integers.

The integers are defined as the set of numbers that includes all counting numbers, negative of all counting numbers and zero. Integers do not have a fractional or decimal part in them. We may divide integers in three parts -
(1) Positive integers - counting numbers
(2) Negative integers - negative of counting numbers
(3) Zero - 0

Let us discuss about  positive and negative integers. The positive integers are nothing but the collection of 'n' individuals which no decimal or fractional part.The whole numbers more than zero are termed as positive integers. These positive integers are represented as by the sign (+) in front of the each 'n' integer. The set of positive integers may be denoted by $\mathbb{Z}^{+}$. Positive integers are -
$\mathbb{Z}^{+}$ = {1, 2, 3, 4, 5, .....}The negative numbers are the collection of real numbers with negative sign (-) in front of the standard numerals and are always less than zero. The set of negative integers is represented by $\mathbb{Z}^{-}$. Negative integers are written as-
$\mathbb{Z}^{-}$ = {...., -5, -4, -3, -2, -1}.

 Related Calculators Adding Integer Calculating Integers Multiplying Integer Positive Coterminal Angle

## Positive and Negative Integers Rules

The n positive integers are the whole numbers which is used for the general terms like counting etc.
The discrete continuous values are made to have in the line.
The negative integers are the inverse of the positive numbers.
The negative integers are made to have the separate values found in a number line.
The negative integers are less than zero, denoted as (e.g. -5).
The positive integers are greater than zero.
The zero is neither a positive nor a negative number.
The number line represents both the positive and negative integers.
The negative numbers are representing from the left to right.
The positive numbers are representing from the right to left.

The above diagram shows the number line in which the red arrow indicates the negative integers and the yellow arrow indicates the positive integers.

## Adding Positive and Negative Integers

We can add the two numbers together and give the answer either a positive or a negative sign. The sign that will go with the number in the answer is the sign from the number with the greater absolute value, the larger number.

### Solved Examples

Question 1: Add 7 + (- 6)
Solution:

7 + (- 6)

= 7 - 6

= 1

Question 2: Add -10 + 5
Solution:

-10 + 5

= - 5

## Subtracting Positive and Negative integers

When we subtract positive and negative integers, we will change the sign of the number being subtracted and then add integers.

### Solved Examples

Question 1: Subtract 5 from - 8
Solution:

- 8 - 5 = - (8 + 5)

= - 13.

Question 2: Subtract -15 from 18
Solution:

18 - (-15)

= 18 + 15

= 33

## Multiplying Positive and Negative Integers

While we multiply integers, the product of two integers may be positive or negative. There is variations in the resultant integer because of given integers signs. The product of a negative number and a positive number is a negative number.

Positive * Positive = Positive

Positive * Negative = Negative

Negative * Positive = Negative

Negative * Negative = Positive

### Solved Examples

Question 1: Multiply -2 and 5
Solution:

- 2 * 5 = -10

(Negative * Positive = Negative)

Question 2: Multiply -4 and -7
Solution:

- 4 * - 7 = 28

(Negative * Negative = Positive)

## Dividing Positive and Negative Integers

Division is the opposite operation of multiplication. If a, b, c are integers, where b ≠ 0, then division a ÷ b is written as $\frac{a}{b}$ and is defined in terms of multiplication.

### Solved Examples

Question 1: Solve -15 ÷ 5
Solution:

-15 ÷ 5 = -15 x $\frac{1}{5}$

= - 3

Question 2: Solve 12 ÷ (- 5)
Solution:

12 ÷ (- 5) = 12 x $\frac{1}{- 5}$

= $\frac{- 12}{5}$

## Solving Integers

Here are the examples on positive and negative integers -

### Solved Examples

Question 1: What is (+6) + (+2)?
Solution:

From above: + (+) becomes a positive sign.

(+6) + (+2) = +6 + 2

Start at +6 on the number line, move forward 2, and you end up at 8

Question 2: What is (+15) + (+7)?
Solution:

From above: + (+) becomes a positive sign.

(+15) + (+7) = (+15) + 7

Start at +15 on the number line, move forward 7, and you end up at 22

Answer: 15 + (+7) = 22

Question 3: What is (-12) + (-2)?
Solution:

From above: + (-) becomes a negative sign.

(-12) + (-2) = (-12) - 2

Start at -12 on the number line, move backward 2, and you end up at -14

Answer: (-12) + (-2) = -14

Question 4: What is (-12) - (-2)?
Solution:

From above: - (-) becomes a negative sign.

(-12) - (-2) = (-12) + 2

Start at -12 on the number line, move forward 2, and you end up at -10

Answer: (-12) - (-2) = -10

Question 5: What is (-6) + (+3)?
Solution:

From above: + (+) becomes a positive sign.

(-6) + (+3) = (-6) + 3

Start at -6 on the number line, move forward 3, and you end up at -3

Answer: (-6) + (+3) = -3

Question 6: What is 5 + (-2) ?
Solution:

From above: + (-) becomes a negative sign.

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

Start at 5 on the number line, move backward 2, and you end up at 3

Answer: 5 + (-2) = 3

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