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# Positive and Negative Numbers

Top
 Sub Topics Number system provides various types of number patterns to solve various types of problems. From those number patterns, we are going to discuss about the positive and negative numbers. In general aspect, both can be considered as integer.Positive numbers are those numbers which have value greater than zero and negative numbers are those numbers which have the value less than zero. Examples of positive numbers are 0.001, 1, 1.1, 400 and so on. Examples of negative numbers are -1, -2, -.002, -15 and so on.If we have a collection of several numbers, which contains the combination of negative and positive numbers, then we have to remember that in ascending order, we first place the negative values and after that positive values because positive numbers are greater than the negative numbers. Arithmetic operations can be easily performed on positive and negative numbers.

## Condition for Zero

The zero is neither a positive nor a negative number. On the number line, zero is exactly in the middle. There are positive number on its right, while negative numbers on its left side.

The positive and negative numbers start from zero and continue till infinity. The condition for a number to be positive number is that it must be greater than zero. Similarly, for a negative number, this condition is that it must be smaller than zero. It means that zero is included neither in positive numbers nor in negative numbers.

### Solved Example

Question: Add -4 + 0 + 8 - 0
Solution:
Given:  -4 + 0 8 - 0
We know that  -4 + 0 8 - 0 = -4 + 8 = 4
As 8 is larger and the sign is positive, we get positive number as the solution. (No need to change the sign)
Therefore, -4 + 8 = 8 - 4 = 4

## Rules

One golden rules that is to be taken care of while dealing with positive and negative numbers are:

i) Like signs become positive:

It means that if a positive and a positive sign interact, then they result in positive. Similarly, if a negative and a negative sign interact, then they also provide a positive result. i.e.

(+)(+) = (+)

(-)(-) = (+)

ii) Unlike sign become negative:

It means that if a positive and negative sign interact, they give negative sign, i.e.

(+)(-) = (-)

(-)(+) = (-)

### Solved Example

Question: Solve 21 - (+ 2).
Solution:
Given: 21 - (+2)
We know that 21 - 2 = 19
As 21 is larger and the sign is positive, we get 19 as the solution.
Therefore, 21 - (+2) = 19

A number can be positive or negative. If a number has no sign, it usually means that it is a positive number.

Given below are the rules to be followed when adding positive and negative numbers:
• If the signs of both the numbers are same, ignore the signs and add the numbers. In the result, put the sign of addends in front of the answer.
• When the signs are different, pretend the signs aren't there. Subtract the smaller from the larger one and put the sign of the larger one in front of your answer.

## Subtracting

In order to subtract positive and negative numbers, change the sign on the integer that is to be subtracted and then, add them.
• Two like signs become a positive sign and two unlike signs become a negative sign.
• When the signs are different, subtract the smaller value from the larger value. Place the sign of the larger value in the solution.

## Multiplying

Multiplying positive and negative numbers is very easy once you know the basic rules. Here, the sign of the product needs to be determined.
1. If both factors are positive, the product will be positive.
2. If both factors are negative, the product will be positive.
3. If any one of the factors is negative, the product will be negative.

### Solved Examples

Question 1: What is the product of -9 and 27?
Solution:

To find: -9 x 27

We know the product of 9 and 27 is 243
As one of the factors is negative, the product is negative.
Therefore, the solution of -9 x 27 is -243.

Question 2: What is the product of (-4), (5) and (-2)?
Solution:
First, multiply the first two numbers.
(-4) x (5) = -20
Now, multiply (-20) and (-2)
We get (-20) x (-2) = 40  (Two like signs gives a positive sign)
Therefore, Product of (-4), (5) and (-2) is 40.

## Dividing

Dividing positive and negative number follows the same rules as of multiplying positive and negative numbers. Here, we need to determine the sign of the quotient, we will help you in finding that.
1. If both the dividend and divisor are positive, the quotient will be positive.
2. If both the dividend and divisor are negative, the quotient will be positive.
3. If any one of the dividend or divisor is negative, the quotient will be negative.

### Solved Examples

Question 1: Solve $\frac{28}{7}$
Solution:
$\frac{28}{7}$ = 4  (Two like signs become a positive sign)
Therefore, $\frac{28}{7}$ = 4

Question 2: Solve $\frac{135}{-15}$
Solution:

To find: $\frac{135}{-15}$

$\frac{135}{15}$ = 9  (Two unlike signs become a negative sign)
Therefore, $\frac{135}{-15}$ = -9