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. |

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

Therefore, -4 + 8 = 8 - 4 = 4

**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

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.

- 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.

- If both factors are positive, the product will be positive.
- If both factors are negative, the product will be positive.
- 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

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:**

(-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.

- If both the dividend and divisor are positive, the quotient will be positive.
- If both the dividend and divisor are negative, the quotient will be positive.
- If any one of the dividend or divisor is negative, the quotient will be negative.

### Solved Examples

**Question 1:**Solve $\frac{28}{7}$

**Solution:**

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