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**What are Positive and Negative Numbers?**

Observe this number line. What have you noticed?

Looking at this number line, you will notice that it consists of numbers with a sign and zero. The sign of a number can be a positive or a negative number, and zero is the midpoint of the number line. From zero, all numbers going to the right side are positive numbers. Negative numbers are number from 0 going to the left of the number line. Let’s discuss the signs of a number more.

__Positive numbers__ are all numbers whose value is higher than zero. They’re often called counting numbers. The symbol for all positive numbers (+) is shown before a number, although the positive symbol is usually left off. On a number line, a positive number is on the right side of zero.*Examples:*+5 can be written as 5.

1 or +1 is a positive number.

__Negative numbers__ are numbers whose value is less than zero. Negative numbers are always accompanied by a negative symbol (-) before a number. All numbers to the left of zero on the number line are negative numbers.*Examples:*-1 The negative sign must be before the number

-5 Negative five is five places to the left of 0.

**Addition of Positive or Negative Numbers**

a. When adding a positive number, compute it the usual way.

Let’s have an example: 6 + 3 = x

6 and 3 are both a positive numbers.

6 + 3 = 9

If we add a positive number to a positive number, the answer is always positive.

b. When adding negative numbers, compute it the usual way and copy the negative sign.*Example:*-3 + (-2) = x

-3 and -2 are both negative numbers. Therefore the answer will move more to the left of the number line.

-3 + (-2) = -5

c. Adding a positive number and a negative number can be tricky. The sign of a number and which number is higher must be considered. If numbers have an unlike sign, subtract the number and copy the sign of the number with higher value.*Example:*-6 + 3 = x

The signs are unlike. Take the larger number (6) and subtract the smaller number (3), but copy 6’s sign (-).

-6 + 3 = -3

*Example 2:*9 + (-3) = x

The signs are unlike. Take the larger number (9) and subtract the smaller number (3) and copy the larger number’s sign (+).

9 + (-3) = 6

**Subtraction of a Positive or Negative Numbers**

The general rule for a positive or a negative number is to change the sign of a subtrahend and proceed to addition. A negative subtrahend changes to the positive sign and a positive subtrahend will be negative.

a. Subtracting both a positive number can be computed in the usual way.

Let’s have an example: 5 – 3 = 5 and 3 are a positive number.

5 – 3 = 2

Same if we follow the rule.

5 – 3 = Change the sign of the subtrahend, 3 change to -3 then add

5 + (-3) = Unlike sign subtract

5 + (-3) = 2

b. When subtracting two negative numbers, the general rule must follow.

Example:

-3 – (-2) = (-2) will be 2, then proceed to addition.

-3 + (+2) = -1 The sign negative 3 is greater than 2.

c. Subtracting a positive number and a negative number*Example:*-6 – 3 = Change the sign of 3 to be -3

-6 + (-3) = -9 Add the like sign and the sign is negative.

*Example 2:*9 – (-3) = Change the sign of subtrahend then add

9 + (+3) = 12

Note: In addition or subtraction of positive and negative numbers, copy the sign of the number with greater value.

**Multiplication and Division of Positive or Negative Numbers **

The rules for the sign numbers in multiplying or dividing numbers are below.

The sign of a number is important to indicate what will be the product sign.

Similar sign or Like sign. In either both positive numbers or both negative numbers, the sign of the product/quotient is positive.

a. Positive to positive equals positive.*Example:*3 (2) = 6

6/3 = 2

b. Negative to negative equals positive.*Example:*(-3)(-2) = 6

(-6)/(-3) = 2

Unlike signs. When the signs are different, the answer is negative.

c. Positive to negative is negative.*Example:*3(-2) = -6

6/(-3) = -2

d. Negative to positive is negative.*Example:*(-3)(2) = -6

(-6)/3 = -2

Note: The product or quotient of a similar sign is a positive number and for the different sign is a negative number.