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.
+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.
-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.
-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.
-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
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.
-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
-6 – 3 = Change the sign of 3 to be -3
-6 + (-3) = -9 Add the like sign and the sign is negative.
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.
3 (2) = 6
6/3 = 2
b. Negative to negative equals positive.
(-3)(-2) = 6
(-6)/(-3) = 2
Unlike signs. When the signs are different, the answer is negative.
c. Positive to negative is negative.
3(-2) = -6
6/(-3) = -2
d. Negative to positive is negative.
(-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.